JULY 2010 IEEE MTT-V058-I07B (2010-07) [58, 7 ed.]

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JULY 2010

VOLUME 58

NUMBER 7

IETMAB

(ISSN 0018-9480)

PART II OF TWO PARTS

SPECIAL ISSUE ON TERAHERTZ TECHNOLOGY

Guest Editorial—Terahertz Technology: Bridging the Microwave-to-Photonics Gap .... ......... ........ ......... ......... .. .. ........ ......... ......... ........ ......... ......... .... P. H. Siegel, T. Loffler, D. Mittleman, K. Mizuno, and X.-C. Zhang

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PAPERS

A 10-mW Submillimeter-Wave Solid-State Power-Amplifier Module ... ........ ......... ......... ........ ....... V. Radisic, W. R. Deal, K. M. K. H. Leong, X. B. Mei, W. Yoshida, P.-H. Liu, J. Uyeda, A. Fung, L. Samoska, T. Gaier, and R. Lai 68–110-GHz-Band Low-Noise Amplifier Using Current Reuse Topology ...... . .... M. Sato, T. Takahashi, and T. Hirose A Broadband 835–900-GHz Fundamental Balanced Mixer Based on Monolithic GaAs Membrane Schottky Diodes .. .. .. ........ ......... ......... ........ ......... ... B. Thomas, A. Maestrini, J. Gill, C. Lee, R. Lin, I. Mehdi, and P. de Maagt A Frequency-Multiplied Source With More Than 1 mW of Power Across the 840–900-GHz Band .... ......... ......... .. .. ........ ......... ... A. Maestrini, J. S. Ward, J. J. Gill, C. Lee, B. Thomas, R. H. Lin, G. Chattopadhyay, and I. Mehdi Physics-Based Design and Optimization of Schottky Diode Frequency Multipliers for Terahertz Applications ......... .. .. ........ ......... ......... ........ ......... ......... ........ ......... ......... ........ ......... ......... . J. V. Siles and J. Grajal Integrated 585-GHz Hot-Electron Mixer Focal-Plane Arrays Based on Annular Slot Antennas for Imaging Applications .. .. ........ ......... ......... ........ ......... ......... ........ ......... L. Liu, H. Xu, A. W. Lichtenberger, and R. M. Weikle II A Global Approach for Modeling and Analysis of Edge-Coupled Traveling-Wave Terahertz Photoconductive Sources .. .. ........ ......... ......... ........ ......... ......... ........ ....... M. Neshat, D. Saeedkia, L. Rezaee, and S. Safavi-Naeini Tunable Subterahertz Wave Generation Based on Photonic Frequency Sextupling Using a Polarization Modulator and a Wavelength-Fixed Notch Filter ......... ......... ........ ......... ......... ........ ......... ......... ........ S. Pan and J. Yao Photonic-Crystal-Based Polarization Converter for Terahertz Integrated Circuit ......... ......... ........ ......... ......... .. .. ........ ......... ......... .... K. Bayat, G. Z. Rafi, G. S. A. Shaker, N. Ranjkesh, S. K. Chaudhuri, and S. Safavi-Naeini Single-Mode Terahertz Bragg Fiber Design Using a Modal Filtering Approach ......... ... Y. Zhang and I. D. Robertson A 2-D Artificial Dielectric With for the Terahertz Region .... ........ . ......... R. Mendis and D. M. Mittleman

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(Contents Continued on Back Cover)

(Contents Continued from Front Cover) Time-Delay Multiplexing of Two Beams in a Terahertz Imaging Radar . ........ ......... ......... ........ ......... ......... .. .. ........ ......... ......... .... N. Llombart, K. B. Cooper, R. J. Dengler, T. Bryllert, G. Chattopadhyay, and P. H. Siegel Illumination Aspects in Active Terahertz Imaging ....... ......... ......... ........ ......... ......... ........ ......... ......... .. .. ........ ......... ......... ........ ....... W. von Spiegel, C. am Weg, R. Henneberger, R. Zimmermann, and H. G. Roskos A Novel Approach for Improving Off-Axis Pixel Performance of Terahertz Focal Plane Arrays ........ ......... ......... .. .. ........ ......... ......... ........ ......... ...... G. C. Trichopoulos, G. Mumcu, K. Sertel, H. L. Mosbacker, and P. Smith Hybrid Continuous-Wave Demodulating Multipixel Terahertz Imaging Systems ........ ........ .. ........ .... F. Friederich, G. Spickermann, A. Roggenbuck, A. Deninger, C. am Weg, W. von Spiegel, F. Lison, P. H. Bolívar, and H. G. Roskos Terahertz Imaging Systems With Aperture Synthesis Techniques ........ ........ ......... ......... ........ ......... ......... .. .. V. Krozer, T. Löffler, J. Dall, A. Kusk, F. Eichhorn, R. K. Olsson, J. D. Buron, P. U. Jepsen, V. Zhurbenko, and T. Jensen Optical Scanning Techniques for Characterization of Terahertz Photoconductive Antenna Arrays ...... ......... ......... .. .. ........ ......... ......... ........ ......... ......... ........ ......... H. F. Tiedje, D. Saeedkia, M. Nagel, and H. K. Haugen Terahertz Antenna Technology and Verification: Herschel and Planck—A Review ...... ......... ........ ......... ......... .. .. ........ ......... ......... ........ ..... L. F. Rolo, M. H. Paquay, R. J. Daddato, J. A. Parian, D. Doyle, and P. de Maagt Qualitative and Quantitative Detection of Pesticides With Terahertz Time-Domain Spectroscopy ...... ......... ......... .. .. ........ ......... ......... ........ ......... ......... ........ ......... ......... ........ ......... ......... ... Y. Hua and H. Zhang Information for Authors .. ........ ......... ......... ........ ......... .......... ........ ......... ......... ........ ......... ......... .

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Special Issue on RF Nanoelectronics ..... ......... ........ ......... ......... ........ ......... ......... ........ ......... ......... .

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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 58, NO. 7, JULY 2010

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Guest Editorial—Terahertz Technology: Bridging the Microwave-to-Photonics Gap

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HE submillimeter-wave and terahertz bands (300 GHz–10 THz) have traditionally stood out as high-speed performance goals for RF device engineers pushing the limits of traditional microwave circuits and instruments. Strong science drivers have included molecular spectroscopy, Earth, planetary, and space science and plasma diagnostics. In recent years, there has been an explosion of new interest in this frequency regime both from the traditional microwave community and from those approaching the terahertz performance gap from the optical end of the electromagnetic spectrum. Dramatic advances in semiconductor monolithic microwave integrated circuit (MMIC) technology have pushed three terminal devices well beyond 500 GHz for the first time. Two terminal sources and detectors now appear at spot frequencies from 500 GHz to 2.5 THz. Quantum cascade lasers have come down from the infrared to provide narrowband milliwatt-level power sources below 2 THz. On the optical side of the terahertz Gap, the widespread availability of femtosecond optical lasers and optical-to-terahertz photonic sources and detectors has opened up many new and exciting applications, from ultrafast chemistry to biomedical imaging to security and communications. This influx of new techniques, applications, and researchers has, in turn, stimulated additional investment in traditional microwave applications that have been translated up to terahertz frequencies. These include new terahertz radar imagers, terahertz spectral sensors, and even some sojourns into high bit-rate communications systems. As progress at ultra-high frequencies continues at a rapid pace, advancing from both sides of the electromagnetic spectrum, we are finally beginning to close the terahertz gap. However this is not simply an extension of already available components and technologies, but rather includes substantial new invention that many in the microwave and optical communities can use and benefit from. This TRANSACTIONS’ “Special Issue on Terahertz Technology” hopes to bring a few of these new and exciting developments to the traditional RF community in the hope that it will expand and stimulate existing techniques and concepts. Rather than focusing on review papers, we have instead included mostly technical papers that span a range of new interests in terahertz devices, components, and instruments. The broad range of experience within the editorial committee was purposely selected in order to span both the traditional RF fields and the more recently established terahertz opto-electronics communities. As a general guideline, no papers were specifically solicited for this Special Issue. As such, this Special Issue is inDigital Object Identifier 10.1109/TMTT.2010.2050185

dicative of the mainstream developments that are now ongoing in the terahertz community, and can be used as a gauge for future microwave theory and techniques content in this research area. These papers include semiconductor and superconductor devices, optically generated and traditional RF sources, active and passive imagers, large and small antennas, novel guide structures, and some applications. This Special Issue is organized as follows. The first group of papers covers two- and three-terminal devices being used to bridge the terahertz gap from below. These components are the building blocks for terahertz instruments that are the basis of traditional RF systems. The lead article by Radisic et al. is an example of recent breakthroughs in the design and fabrication of submillimeter-wave, or submillimeter-wave integrated circuit (SMMIC), circuits based around high-speed semiconductors. Amplifiers, mixers, oscillators, and complex passive coupling and guiding structures are now being fabricated using standardized, albeit complex, wafer processing techniques. Extremely exciting results are already leaking out and will soon include full transceiver modules above 500 GHz. More traditional two-terminal semiconductor sources and detectors continue to improve in performance and advance in frequency, as illustrated in the papers by Thomas et al. and Maestrini et al. Similar types of devices have already been integrated into commercial instruments that are bringing calibrated coherent two-port measurements into the submillimeter-wave regime for the first time. Terahertz superconducting detectors and mixers based on tunnel junctions, as well as bolometric mechanisms, have already made their way into space instruments and are now beginning to be used to field the first submillimeter-wave imaging arrays. The paper by Liu et al. is an example of a realized diffraction limited mixer array above 500 GHz, a long-time goal in the astronomical community. Photomixers and photoconductive switches based on tailor-doped semiconductor materials have enabled the explosive growth of the terahertz opto-electronics field. New techniques for realizing photonic-based sources and polarizers are presented in the papers by Neshat et al., Pan et al., and Bayat et al. Terahertz instruments have always been limited by the absence of a flexible low-loss guide medium, equivalent to the optical fiber that has been the foundation for such dramatic advances in the optical domain. Several new ideas have emerged recently for realizing such structures in the terahertz domain, despite strong dielectric absorption. Zhang et al. develop a Bragg fiber concept and Mendis et al. present a novel artificial media with desirable characteristics for terahertz propagation. Imaging in the submillimeter-wave bands has become quite a hot topic area due to strong pull from the defense and security community who are interested in the dielectric penetra-

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tion, but nonionizing properties, of this long wavelength energy. Several papers in this Special Issue are focused on imaging in both the frequency and time domains. The paper by Llombart et al. describes a very novel use, or rather re-use, of signals to demonstrate a working 660–690-GHz two-pixel radar imager that employs only one transceiver. Friederich et al. describe a full multipixel imager based on electrooptic techniques. Array characterization will become more and more important as new subsystems are realized and Tiedje et al. and Krozer et al. introduce some new techniques for measuring radiation characteristics and for aperture synthesis. We should not forget that terahertz antennas and instruments are strongly rooted in the astrophysics community. With the successful launch and deployment of the Herschel Space Telescope in May 2009, these are now space based. The paper by Rolo et al. is an example of the complexity that goes into the design and testing of large aperture terahertz antennas. Finally, an unusual application of terahertz spectroscopy is included from Hua et al., which illustrates the broad scope of disciplines beginning to take note of this rapidly evolving field. All five of the guest editors of this Special Issue, and this TRANSACTIONS co-Editor-in Chief, Dylan Williams, hope you will enjoy this sojourn into what is sure to become a mainstay technology area for microwave theory and techniques.

PETER H. SIEGEL, Guest Editor Departments of Biology and Electrical Engineering Jet Propulsion Laboratory (JPL) California Institute of Technology Pasadena, CA 91109 USA TORSTEN LOFFLER, Guest Editor SynView GmbH Bad Homburg, 61348 Germany DAN MITTLEMAN, Guest Editor Department of Electrical and Computer Engineering Rice University Houston, TX 77005 USA KOJI MIZUNO, Guest Editor Research Institute of Electrical Communication Tohoku University Sendai, 980-8577 Japan XI-CHENG ZHANG, Guest Editor Center for Terahertz Research Rensselaer Polytechnic Institute Troy, NY 12180 USA

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A 10-mW Submillimeter-Wave Solid-State Power-Amplifier Module Vesna Radisic, Senior Member, IEEE, William R. Deal, Senior Member, IEEE, Kevin M. K. H. Leong, X. B. Mei, Wayne Yoshida, Po-Hsin Liu, Jansen Uyeda, Andy Fung, Lorene Samoska, Senior Member, IEEE, Todd Gaier, and Richard Lai, Senior Member, IEEE

Abstract—In this paper, we demonstrate a packaged sub-millimeter wave solid-state power amplifier (SSPA). The SSPA is implemented in coplanar waveguide (CPW) and uses an advanced InP HEMT transistor with a sub 50-nm gate. A high monolithically integrated CPW dipole-to-waveguide transition eliminates the need for wirebonding and additional substrates. On-chip compact tandem couplers are used for power combining. The amplifier demonstrates 15-dB small-signal gain at 340 GHz. Peak saturated output power of 10 mW at 338 GHz is obtained at the waveguide flange output for the SSPA module.

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Index Terms—Coplanar waveguide (CPW), HEMT, millimeter wave, monolithic microwave integrated circuit (MMIC), module, power amplifier.

I. INTRODUCTION

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ECENT improvements in both HEMT and HBT semiconductor technologies have enabled the demonstration of low-noise amplifiers and power amplifiers operating above 300 GHz [1]–[4]. This increase in the threshold of solid-state amplification is significant because it demarks the transition between the millimeter and sub-millimeter wave (SMMW) regimes. If successfully exploited, newly developed SMMW amplifiers would enable new applications in radiometry, sensing, as well as other military and commercial security applications. It has long been shown that power can be generated at SMMW to terahertz frequencies using diode multiplier chains [5]–[8]. The primary application for these multiplier chains has been to generate the local oscillator (LO) for terahertz mixers used in terahertz sensors and radiometers. Notable among recent work is [8], which achieves a peak output power of 26 mW at 318 GHz using a two-way waveguide power combining of two monolithic microwave integrated circuit (MMIC) multipliers. Manuscript received September 23, 2009; accepted February 07, 2010. Date of publication June 01, 2010; date of current version July 14, 2010. This work was supported by the Defense Advanced Research Projects Agency (DARPA) under the SWIFT Program and by the Army Research Laboratory (ARL) under ARL Contract W911QX-06-C-0050. V. Radisic, W. R. Deal, K. M. K. H. Leong, X. B. Mei, W. Yoshida, P.-H. Liu, J. Uyeda, and R. Lai are with the Northrop Grumman Corporation, Redondo Beach, CA 90278 USA (e-mail: [email protected]). A. Fung, L. Samoska, and T. Gaier are with the Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109 USA. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2010.2050105

Ultimately, SMMW SSPAs may significantly improve terahertz multiplier chain efficiency. Assuming a relatively high gain SSPA driver, the dc efficiency of a multiplier chain is simply the product of the dc efficiency of the SSPA driver, and the conversion efficiency of each successive output multiplier. By doubling or tripling the driver operating frequency, the entire chain efficiency can be improved by an order of magnitude for a typical multiplier operating at 5%–10% conversion efficiency. Moreover, SMMW SSPAs open up the possibility of building SMMW transmitters using mixer based up-converters for the first time. This would enable terahertz communications with instantaneous RF bandwidths on the order of tens of gigahertz. The use of high-frequency transistor technologies for power generation at SMMW frequencies has its own set of challenges. These include the low transistor breakdown from the aggressive scaling of the transistor, on-chip power combining losses, and a practical method of placing the MMIC chip into a waveguide fixture. Progress has been made in several of these areas in the last few years. Recently, a single-ended power-amplifier MMIC 5.9 mW of output power at 270 GHz was reported, with which used 120- m transistors [1]. A balanced power amplifier using branchline couplers and 60- m transistors reached 6.1 mW at 270 GHz [3]. Note that both [1] and [3] were measured on-wafer and the amplifier was only partially saturated due to drive power constraints. The InP HBT may be another viable device for SMMW power amplification. In [4], a singlestage power-amplifier MMIC with 1.3 mW of output power at 324 GHz has recently been demonstrated. Note that this power was also measured on wafer. A significant hurdle for the practical adoption of SMMW amplifiers are reliable and effective fixturing techniques for MMICs at these frequencies. Two problems in particular must be tackled. First, MMIC chips fabricated on high-permittivity semiconductor substrates are typically wirebonded to lower permittivity (typically quartz) substrates with waveguide -plane probes printed on them to transition to waveguide. However, the inductive reactance of the wirebonds increases with frequency, which makes wirebonding increasingly impractical as operating frequency increases. The authors know of no published substrate-to-substrate bonds performed above 320 GHz [9]. A solution to this is to monolithically fabricate the electromagnetic transition directly on the semiconductor substrate, which has been demonstrated in [10] and [11] with monolithically fabricated -plane probes. However, challenges still exist in directly using this technique for SSPA chips at SMMW frequencies. This is because the MMICs must be electrically wide to accommodate on-chip

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Fig. 1. DC Ids versus V ds burnout curves.

power-combining networks of multiple transistors, biasing pads, and decoupling networks. This makes it challenging to keep the MMIC channel cutoff when using an -plane probe fabricated on a high-permittivity semiconductor substrate. An alternative approach has been recently developed, which we adopt in this paper [12]. This technique uses a monolithically fabricated dipole probe, which accommodates wider MMIC widths required by SSPA on-chip power-combining networks. The dipole performs well on high-permittivity semiconductor substrates, and requires dimensions comparable to that of the coplanar waveguide (CPW) transmission lines fabricated at these frequencies. The final challenge is the development of suitable on-chip power-combining networks. Both binary type and branchline couplers have been demonstrated. In this paper, we use a CPW tandem coupler similar to the one presented in [13], but scaled to operate at SMMW frequencies. The CPW tandem coupler enables bandwidth comparable to microstrip Lange couplers, without the requirement for dramatic linewidth scaling required 50 m . thin substrates used at SMMW frequencies The MMIC is fabricated using the same InP HEMT process used in [1]–[3] and demonstrates 15 dB of small-signal gain at 340 GHz with a saturated output power of 10 mW at 338 GHz. The combination of high output power and gain indicate that power-amplifier modules are a viable method for generating power at these frequencies. II. SUB-50-nm InP HEMT TECHNOLOGY Fundamental to this work, SSPA is the development of devices with sufficiently good gain and breakdown characteristics at the targeted operating frequency. The InP HEMT epi wafers are grown by molecular beam epitaxy (MBE) and employ a composite InAs/InGaAs channel and InGaAs/InAlAs composite cap layer structure, a silicon delta-doping layer as the electron supply, an In Al As buffer layer, and an InP substrate. Room-temperature electron mobility over 15000 cm V s has been achieved with a sheet charge of cm . Excellent dc performance has also been achieved with a breakdown voltage above 2.5 V, which is beneficial for power applications. The safe operating region for the transistors has been mapped through dc I–V burnout measurements, with and shown in Fig. 1. The the burnout locus for different dc I–V characteristics exhibit excellent channel control with a ratio of 10. This low output conductance and a high has been achieved through carefully optimized gate recess etch and epitaxial structure design. The sub-50-nm T-gate has been

Fig. 2. Map of device Gmp at V d

= 1 V over 3-in InP wafer.

Fig. 3. Extracted f versus drain bias voltage and current for two-finger 20-m transistors.

fabricated with over 90% device yield and excellent uniformity. Shown in Fig. 2 is a wafer map of measured test devices over a shows an average fabricated wafer. For this wafer, the peak of 2300 mS/mm with a sigma of less than 5% and threshold ) sigma of only 23 mV. voltage ( The result of combining the high-performance epi profile and aggressive gate is a device with excellent RF characteristics. Transistors have been characterized using an on-wafer extended reference plane calibration structures from 1 to 110 GHz on fabricated wafers thinned to 50 m. Based on calculated unilateral gain (U) and maximum stable gain (MSG), and extracted equivalent-circuit model, the transistor demonstrates an extrapolated of 1.2 THz and a cutoff frequency of 500 GHz [14]. The small-signal equivalent-circuit model has been validated in [15] where the highest frequency amplifier MMIC with 16-dB measured gain at 340 GHz was demonstrated with an excellent match between measured versus modeled. A significant challenge for achieving output power is maintaining transistor performance across the range of the RF swing. Fig. 3 shows over varying drain bias and drain currents. The the extracted transistor can operate with usable gain over a wide range of bias conditions required for power amplification. III. MMIC POWER-AMPLIFIER DESIGN The four-stage MMIC SSPA is a balanced power amplifier realized in CPW. The balanced topology has been chosen for efficient power combining. Fig. 4 shows the simplified

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Fig. 4. Simplified schematic of the single-ended amplifier. Fig. 6. Microphotograph of back-to-back test structure for tandem coupler evaluation.

Fig. 5. Microphotograph of balanced four-stage power-amplifier MMIC with integrated waveguide probes. Total die size is 1085 450 m .

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schematic of the single-ended amplifier. The output stage of the single-ended amplifier uses 80- m transistors for achieving high output power. The input stages use 30, 30, and 40 m for maximizing gain. Since the chip is quite small, only two sets of drain and bias pads can be accommodated. We have chosen to tie the first three stages together, and allow the output stage bias to be independently adjusted. At the input, a parallel RC filter is used to reduce gain and potential oscillations at the lower frequencies. Bias lines used small resistors and shunt capacitors for creating RF ground and suppressing low-frequency oscillations. A microphotograph of the MMIC amplifier used for module fixturing is shown in Fig. 5. The chip itself is extremely compact, with a dimension of only 1085 450 m for a total die size of 0.49 mm . The RF matching networks are extremely compact, separation between transistors is very short, and small metal–insulator–metal (MIM) capacitors are used because of their low parasitic inductance. Air bridges are used at each discontinuity to suppress slot modes. The amplifier is implemented on a 2-mil-thick InP substrate, which is electrically thick at frequencies above 300 GHz. Therefore, a high density of vias between top metal and backside metal is used to suppress the substrate modes. Bias is provided for top and bottom single-ended amplifiers separately. Only four dc pads are used on the top and bottom so that waveguide opening for dc bias is not too large to create multimoding. The coupler used in this design is based on the CPW tandem coupler reported in [13]. It consists of two-section parallel-coupled lines and air-bridge crossovers. The tandem couplers. This coupler can be made smaller than traditional was critical for this design since the chip size was fixed and the large coupler would make layout of a balanced amplifier impossible. A CPW-based coupler also allows easy integration and layout with a CPW amplifier. A CPW tandem coupler

Fig. 7. Measured S -parameters of back-to-back tandem coupler test structure.

was simulated using Ansoft Technologies’ High Frequency Structure Simulator (HFSS) software. A test structure with a back-to-back tandem coupler was also placed on the mask for coupler evaluation, as shown in Fig. 6. Measured -parameters for this test structure are shown in Fig. 7. loss at 320 GHz is 2.8 dB, which corresponds to 1.2-dB loss per coupler if the transmission lines are de-embedded from this measurement. Two versions of this amplifier were placed on the mask: one with on-wafer probable pads (used for on-wafer testing) and another with integrated dipole for fixturing in module. This allows for on-wafer screening of the designs. The MMIC chips selection for module can only be done by dc screening. In addition, a single-ended version of the amplifiers with probable pads was placed on the mask. This allows for evaluation and troubleshooting of this amplifier. IV. MODULE DESIGN AND ASSEMBLY The SSPA module is a WR-3 split block design. The transition from MMIC to waveguide is done using the integrated CPW to waveguide transition, which is similar to the one reported in [12]. This transition is chosen due to its compact size and allows for a large MMIC area, which is needed for power combining. It was modified from [12] to an offset design, as shown in Fig. 8. This eliminates the need for a bend when used with a coupler with an offset feed. The transition allows chip width of 450 m compared with 320- m width when -plane transition is used [11]. The offset was specifically chosen to match the offset of the tandem coupler size.

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Fig. 8. Photograph of the offset dipole test circuit. The size of the test circuit is the same as power-amplifier MMIC: 1085 450 m .

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Fig. 10. (a) Photograph of MMIC in module. (b) Zoomed-out photograph showing bias network. (c) Completed module photograph with dimensions.

The offset transition was verified by testing a thru line with CPW-to-waveguide transition at the input and output, as shown in Fig. 8. This test circuit has the same size as the amplifier and was bonded into the same module. This module was tested using a WR-3 Oleson Microwave Laboratory (OML) frequency extender with an Agilent 8510c network analyzer. Measured and HFSS simulated results are shown in Fig. 9. A good agreement in bandwidth, insertion loss, and return loss was achieved. The glitch in -parameters around 315 GHz is related to an extender spur. The measured insertion loss of 6.8 dB between 300–320 GHz includes the loss of two transitions and loss of the line between two transitions, which is 876- m long. If this line is de-embedded out, the insertion loss per transition is 1.3 dB from 300 to 320 GHz. The test circuit was not measured using WR-2.2 setup, but based on HFSS simulation, it is our estimate that the transition performance extends to 340 GHz. The MMIC amplifier chip was bonded into the module with conductive epoxy, as shown in Fig. 10(a). Wire bonds from the dc source and drain pads are connected to off-chip 51-pF bypass capacitors with additional off-chip capacitors and resistors to ensure low-frequency stability of the circuit [see Fig. 10(b)]. The complete module is compact in size, as shown in Fig. 10(c).

V. EXPERIMENTAL RESULTS

Fig. 9. Measured and simulated (HFSS): (a) S 11, (b) S 22, and (c) S 21 for the offset dipole test structure.

Small-signal -parameters and saturated output power were measured at the Jet Propulsion Laboratory, California Institute of Technology, Pasadena. Fig. 11 shows the measured gain and return loss for the amplifier biased at 1.4 V and a total current of 100 mA shared among the ten devices in the MMIC. Gain was measured using OML frequency extenders. Both WR-3 and WR-2.2 frequency extenders are used to view the broadband frequency response of the amplifier. The overlap between WR-3 and WR2.2 gain data is within 1 dB from 325 to 340 GHz, which validates our calibration. Gain greater than 11.5 dB is measured

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Fig. 12. Measured output power and power gain at 338 GHz. All points have different bias, which was tuned for maximum output power. Bias 1 corresponds to V d = 1:5 V, total Id = 112 mA. Bias 2 corresponds to V d = 2:2 V , total Id = 134 mA.

frequencies has not been measured, but we believe that the module has at least several gigahertz bandwidth. The module output was connected to WR-3 to WR-10 transition and then to a PM2 calorimeter. Fig. 12 shows the output power and gain data for several different bias points. Bias was adjusted as the input power was increased to obtain maximum output power. Bias 1 in Fig. 12 corresponds to small-signal bias in Fig. 11. The gain for these two points is within 1 dB. The maximum bias of measured output power of 10 mW was obtained at 2.2 V and total current of 134 mA. The corresponding power gain was 3.3 dB. VI. CONCLUSION In this paper, we reported on a 10-mW 338-GHz SSPA module with a comparatively large output periphery of 160 m. A tandem coupler is used for power combining and integrated dipole-to-waveguide transition is used for low-loss fixturing. This study has demonstrated that InP HEMT MMIC technology can be used for power amplification at SMMW frequencies. This module can be easily integrated with mixers and multipliers for building high-frequency transmit and receive systems at SMMW frequencies. Fig. 11. Measured and simulated: (a) S 21, (b) S 11, and (c) S 22 of the poweramplifier module. The corresponding bias is V d = 1:4 V and Id = 100 mA. Two measured curves correspond to data from the WR-3 and WR-2.2 extender setup.

from 334 to 344 GHz with a peak gain of 15 dB at 340 GHz. The loss estimate for the waveguide transitions is 1.3 dB, which give the gain of MMIC itself of 14.1 dB from 334 to 344. The tandem coupler loss is estimated to be 1.2 dB. Therefore, the MMIC gain per stage is 4.1 dB. Output return loss at the module is quite good, better than 10 dB across the 304–344-GHz bandwidth. positive return loss glitch around 292 GHz is related The to the systematic spur in the test equipment and has also been reported in [11]. Saturated output power and power gain measurement is complicated by lack of off-the-shelf test equipment and difficulty in performing systematic power calibrations at SMMW frequencies. The test was performed at 338 GHz due to availability of source at that frequency. The output power at other

ACKNOWLEDGMENT The authors would like to thank Dr. M. Rosker, Defense Advanced Research Projects Agency (DARPA), Arlington, VA, and Dr. A. Hung, Army Research Laboratory (ARL), Adelphi, MD. The authors would like to thank members of the Northrop Grumman Corporation, Redondo Beach, CA, from monolithic microwave integrated circuit (MMIC) layout support with J. Coakley, S. Makishi, and B. Bayuk; MBE material growth lead by M. Lange; MMIC wafer fabrication with Y.-M. Kim, D. Farkas, J. Lee, D. Li, L. Dang, J. Wang, K. Kho, P. Oliver, J. Kane, and T. Naeole; module fabrication with R. Lyons and J. Ingram; and module assembly and test with B. Gorospe. The authors would also like to thank A. Oki and R. Kagiwada for their guidance in this project. This research was carried out in part at the Jet Propulsion Laboratory, California Institute of Technology, Pasadena, under a contract with the National Aeronautics and Space Administration (NASA).

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REFERENCES [1] W. R. Deal, X. B. Mei, V. Radisic, B. Bayuk, A. Fung, W. Yoshida, P. H. Liu, J. Uyeda, L. Samoska, T. Gaier, and R. Lai, “A new sub-millimeter wave power amplifier topology using large transistors,” IEEE Microw. Wireless Compon. Lett., vol. 18, no. 8, pp. 542–544, Aug. 2008. [2] W. R. Deal, X. B. Mei, V. Radisic, M. D. Lange, W. Yoshida, P. H. Liu, J. Uyeda, M. E. Barsky, A. Fung, T. Gaier, and R. Lai, “Development of sub-millimeter-wave power amplifiers,” IEEE Trans. Microw. Theory Tech., vol. 55, no. 12, pp. 2719–2726, Dec. 2007. [3] W. R. Deal, X. B. Mei, V. Radisic, A. Bayuk, W. Fung, P. H. Yoshida, P. H. Liu, J. Uyeda, L. Samoska, T. Gaier, and R. Lai, “A balanced sub-millimeter wave power amplifier,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2008, pp. 399–402. [4] J. Hacker, M. Urteaga, D. Mensa, R. Pierson, M. Jones, Z. Griffith, and M. Rodwell, “250 nm InP DHBT monolithic amplifiers with 4.8 dB gain at 324 GHz,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2008, pp. 403–406. [5] P. H. Siegel, “Terahertz technology,” IEEE Trans. Microw. Theory Tech., vol. 50, no. 3, pp. 910–928, Mar. 2002. [6] T. W. Crowe, W. L. Bishop, D. W. Porterfield, J. L. Hesler, and R. M. Weikle, II, “Opening the terahertz window with integrated diode circuits,” IEEE J. Solid-State Circuits, vol. 40, no. 10, pp. 2104–2110, Oct. 2005. [7] M. Morgan, E. Bryerton, P. Cesarano, T. Boyd, D. Thacker, K. Saini, and S. Weinreb, “A millimeter-wave diode-MMIC chipset for local oscillator generation in the ALMA telescope,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2005, pp. 1587–1590. [8] A. Maestrini, J. S. Ward, C. Tripon-Canseliet, J. J. Gill, L. Choonsup, H. Javadi, G. Chattopadhyay, and I. Mehdi, “In-phase power-combined frequency triplers at 300 GHz,” IEEE Microw. Wireless Compon. Lett., vol. 18, no. 3, pp. 218–220, Mar. 2008. [9] A. Tessmann, A. Leuther, V. Hurm, H. Massler, M. Zink, M. Kuri, M. Riessle, R. Losch, M. Schlechtweg, and O. Ambacher, “A 300 GHz MHEMT amplifier module,” in Proc. InP Rel. Mater. Conf., May 2009, pp. 196–199. [10] S. Weinreb, T. Gaier, R. Lai, M. Barsky, Y. C. Leong, and L. Samoska, “High gain 150–215 GHz MMIC amplifier with integrated waveguide transitions,” IEEE Microw. Wireless Compon. Lett., vol. 9, no. 7, pp. 1435–1438, Jul. 1999. [11] L. Samoska, W. R. Deal, G. Chattopadhyay, D. Pukala, A. Fung, T. Gaier, M. Soria, V. Radisic, X. B. Mei, and R. Lai, “A submillimeterwave HEMT amplifier module with integrated waveguide transitions operating above 300 GHz,” IEEE Trans. Microw. Theory Tech., vol. 56, pp. 1380–1386, Jun. 2008. [12] K. Leong, W. R. Deal, V. Radisic, X. B. Mei, J. Uyeda, L. Samoska, A. Fung, T. Gaier, and R. Lai, “A 340 GHz integrated CB-CPW-to-waveguide transition for sub millimeter-wave MMIC packaging,” IEEE Microw. Wireless Compon. Lett., vol. 19, no. 6, pp. 413–415, Jun. 2009. [13] M.-K. Lee, B.-O. Lim, S.-J. Lee, D.-S. Ko, S.-W. Moon, D. An, Y.-H. Kim, S.-D. Kim, H.-C. Park, and J.-K. Rhee, “A novel 94-GHz MHEMT-based diode mixer using a 3-dB tandem coupler,” IEEE Microw. Wireless Compon. Lett., vol. 18, no. 9, pp. 626–628, Sep. 2008. [14] R. Lai, X. B. Mei, W. R. Deal, W. Yoshida, Y. M. Kim, P. H. Liu, J. Lee, J. Uyeda, V. Radisic, M. Lange, L. Dang, T. Gaier, L. Samoska, and A. Fung, “Fabrication of InP HEMT devices with extremely high F ,” in Proc. InP Relat. Mater. Conf., May 2008, pp. 1–3. [15] W. R. Deal, X. B. Mei, V. Radisic, W. Yoshida, P. H. Liu, J. Uyeda, M. Barsky, A. Fung, T. Gaier, and R. Lai, “Demonstration of a S-MMIC LNA with 16-dB gain at 340-GHz,” in IEEE Compound Semiconduct. Integr. Circuits Symp., Oct. 2007, pp. 1–4.

max

Vesna Radisic (M’92–SM’04) received the B. S. degree from the University of Belgrade, Belgrade, Serbia, in 1991, the M.S. degree from the University of Colorado at Boulder, in 1993, and the Ph.D. degree from the University of California at Los Angeles (UCLA), in 1998, all in electrical engineering. She is currently a Senior Section Head with the RF Product Center, Northrop Grumman, Redondo Beach, CA. She mentors a team of MMIC design engineers, as well as pursues her own development efforts in millimeter-wave MMIC design. Her research interests include high-frequency circuits, wideband amplifiers, and passive components. Dr. Radisic was the recipient of the 2007 Outstanding Young Engineer Award.

William R. Deal (M’96–SM’06) received the B. S. degree in electrical engineering from the University of Virginia, C harlottesville, in 1996, and the M.S. and Ph.D. degree from the University of California at Los Angeles (UCLA), in 1998 and 2000, respectively. He is currently a Senior Department Staff Engineer with the RF Product Center, Northrop Grumman, Redondo Beach, CA. He leads several MMIC development efforts including Northrop Grumman’s contract for the Defense Advanced Research Projects Agency (DARPA) Terahertz (THz) Electronics program, as well as developing his own microwave and millimeter-wave designs. He is actively engaged in the development of electronics in GaAs, InP, ABCS, and GaN technologies. He has authored or coauthored over 100 journal and conference papers, as well as four book chapters. Dr. Deal was the recipient of the 2009 Outstanding Young Engineer Award.

Kevin M. K. H. Leong received the B. S. degree in electrical engineering from the University of Hawaii at Manoa, in 1999, and the M. S. and Ph.D. degrees in electrical engineering from the University of California at Los Angeles (UCLA), in 2001 and 2004, respectively. From 2004 to 2007, he was a Postdoctoral Researcher with UCLA. He is currently with Aerospace Systems, Northrop Grumman Corporation, Redondo Beach, CA. His research interests include planar antennas and millimeter-wave circuits. Dr. Leong was the recipient of the 2006 Microwave Prize of the Asia–Pacific Microwave Conference.

X. B. (Gerry) Mei received the B.S. degree in physics from the University of Science and Technology of China, Hefei, China, in 1987, and the Ph.D. degree in electrical engineering from the University of California at San Diego, in 1997. He is currently a Senior Staff Engineer with the Micro Electronics Center, Northrop Grumman Corporation, Redondo Beach, CA, where he leads advanced InP HEMT technology development. He was a Senior MBE Engineer and then an Integration Engineer with Hewlett-Packard/Agilent Technologies. He was then a Senior Member of Technical Staff with Celeritek, where he was involved with GaAs psedumorphic HEMT (pHEMT) development.

Wayne Yoshida received the B.S. degree in chemical engineering from the California Institute of Technology, Pasadena, in 1996, and the Ph.D. degree from the University of California at Los Angeles (UCLA), in 2003. He is currently a Technical Staff Member Senior in electron beam lithography with the Northrop Grumman Corporation, Redondo Beach, CA. His research interests include advanced lithography, surface science, and applications in nanoscale structures.

Po-Hsin Li, photograph and biography not available at time of publication.

Jansen Uyeda received the B.S.E.E. degree from the University of Hawaii at Manoa, in 1997, and the M.S.E.E. degree from the University of Southern California, Los Angeles, in 1999. He is currently an Engineering Manager with the Microelectronics Center, Northrop Grumman Corporation, Redondo Beach, CA, where he leads a team of process engineers in the development of fabrication processes for GaAs and InP HBT devices, GaAs, InP, and GaN HEMT devices, RF microelectromechanical systems (MEMS), surface acoustic wave (SAW), and other advanced technologies. The team is also responsible for maintaining flight and commercial production of GaAs and InP MMICs.

RADISIC et al.: 10-mW SUBMILLIMETER-WAVE SSPA MODULE

Andy Fung received the B.E.E., M.S.E.E., and Ph.D. degrees in electrical engineering from the University of Minnesota at Minneapolis–St. Paul, in 1993, 1995 and 1999, respectively. In 1999, he joined the Jet Propulsion Laboratory, California Institute of Technology, Pasadena. His research has involved the development of InP HBTs and GaAs Schottky diodes for millimeter- to submillimeter-wave applications. His current interest is in the development of high-frequency test methods.

Lorene Samoska (M’95–SM’04) received the B.S. degree in engineering physics from the University of Illinois at Urbana-Champaign, in 1989, and the Ph.D. degree in materials engineering from the University of California at Santa Barbara, in 1995. She was a Post-Doctoral Researcher with the University of California at Santa Barbara, during which time she was involved in the design and fabrication of state-of-the-art InP HBT microwave digital circuits. In 1998, she joined the Jet Propulsion Laboratory, Pasadena, where she is currently a Senior Engineer involved in the design and testing of 100–400-GHz HEMT and HBT MMIC amplifiers for receivers and local oscillator sources in future space missions.

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Todd Gaier received the Ph.D. degree in physics from the University of California at Santa Barbara, in 1993. He is the Supervisor for the Microwave Astrophysics and Earth Science Systems Group, Jet Propulsion Laboratory (JPL), Pasadena. His research interests include millimeter-wave electronics for applications in astrophysics and Earth remote sensing. His group develops technologies and instruments using MMIC components operating at frequencies of 10–350 GHz.

Richard Lai (M’85–SM’01) received the Ph.D. degree from The University of Michigan at Ann Arbor, in 1991. He possesses 20 years of experience in the research, development, and production of advanced GaAs- and InP-based HEMT device and MMIC RF technologies. Since 1994, he has been the Principal Investigator for advanced HEMT research and development at the Northrop Grumman Corporation, Redondo Beach, CA. He has authored or coauthored over 150 total papers, patents, and conference presentations in the area of advanced GaAs- and InP-based device and circuit technology, establishing world-record performance for the lowest noise amplifiers, highest frequency amplifiers, and highest power amplifiers.

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68–110-GHz-Band Low-Noise Amplifier Using Current Reuse Topology Masaru Sato, Tsuyoshi Takahashi, and Tatsuya Hirose, Member, IEEE

Abstract—This paper proposes a new topology for a broadband low-noise-amplifier (LNA). A common-gate (CG) amplifier with a matching inductor composes a unit cell, and the unit cells are cascaded to increase gain. As both the input and output impedances for a wide frequency range, of the unit cell are matched to 50 it is possible to increase the gain while maintaining wide bandwidth. Thus, high-gain and broadband performance can be obtained using this topology. The other features of the amplifier are its small size, low power consumption, and current reuse topology. This paper presents the design methodology of a multistage CG amplifier with a matching inductor. Fabricated in an 80-nm InP HEMT process, we developed an ultra-broadband LNA. The LNA with a three-stage CG amplifier exhibited a gain of 18 dB and a noise figure of 3.5 dB from 68 to over 110 GHz. The power consumption was 12 mW under a power supply voltage of 3 V. The chip size is 0.55 0.75 mm2 . Furthermore, we developed a receiver for passive millimeter-wave imagers by integrating a sixstage LNA with a power detector. The chip size of the receiver is 1.1 0.75 mm2 . The sensitivity of the pre-amplified detector was more than 2 000 V/mW from 75 to 100 GHz. These results show that the topology is one of the best candidates for high-gain and broadband LNA with small size and low power consumption.



Index Terms—Common gate (CG) amplifier, current reuse, HEMT, impedance matching, low-noise amplifier (LNA), passive millimeter-wave (PMMW) sensor.

I. INTRODUCTION

UR LIVES are becoming convenient by using infrastructure that employs millimeter-wave systems. Recently, applications using millimeter-waves have become widespread. In particular, broadband communication systems using 60-GHz-band [1], [2], 77-GHz-band automotive radars [3], [4], and 94-GHz-band millimeter-wave imagers [5] are hot applications and a number of studies have been reported. Low-noise amplifiers (LNAs) are very important building blocks, and are placed in the front-end of receivers regardless of the receiver architecture. In order to boost the received signal to a sufficient level for the following stage, the gain and noise figure (NF) of the LNA should be properly determined. Furthermore, RF designers also have to take into account the LNA’s properties of having a broader bandwidth, lower power

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Manuscript received October 01, 2009; revised March 09, 2010; accepted March 26, 2010. Date of publication June 07, 2010; date of current version July 14, 2010. The authors are with Fujitsu Laboratories Ltd., Atsugi 243-0197, Japan (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2010.2050374

consumption, smaller chip size, and having the electrostatic discharge (ESD) protection. To date, a number of broadband LNAs have been reported with respectable performance using metamorphic HEMT (mHEMT) [6], InP HEMT [7], SiGe [8], and CMOS [9] technology. Most reported LNAs are implemented by common-source (CS) amplifiers or feedback amplifiers. The input impedance-matching network of a CS amplifier was and the gate . achieved by series inductance at the source is used to match the real part of the The source inductance input impedance with the source impedance. The combination and cancels the reactance of gate–source capacitance at the resonant frequency. Since the CS amplifier requires matching networks composed of the – network at the input, intermediate, and output stages, the bandwidth is relatively small. The LNA with a resistive feedback configuration [9] achieved better broadband gain characteristics than the CS amplifier. However, the existence of parasitic capacitance in the transistor degrades the RF performance at high frequency, and the noise derived from the feedback resistor would degrade the NF of the amplifier. A common-gate (CG) amplifier is also well known as a broadband amplifier. The input impedance of a CG amplifier maintains for a wide frequency range, where is the transconductance of the transistor. By choosing the gatewidth of to be 50 , the gain profile of the transistor to satisfy the the CG amplifier realizes almost constant for a wide frequency range. Thus, this topology is used for an ultra-wideband (UWB) amplifier [10] and transimpedance amplifier for fiber-optic systems [11]. However, a CG amplifier is usually placed only at the first stage because the gain of the CG amplifier is generally small. Thus, the CS amplifier or the cascode amplifier is usually followed by the CG amplifier in order to increase the total gain of the amplifiers, but in this case, the overall bandwidth was limited by the CS or cascode amplifier. In this paper, we propose a new topology for a broadband LNA consisting of a multistage CG amplifier with a matching inductor, which enables increase of the gain while maintaining the broadband characteristics. This technique is simple and efficient. As both the input and output impedances are matched to 50 for a wide frequency range, the gain of the amplifier is increased without deterioration in bandwidth. In addition, as the amplifier is current reuse topology, bias circuits are required only at the input and output stages. Thus, an extreme chip size reduction is possible using the topology. Section II describes the design methodology of the proposed CG amplifier. The design and the measured results of the LNAs using InP HEMT technology are shown in Section III. To apply the LNA to the

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2) Output Impedance: On the other hand, the simplified output impedance of the CG amplifier is expressed as follows:

(3) As the dimensions of the transistor are small, the output impedance of CG amplifiers is generally high. When the CG amplifier is cascaded with the same CG amplifier, impedance mismatching with the following stage would be occurs. 3) Gain: The gain of the conventional CG amplifier is expressed as

Fig. 1. Simplified small-signal model of a CG amplifier.

(4)

Fig. 2. Schematic and output impedance trace of proposed CG amplifier. (a) Schematic. (b) Trace of output impedance.

is much smaller than and The drain–source admittance , when the load impedance is chosen to be 50 . Therefore, the voltage gain of the CG amplifier becomes 1 . , 4) Noise Parameters: The minimum noise temperature optimal source impedance of the CG amplifier using the Pospiezalski model [12] can be expressed as

RF front-end of passive millimeter-wave (PMMW) imagers, we integrated the six-stage LNA with a diode detector in a single chip. The sensitivity of the pre-amplified detector was achieved at more than 2000 V/mW. Finally, conclusions are presented in Section V.

(5) (6) (7)

II. DESIGN METHODOLOGY FOR BROADBAND AMPLIFIER A. Conventional CG Amplifier 1) Input Impedance: CG amplifiers have been commonly used for high-frequency amplifiers. A simplified small-signal model of a CG amplifier is shown in Fig. 1. The input impedance of the CG amplifier is expressed as follows:

(1) is the transconductance, is the drain–source adwhere is the load impedance, and is mittance of the transistor, is much smaller than the angular frequency. As the value of and , the input impedance can be simplified as

and are equivalent noise temperature of equivawhere lent circuit and , respectively. These noise parameters are identical to the CS amplifier reported in [12]. B. Proposed CG Amplifier With a Matching Inductor 1) Output and Input Impedance: In order to decrease the impedance mismatching at the output with the following stage, we added a series inductor and shunt capacitor, as shown in Fig. 2(a), in order to match the output impedance to 50 . Fig. 2(b) illustrates the impedance chart of the output . The output impedance looking from impedance ( ), will move to by the drain terminal using the series inductor and the shunt capacitor. Thus, is matched to the load impedance . In this case, the output impedance is modified to be

(2) (8) As the is proportional to the total gatewidth of the transistor, the input impedance of the CG amplifier can be matched to be 20 mS. As the dimensions of the to 50 by setting the to be 20 mS, transistor are usually small in order to obtain the gate–source capacitance becomes small. Thus, the input impedance can be matched to 50 for a wide frequency range.

As will be discussed later, the matching components and are comprised of an on-chip spiral inductor. By optimizing the parameters of the spiral inductor, such as linewidth, length, and becomes close to the number of turns, output impedance 50 .

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Fig. 3. Schematic of proposed CG amplifier.

Fig. 4. Schematic of the 80-nm gate InP HEMT.

The input impedance of the proposed CG amplifier is expressed as

(9) As both the input and output impedance of the CG amplifier are matched to about 50 , the gain is boosted by cascading the amplifier stage without sacrificing the bandwidth of the gain profile. 2) Gain: The gain of the proposed CG amplifier is expressed as

(10) where

is the impedance looking from the drain terminal

(11) The magnitude of the voltage gain is modified as

(12) We can see that the magnitude of the voltage gain is enhanced by inserting the series inductor . 3) Noise: The noise parameters of the proposed CG amplifier are the same as the conventional CG amplifier expressed in (5)–(7). Since the source impedance is inconsistent with the optimum impedance, the proposed CG amplifier is expected to . However, have an increased NF from the minimum NF a better figure-of-merit (FOM) than the NF is noise measure , where is the associated gain. The gain of the proposed CG amplifier is enhanced as expressed in (12), and the noise measure is also improved compared with the conventional CG amplifier. Moreover, the proposed CG amplifier can suppress the loss of input matching circuit, which enables low noise performance. III. MMIC DESIGN AND MEASURED RESULTS A. LNA Design We designed and fabricated ultra-broadband LNAs using a multistage CG amplifier. Fig. 3 shows a schematic of the pro-

posed amplifier. We used a three-stage amplifier, which consists of the CG amplifier with the matching inductor. Both the input and output impedances are matched to 50 , as described in Section II. A CG amplifier easily becomes unstable operation, when the impedance looking from the gate terminal is inductive [13] due to the transmission length and . as short as possible to avoid unstable operThus, we chose ation. The transmission lines between each amplifier stage are comprised of a thin-film microstrip (TFMS) line. The linewidth was chosen to be 2 m to obtain the characteristic impedance to be 50 . Bias choke was placed only at the input and output stages. The drain current flows from the output RF choke through CG amplifiers to the input RF choke as a current return. The number of bias circuits is decreased compared with a traditional CS amplifier, which requires bias circuits in each amplifier stage. This allows drastic reduction of the chip size. Moreover, this topology contains ESD protection. As the input of the amplifier is connected to the ground via the input RF choke, the charged electron flows to the ground. In order to validate this design methodology, we designed and fabricated LNAs using InP HEMT technology. B. InP HEMT Technology The gate was a T-shaped Ti/Pt/Au structure that was fabricated using electron beam (EB) lithography. Fig. 4 shows a schematic view of the 80-nm gate InP HEMT. As the parasitic capacitances of the field-effect transistor (FET) degrade the RF performance at the operating frequency, the cave structure [14] was applied for the gate in order to reduce the parasitic capacitance because and degrade the frequency dependence on and gain. The current cutoff frequency and of an 80-nm InP-based maximum oscillation frequency HEMT are 380 and 283 GHz. The minimum NF at 94 GHz was 1.0 dB. The gatewidth of 10 m 2 fingers was chosen for each unit amplifier. The extracted parameters of the HEMT on the Pospieszalski model are listed in Table I. C. Spiral Inductor Matching inductors are made by the on-chip spiral inductor. By optimizing the linewidth, space, and the number of turns of the spiral inductor, we can optimize the value of the series inductor and shunt capacitance.

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TABLE I EXTRACTED HEMT PARAMETERS

Fig. 7. Simulated (dashed line) and measured (solid line) three-stage CG amplifier.

S -parameters

of

Fig. 5. Die photograph of spiral inductor TEG.

Fig. 8. Measured NF and gain of three-stage CG amplifier.

Fig. 6. Die photograph of three-stage CG amplifier. The chip size is 0.55 0.75 mm .

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In the case of CMOS on Si, Metal 1 is usually used for the ground in order to shield the substrate. Since the resistivity of Si is as low as 1 10 cm, the factor is decreased. However, the resistivity of InP is more than 1 10 cm. Therefore, shielding metal is not required, and an inductor with high in the highfrequency range can be realized. Fig. 5 shows a photograph of the spiral inductor test element group (TEG). A triple interconnect layer was used. Spiral inductors were composed of top metal (Metal 3). In the area of spiral inductors, ground metal composed of Metal 1 is hollowed out, as shown in Fig. 5. Linewidth and spacing are determined to match the output impedance of the CG amplifier to 50 . Electromagnetic (EM) simulation using Microwave Office was used to extract the inductance and shunt capacitance. The linewidth, spacing, and the number of turns are 2 m, 3 m and 3, respectively. The size of the spiral inductor is 55 50 m . In this case, the series inductance and shunt capacitance were 250 pH and 2.5 fF, respectively. The spiral inductors are also used at the input and output RF chokes. The linewidth, spacing, and the number of turns are 2,

Fig. 9. Measured large-signal nonlinearity of three-stage CG amplifier.

3 m, and 2 turns, respectively. The extracted inductor and shunt capacitor from the measured data were 117 pH and 1.4 fF, respectively. D. Measured Results of Three-Stage CG Amplifier A die photograph of the three-stage CG amplifier is shown in Fig. 6. The size of the chip is 0.55 0.75 mm including the large area occupied by the pads. The size of the circuit core is 0.3 0.3 mm . The LNA draws 4 mA from a 3-V supply voltage. The bias voltages for each CG amplifier were generated by the internal bias circuit.

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TABLE II PERFORMANCE COMPARISON

Fig. 7 shows the measured and simulated -parameters. Solid lines represent the measured data using Agilent technologies’ 8510C and dashed lines represent the simulated results (Microwave Office). The measured results are in good agreement with the simulated results. A 3-dB bandwidth of over 42 GHz was obtained from 68 to over 110 GHz. From the simulation results, the bandwidth is estimated to be 51 GHz. The peak gain and remain less than 15 and 10 dB, was 18 dB, while respectively. Fig. 8 shows the measured NF and associated gain. The NF and gain were measured using Agilent Technologies’ N8973A. The noise source for the measurement was Elva-1’s ISSN-10 with 10–12 dB excess noise ratio (ENR). The measured NF was between 3–4 dB with full -band (75–110 GHz). Fig. 9 reports the measured large-signal nonlinearity at 94 GHz. The input-referred 1-dB compression point appears at 22 dBm. According to [15], the FOM for the wideband LNA was defined as Bandwidth GHz

Gain mW

Fig. 11. Die photograph of six-stage CG amplifier. The chip size is 1.1 0.75 mm .

(13)

is the average noise factor within the band. The where FOM1 of this LNA achieved 178. We also defined a FOM2. In this FOM2, gain in decibels was used because the power consumption is proportional to the gain in decibels as Bandwidth GHz

Gain dB mW

Fig. 10. Schematic of six-stage CG amplifier.

(14)

The performance is listed in Table II. The state-of-the-art FOM2 of 51 was realized. IV. RECEIVER FRONT-END FOR PASSIVE MILLIMETER-WAVE IMAGING SENSOR Broadband LNAs can be applied to various applications. One of the attractive applications is a passive imaging sensor. The

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received power is expressed as , where is the Boltzmann constant, is the temperature, and is the bandwidth. As the bandwidth of the LNA is wider, the total received power will be increased. We first cascaded the three-stage LNA to boost the gain, then integrated the six-stage CG amplifier with a square-law detector. A. Six-Stage CG Amplifier The schematic of six-stage LNA is shown in Fig. 10. A 6-dB attenuator was inserted between amplifier stages in order to reduce the gain. Fig. 11 shows a die photograph of the six-stage CG amplifier. The size of the chip is 1.1 0.75 mm . The power consumption was 24 mW. Fig. 12 shows the measured -parameters of the six-stage CG amplifier. Although the gain of the LNA was more than 30 dB,

SATO et al.: 68–110-GHz-BAND LNA USING CURRENT REUSE TOPOLOGY

Fig. 12. Measured S -parameters of six-stage CG amplifier.

Fig. 13. Die photograph of pre-amplified detector. The chip size is 1.1 0.75 mm .

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the gain profile has peaks at 74, 86, and 105 GHz. And the output is larger than 0 dB at those frequencies. reflection, The bandwidth of the six-stage LNA was much narrower than that of the three-stage amplifier. One possible reason for this narrower bandwidth is that the LNA was unstable around those frequencies. This is due to feedback through substrate in a parallel-plate mode. Although TFMS lines were used for the circuit core in order to shield from the substrate, the input and output pads were exposed to the substrate. The pad’s size is as large as 50 100 m . Therefore, the feedback power transmitted from the output pad to the input pad through the substrate. From the 3-D EM simulation result, the feedback power transmitted from the output pad to the input pad was around 30 dB, where all the active components were removed in this simulation. Thus, the amplifier with an over 30-dB gain may become unstable in operation. Although the six-stage amplifier does not achieve the broadband characteristics, the pre-amplified detector using the six-stage LNA shows broadband characteristics, which will be described in Section IV-B. B. Pre-Amplified Detector Fig. 13 shows a die photograph of a pre-amplified detector. The size of the chip is the same as the six-stage CG amplifier (1.1 0.75 mm ). The detector is constructed by a Schottky barrier diode [16], which is made by the same technology as the HEMT process. The gate length and gatewidth are 4 and 5 m, respectively. The input matching network was used in front of the detector diode.

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Fig. 14. Measured detected dc voltage as a function of input RF power. The input frequency was from 75 to 100 GHz.

We measured the sensitivity of the pre-amplified detector by calculating the ratio of the detected dc voltage for the input millimeter-wave power. For this measurement, we used continuous wave (CW) sources as the input. Fig. 14 shows the detected dc voltage as a function of the input RF power level, where the frequency of the RF is from 75 to 100 GHz. As the input power was increased more than 40 dBm, the detected power will be saturated. The sensitivity of the detector monolithic microwave integrated circuit (MMIC) was 2000 V/mW, and around 70-dBm input power can be detected. Thus, this MMIC is usable for passive millimeter-wave sensors. The detected voltage of the MMIC is almost the same from 75 to 100 GHz. Although the measured bandwidth of the six-stage LNA was as narrow as 10 GHz, the sensitivity of the pre-amplified detector is almost the same from 75 to 100 GHz. This shows that the gain profile of the six-stage amplifier core is flat. The instability of the six-stage LNA was caused by the feedback from the output pad to the input pad via the InP substrate. As the detector is connected to LNA’s output directly (without output pad), unwanted feedback was suppressed. Therefore, the pre-amplified detector becomes stable, and the broadband characteristics were realized. V. CONCLUSION This paper has presented the design methodology for ultra-broadband LNA. We used a multistage CG amplifier with a matching inductor for each stage. By introducing the matching inductor, the gain of the unit cells is increased and output impedance is matched to the following stage. This topology can realize high gain and broadband characteristics for an LNA. Experimental results of the three-stage amplifier show a gain of 18 dB from 68 to more than 110 GHz, and a flat NF of 3.5 dB with power consumption of 12 mW. The LNA with the six-stage amplifier shows a gain of 35 dB, the NF of 3.5 dB, and 3-dB bandwidth of 10 GHz, while consuming 24 mW. Furthermore, we developed a receiver front-end for a PMMW imager consisting of a six-stage LNA and the square-law detector. The measured sensitivity of the receiver was over 2000 V/mW from 75 to 100 GHz. These results show that the proposed topology is one of the best candidates for ultra-broadband and high-gain LNA.

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ACKNOWLEDGMENT The authors would like to thank Y. Nakasha, K. Joshin, and N. Hara, all with Fujitsu Laboratories Ltd., Atsugi, Japan, for their support. The authors would also like to thank the Device Processing Group, Fujitsu Laboratories Ltd., for the fabrication.

[15] A. Goel and H. Hashemi, “Toward a sub-decibel noise figure broadband monolithic LNA in silicon,” IEEE Trans. Microw. Theory Tech., vol. 56, no. 11, pp. 2389–2398, Nov. 2008. [16] M. Sato, T. Hirose, T. Ohki, H. Sato, K. Sawaya, and K. Mizuno, “94-GHz band high-gain and low-noise amplifier using InP-HEMTs for passive millimeter wave imager,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2007, pp. 1775–1778. [17] J. B. Hacker, J. Bergman, G. Nagy, G. Sullivan, C. Kadow, H.-K. Lin, A. C. Gossard, M. Rodwell, and B. Brar, “An ultra-low power InAs/ AlSb HEMT -band low-noise amplifier,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2005, pp. 1029–1032. [18] N. Tanahashi, K. Kanaya, T. Matsuzaka, T. Katoh, Y. Notani, T. Ishida, T. Oku, T. Ishikawa, M. Komaru, and Y. Matsuda, “A -band ultra low noise amplifier MMIC using GaAs pHEMT,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2003, pp. 2225–2228.

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REFERENCES [1] C. Marcu, D. Chowdhury, C. Thakkar, L.-K. Kong, M. Tabesh, J.-D. Park, Y. Wang, B. Afshar, A. Gupta, A. Arbabian, S. Gambini, R. Zamani, A. M. Niknejad, and E. Alon, “A 90 nm CMOS low-power 60 GHz transceiver with integrated baseband circuitry,” in IEEE Int. Solid-State Circuits Conf., Feb. 2009, pp. 314–315. [2] S. Pinel, S. Sarkar, P. Sen, B. Perumana, D. Yeh, D. Dawn, and J. Laskar, “A 90 nm CMOS 60 GHz radio,” in IEEE Int. Solid-State Circuits Conf., Feb. 2008, pp. 130–131. [3] Y. Kawano, T. Suzuki, M. Sato, T. Hirose, and K. Joshin, “A 77 GHz transceiver in 90 nm CMOS,” in IEEE Solid-State Circuits Conf., Feb. 2009, pp. 310–311. [4] F. Folster, H. Rohling, and U. Lubbert, “An automotive radar network based on 77 GHz FMCW sensors,” in IEEE Int. Radar Conf., May 2005, pp. 871–876. [5] L. Yujiri, “Passive millimeter wave imaging,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2006, pp. 98–101. [6] A. Tessmann, I. Kallfass, A. Leuther, H. Massler, M. Kuri, M. Riessle, M. Zink, R. Sommer, A. Wahlen, H. Essen, V. Hurm, M. Schlechtweg, and O. Ambacher, “Metamorphic HEMT MMICs and modules for use in a high-bandwidth 210 GHz radar,” IEEE J. Solid-State Circuits, vol. 43, no. 10, pp. 2194–2205, Oct. 2008. [7] H. Wang, R. Lai, T. H. Chen, P. D. Chow, J. Velebir, K. L. Tan, D. C. Streit, P. H. Liu, and G. Ponchak, “A monolithic -band three-stage LNA using 0.1 m InAlAs/InGaAs/ InP HEMT technology,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 1993, pp. 519–522. [8] J. W. May and G. M. Rebeitz, “High-performance -band SiGe RFICs for passive millimeter-wave imaging,” in IEEE Radio Frequ. Integr. Circuits Symp., Jun. 2009, pp. 437–440. [9] B. G. Perumana, J.-H. C. Zhan, S. S. Taylor, B. R. Carlton, and J. Laskar, “Resistive-feedback CMOS low-noise amplifiers for multiband applications,” IEEE Trans. Microw. Theory Tech., vol. 56, no. 5, pp. 1218–1225, May 2008. [10] Y. Shim, C.-W. Kim, J. Lee, and S.-G. Lee, “Design of full band UWB common-gate LNA,” IEEE Microw. Wireless Compon. Lett., vol. 17, no. 10, pp. 721–723, Oct. 2007. [11] H. Shigematsu, M. Sato, T. Takahashi, K. Imanishi, N. Hara, H. Ohnishi, and Y. Watanabe, “49-GHz preamplifier with a transimpedance gain of 52 dB using InP HEMTs,” in IEEE Gallium Arsenide Integr. Circuit Symp., Oct. 2001, pp. 137–140. [12] M. W. Pospieszalski, “Modeling of noise parameters of MESFET’s and MODFET’s and their frequency and temperature dependence,” IEEE Trans. Microw. Theory Tech., vol. 37, no. 9, pp. 1340–1350, Sep. 1989. [13] H. Shigematsu, M. Sato, T. Hirose, and Y. Watanabe, “A 54-GHz distributed amplifier with 6-V output for a 40-Gb/s LiNbO modulator driver,” IEEE J. Solid-State Circuits, vol. 37, no. 9, pp. 1100–1105, Sep. 2002. [14] K. Makiyama, T. Takahashi, T. Suzuki, K. Sawada, T. Ohki, M. Nishi, N. Hara, and M. Takikawa, “Improvement of circuit-speed of HEMTs IC by reducing the parasitic capacitance,” in IEEE Int. Electron Devices Meeting Tech. Dig., Dec. 2003, pp. 30.6.1–30.6.4.



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Masaru Sato received the B.E. and M.E. degrees in electrical engineering from Tohoku University, Sendai, Japan, in 1996 and 1999, respectively. In 1999, he joined Fujitsu Laboratories Ltd., Atsugi, Japan, where he has been engaged in research on high-speed GaAs- and InP-based HEMT circuits for fiber-optic communication systems and 94-GHzband PMMW imager. He is currently engaged in the development of RF front-end circuits and antennas. Mr. Sato is a member of the Institute of Electronics, Information and Communication Engineers (IEICE), Japan. He was the recipient of the 2006 Young Researcher’s Award of the IEICE.

Tsuyoshi Takahashi received the B.S. and M.S. degrees in science and engineering from the University of Tsukuba, Ibaraki, Japan in 1985 and 1987, respectively. In 1987, he joined Fujitsu Laboratories Ltd., Atsugi, Japan, where he has been engaged in research and development of fabrication technology for InPbased HEMTs and InGaP-emitter HBTs. Mr. Takahashi is a member of the Japan Society of Applied Physics and the Institute of Electronics, Information and Communication Engineers (IEICE),

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Japan.

Tatsuya Hirose (M’00) received the B.E. degree from Tokyo Denki University, Tokyo, Japan, in 1987, the M.E degree from Hokkaido University, Sapporo, Japan, in 1989, and the Ph.D. degree in electrical engineering from Tohoku University, Sendai, Japan, in 2004. In 1989, he joined Fujitsu Laboratories, Ltd., Atsugi, Japan, where he has been engaged in research on the design and modeling of HEMTs and the development of MMICs based on their technologies. His current research interests include high-speed and high-frequency integrated circuits for optical and wireless communication systems. Dr. Hirose was the recipient of the 2003 Outstanding Young Engineer’s Award of the IEEE Microwave Theory and Techniques Society (IEEE MTT-S).

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A Broadband 835–900-GHz Fundamental Balanced Mixer Based on Monolithic GaAs Membrane Schottky Diodes Bertrand Thomas, Alain Maestrini, Member, IEEE, John Gill, Choonsup Lee, Robert Lin, Imran Mehdi, Fellow, IEEE, and Peter de Maagt, Fellow, IEEE

Abstract—The development of a 835–900-GHz biasable fundamental balanced mixer using planar GaAs Schottky diodes is presented. The monolithic microwave integrated circuit integrates two planar Schottky anodes in a balanced configuration, stripline filtering elements, and on-chip capacitor on a thin GaAs membrane. At 850 GHz, double side-band (DSB) mixer noise temperature of 2660 K and conversion loss of 9.25 dB are measured, respectively, at room temperature. When the mixer is cooled to 120 K, the DSB mixer noise temperature and conversion loss improve to 1910 K and 8.84 dB, respectively. Index Terms—Cryogenic test bench, fundamental balanced mixer (FBM), monolithic microwave integrated circuit (MMIC), passive cooling, planar Schottky diode, submillimeter wavelengths, vacuum chamber.

I. INTRODUCTION HE submillimeter-wave domain offers the advantage of enhanced transparency through a wet and/or cloudy atmosphere compared to the optical/UV domains. This effect has been exploited for ground-based observations in radio astronomy and in remote sensing of the Earth’s atmosphere for many decades. A breakthrough for this technology in Earth observation was the launch of the Microwave Limb Sounder (MLS), with a number of submillimeter-wave heterodyne channels, onboard the Upper Atmosphere Research Satellite (UARS) in 1991 [1]. The observations made by MLS greatly contributed to the explanation of the Ozone hole and the improvement of the understanding of stratospheric chemistry in general. Besides the observation of chemical species in the limb-sounding geometry, the characteristics of the submillimeter-wave domain also allowed one to study meteorological

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Manuscript received September 10, 2009; revised February 16, 2010; accepted March 15, 2010. Date of publication June 21, 2010; date of current version July 14, 2010. This work was supported in part by the National Aeronautics and Space Administration (NASA) under a contract and by the European Space Agency under Contract ESTEC/RFQ/3-12604/08/NK/\FM. The work of B. Thomas was supported by the Oak Ridge Associated University under the NASA Postdoctoral Program. B. Thomas, J. Gill, C. Lee, R. Lin, and I. Mehdi are with the Jet Propulsion Laboratory (JPL), California Institute of Technology, Pasadena, CA 91109 USA (e-mail: [email protected]). A. Maestrini is with the Laboratoire des Instruments et Systèmes d’Ile de France, Université Pierre et Marie Curie–VI, 75252 Paris, France, and also with the Observatoire de Paris, LERMA, 75014 Paris, France. P. de Maagt is with the European Space Research and Technology Center (ESTEC), European Space Agency (ESA), Noordwijk 2201 AG, The Netherlands. Digital Object Identifier 10.1109/TMTT.2010.2050181

phenomena related to clouds in a down-looking observation geometry. The remote sensing of stratospheric ice clouds is of key interest in understanding the hydrological cycle of climate systems for life on Earth. Several missions have been proposed that would monitor globally the ice water content of cirrus clouds using passive submillimeter radiometer instruments up to 850 GHz [2]. Therefore, highly sensitive heterodyne receivers operating at room temperature in the submillimeter-wave range are needed for such applications. Development of compact and broadband receivers in this frequency range can also benefit terahertz imaging applications by providing higher resolution [3]. Submillimeter-wave heterodyne receivers based on planar Schottky diodes are usually preferred when high sensitivity, high spectral resolution, and long life at frequencies up to 2.5 THz [4] are required. These instruments can operate at both room or cryogenic temperatures, which can be easily achieved with compact active cooling systems or using passive cooling systems in space [5]. Single-diode fundamental mixers using whisker-contacted diodes [6], [7] as well as planar diodes [8] have been used in the past for their simplicity in biasing scheme, but they need a beam splitter in the field-of-view to inject the local oscillator (LO) signal, introducing losses in the RF path and resulting in a slightly more complicated receiver front end. Subharmonic mixers using planar Schottky diodes have been the preferred choice so far for the 800–900-GHz band due to the fact that they require LO sources at half the operating frequency and that the LO injection does not require beam-splitters. Subharmonic mixers working up to 874 GHz [9], [10] have been demonstrated. However, previous studies have shown that fundamental mixers exhibit better noise performances than subharmonic types [11]. On the other hand, fundamental balanced mixers using two diodes in balanced configuration can benefit from inherent mode isolation between the RF and LO inputs, as well as LO noise cancellation [12]–[14]. They rely on a cross-bar balanced architecture with a pair of balanced diodes physically located either inside the LO waveguide [13] or in the RF waveguide [12], [14]. However, the biasing scheme is more complicated than that of a single diode device. In this paper, we present the design, development, and characterization of a fully monolithic 835–900-GHz biasable fundamental balanced mixer (FBM) using a GaAs Schottky-diode MMIC developed at the Jet Propulsion Laboratory (JPL), Pasadena, CA. The mixer is pumped by a powerful compact

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LO chain based on solid-state power-combined amplifiers and multipliers, resulting in the highest frequency all-solid-state compact broadband heterodyne receiver operating at room temperature with state-of-the-art performance. The front-end has been tested at both room and cryogenic temperatures (120 K) using a dedicated cryogenic test system. II. DESIGN METHODOLOGY Here, we describe the methodology employed to design the 835–900-GHz FBM, including the determination and optimization of the diodes geometrical and electrical parameters. It combines aspects of design procedure previously reported for subharmonic mixers [15] and balanced doublers [16]. 1) Linearization of the Ideal Mixer: Nonlinear circuit simulation of an ideal pair of Schottky diodes is performed using the harmonic balance code of the ADS Software Suite [17]. The goal is to determine the anode size of the diodes in order to get the best mixer conversion losses, lowest RF and LO input return losses, and linearize the diode model around optimum bias, LO pump power, and embedding impedances conditions. In this study, the architecture of the balanced mixer implies that the pair of Schottky diodes are seen in series by the RF signal and in anti-parallel configuration by the LO and IF signals. In the nonlinear simulation bench, this is achieved by using ideal narrowband filters centered around the RF and LO sources along with the IF termination. The LO signal is swept between 820–920 GHz. The IF signal is fixed at 5 GHz, resulting in an RF signal varying from 825 to 925 GHz. With an estimated LO power of 0.5 mW reaching the diodes, the mixer conversion losses are minimized by tuning the bias voltage and ideal embedding imof pedances. Assuming an epilayer doping concentration 5.10 cm , it is found that best conversion losses are obtained for anode area A of approximately 0.4 m , a bias voltage of 1.3 V, and ideal embedding impedances of approxifor the LO at 870 GHz, of approximately mately for the RF at 875 GHz, and of 200 for the IF at 5 GHz. The resulting electrical parameters used at room temperature for the Schottky diode model are a zero voltage caof 1 fF, a saturation current of 2.10 A, pacitance of 0.73 V, ideality factor of 1.4, and series barrier height of 30 . From these results, impedance tables of resistance the nonlinear diodes model for the RF and LO signals versus frequency are built and used in the following part to define the complex impedance the diode’s port. 2) Synthesis of the Mixer Circuit: 3-D electromagnetic (EM) simulations of the different parts of the mixer circuit are simulated separately using High Frequency Software Simulator (HFSS) from Ansys [18] and exported as -parameter Touchstone files into ADS. These parts include the RF and LO waveguides-to-stripline transitions, diode cells, high–low suspended stripline transitions and dc/IF transmission lines. Conduction and dielectric losses are also included in the EM simulation. The diode cell is simulated from the stripline accesses to the diode ports. Each diode port is defined as a 2-D micro-coaxial hollow rectangle that takes as inner boundary the rectangular anode and as outer boundary a 2-D rectangle defined by the anode rectangular cross section plus a gap equal

to the thickness of the epi-layer [19], [20]. An integration line between the outer and inner conductor of the port is used to set the right polarity of the diodes when performing subsequent nonlinear and linear circuit simulations. This polarity needs to be respected when connecting the resulting -parameter file extracted from the EM simulation to the nonlinear electrical model of the diode for correct synthesis of the circuit and determination of the mixer performance. Using ADS, a linear simulation bench of the mixer circuit is built which includes the -parameter files, RF and LO diode’s impedance ports obtained previously, electrical transmission lines, and the waveguide ports. This bench has two separate subcircuits: one for the RF signal propagating from the wavemode, and the other for guide to the diodes’ port with a the LO signal propagating with a TEM mode. The diode cell is also optimized by varying the position of the diodes between the middle gold stripline and the grounding beamlead in order to balance the RF and LO power coupling for both diodes. The resulting coupling efficiency from waveguides to both diode ports is predicted to be approximately 80% between 840–910 GHz for the RF, and 40%–45% between 850–900 GHz for the LO. 3) Prediction of the Mixer Performance: A set of nonlinear simulations is performed to fine tune the circuit and predict the performances of the mixer. For the conversion loss calculation, the standard ADS model of the Schottky diode [17] is used. It has been shown that additional high-frequency effects such as displacement current and carrier inertia are not significant in this frequency range and thus are not included here [21]. For the mixer noise-temperature calculation, the standard ADS model includes thermal and shot noise sources, but does not include any other sources that account for hot electron noise. As this effect can becomes significant at submillimeter-wave frequencies for small anode devices, an additional noise source is added in series with the standard ADS Schottky model [22]. The spectral power density of the noise source, derived from [23], can be expressed as follows: (1) where is the relaxation time 1 ps , is the electron charge, and is the electron mobility of the epi-layer 3100 cm V s and 2500 cm V s, respectively, for ( 295 K and 120 K operation [24], [25]). A preliminary simulation of the mixer circuit including the standard ADS Schottky model is performed to determine the most powerful harmonic currents passing through the diode. These are used to set an external noise source proportional to the sum of the square of these harmonic currents according to (1) that is added in series to each of the Schottky diode model, and the mixer noise temperature is computed in a subsequent simulation. In order to match the simulation results with the actual measurements, estimated 0.7 dB of losses for the feed-horn and 1.2 dB of insertion losses for the IF transformer, connector, and cable are also included. Results are shown in Fig. 4 as continuous lines. The predicted RF/LO isolation ranges from 29 to 33 dB between 830–900 GHz.

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Fig. 1. View of the 835–900-GHz FBM circuit mounted inside the lower half of the mechanical block, including an MMIC mixer device (center) mounted with dc chip capacitor (top) and IF transformer (right), dc bias, ground and IF gold beam-leads, and diodes cell close-up (insert on the top left corner) including the on-chip MIM capacitor. The device is approximately 0.7 mm long.

III. 835–900-GHZ FBM TOPOLOGY AND ARCHITECTURE The topology of the 835–900-GHz FBM is based on a cross-bar balanced architecture introduced earlier by [26] and subsequently used at higher frequencies [13], [14]. For the present design, both diodes are located inside the RF waveguide in a series configuration across the central suspended stripline, as illustrated in Fig. 1. The circuit is based on a thin GaAs membrane and uses beamleads for connections and handling [27]. The Schottky contacts, defined using E-beam lithography, are connected to the circuit via air-bridges. The JPL MMIC membrane Schottky process described in [27] is specially suited for the realization of FBMs at these frequencies. Indeed, the thin membrane prevents excessive dielectric loading of the waveguides and channels, and the beamleads allow for a precise grounding, centering, and dc/IF connection of the MMIC to the block and dc/IF circuits. The on-chip MIM capacitor allows to dc bias the mixer with minimum RF/LO fields disturbance. Finally, the MMIC process reduces the uncertainties associated with handling and placing the device inside the block. The LO signal is coupled via a bowtie -plane probe with integrated dc/IF line to the diode. This transition is adapted from a previous design that uses an integrated dc bias line [28]. The length of the narrow line connecting the bowtie antenna is optimized to prevent any resonance in the desired LO band. The bandwidth of this bowtie-type transition is also improved by adding narrow steps inside the LO waveguide, as demonstrated by [29]. A dc bias line on a metal–insulator–metal (MIM) capacitor similar to [30] is used to bias the diodes in series while providing an efficient IF, LO, and RF ground. The mixer block also includes a diagonal feed-horn antenna [31] for the RF input coupling and a WR-1.2 LO input waveguide with UG-387 flange. The measured dc characteristics of the diode MMIC are consistent with the theoretically expected numbers described above. External chip capacitors are used for the dc bias and further filtering of any unwanted IF residue. The IF signal is output

Fig. 2. View of the lower half of the mechanical split-block, showing from left to right the SMA-type dc glass bead, dc chip capacitors, the IF impedance transformer, and the K-type IF glass bead.

through an IF impedance transformer to the K-type connector. The IF transformer circuit is designed to improve the voltage standing wave ratio between the mixer and the external first low-noise amplifier (LNA) in the 2–11-GHz range. A view of the IF transformer mounted inside the lower half of the mechanical block is shown in Fig. 2. It consists of a meandering line to match from 200 to 50 in four-section impedance steps. The circuit is based on gold microstrip lines deposited on a 1.27-mmthick aluminum–nitride substrate. This enables to keep return losses above 10 dB and insertion losses below 1 dB over a relatively broad bandwidth of 2–11 GHz. The dc bias chip capacitors are connected with thermo-compressed bond wires to a SMA-type glass bead. An SMA flange launcher connector is mounted afterwards to the block. The IF circuit is connected to a K-type glass bead via a stripline stress relief contact1 inserted on the tip of the glass bead and silver-epoxy glued on the ending of the microstrip line section. 1Anritsu

Corporation. [Online]. Available: http://www.anritsu.com.

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Fig. 3. Cryogenic mixer test setup, including the vacuum chamber (middle), a liquid nitrogen dewar, vacuum pump, and cryo-cooler (left-hand side), and external electronic system LO/IF/dc and control system (right-hand side). Details of the arrangement inside the test chamber include front-end multipliers/mixer, heated copper bracket mounting fixture, gold-plated chopper blade and motor, and two reference targets for hot and cold calibrations.

IV. CRYOGENIC TEST SETUP The test bench shown in Fig. 3 allows for the characterization of submillimeter-wave mixers and receivers in a vacuum environment and at temperatures compatible with passive cooling in space, i.e., within the range 80–300 K. It includes a cryogenic vacuum test chamber connected to an external vacuum mechanical and turbo pump, a cryo-cooler, and a custom-made liquid nitrogen LN dewar. The calibration system is located completely inside the test chamber and includes a room temperature load, a LN cooled load, a dual-blade chopper, and vacuum stepper motor. This arrangement allows for direct -factor measurements without any additional corrections for atmospheric losses, added optics, and windows. The hot load is made of small tiles of TK-RAM material (from Thomas Keating) and sitting on the bottom of the test chamber. The load is thermally strapped to the 295 K walls of the vacuum chamber. The cold load is made of MF 116 Eccosorb material (from Emerson and Cuming) machined into pyramidal shapes and is connected via a thermal vacuum feed-through to the external LN dewar. Hot and cold loads are measured at approximately 294 and 115 K, respectively, for room-temperature measurements and 283 and 105 K, respectively, for 120-K measurements. Their temperature is constantly monitored using temperature sensors and controller (Lakeshore 330) and is very stable over a -factor measurement cycle (variation of less than 0.2 K). The LO signal is provided by an Agilent -band source connected to an Agilent synthesizer and a set of power-combined -band amplifier module that can output over 500 mW in the frequency range 90–100 GHz located outside the test chamber. The -band LO signal is then coupled into the test chamber via a WR-10 waveguide vacuum feed-through and waveguide into a powerful 300-GHz quad-chip tripler and 900-GHz dualchip tripler that outputs over 1 mW at room temperature between 840–900 GHz, and over 1.5 mW when cooled at 120 K between 850–906 GHz [32]. The physical temperature of the front-end elements is controlled to within 2 K of the target value by external heat controlling system. The dc connection

between the mixer multipliers and the dc bias supplies outside the test chamber is done via SMA flexible cables and vacuum feed-throughs. A 15-MHz dc low-pass filter is inserted between the bias box and vacuum chamber to filter any unwanted EM pollution from the environment. A shielded 2-4-GHz dc-block is inserted between the IF output connector of the test chamber and the IF processor in order to bias both mixer diodes in series using the dc bias line. Insertion losses of 0.64 dB in average between the output IF connector of the mixer and the input connector of the IF processor have been measured independently from 2 to 4 GHz at room temperature. The 2–4-GHz IF processor outside the test chamber comprises of input isolator, a 20-dB hybrid coupler, a low-noise preamplifier, a 2–4-GHz filter, a low-cost amplifier, and a final isolator. A 2–4-GHz noise source with an excess noise ratio of 15.5 dB is connected to the coupled port of the 20-dB coupler. Biasing the noise source enables to change accurately the noise temperature of the IF processor from 84.6 0.5 K (OFF state) to 191.8 1.1 K (ON state). The output of the IF processor is connected to an Agilent average power sensor and power meter with 0.001 dB of resolution. The independent full calibration of the IF processor as well as the test procedure to retrieve the DSB mixer noise temperature and conversion losses from the -factor measurement are detailed in [33]. V. MIXER MEASUREMENTS AND ANALYSIS The measurement results including the DSB mixer noise temperature and DSB mixer conversion losses versus LO frequency at both room temperature and 120 K are presented in Fig. 4. Predicted performances based on the designed procedure and parameters described in Section III) are also shown in the same figure for comparison. For each frequency point, the receiver noise temperature is optimized using the bias voltage of both triplers and the 835–900-GHz mixer. Tuning of the triplers bias voltage allows for adjusting the LO pump power and not over pump the mixer. The dc bias tuning of the mixer allows for adjusting the mixer current in order to get optimum performance. Due to the high

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Fig. 4. Measurement and predicted results of the 835–900-GHz fundamental balanced MMIC mixer at 295 K (black dotted curves) and 120 K (white dotted curves) of operating temperature versus central RF frequency. The upper part of the graph shows the DSB mixer conversion losses in decibels and the lower part shows the DSB mixer noise temperature in Kelvin. The continuous full and dashed curves represent the predicted DSB mixer conversion losses (upper part) and DSB mixer noise temperature (lower part) at 295 and 120 K, respectively. The IF band is 2–4 GHz.

accuracy of the power level measured 0.001 dB , a reading uncertainty of 0.4 dB on the conversion losses and 90 K on the DSB mixer noise temperature are obtained in measurements. Furthermore, an estimated emissivity of 99% on the calibration load give systematic maximum error on the cold load of 2 K, overestimating the mixer noise temperature by approximately 30 K and 0.08 dB. Additional uncertainties such as standing waves in the optical path are not considered in this error budget. These results are uncorrected for any IF mismatch and IF cable and feed-through losses between the mixer and the IF processor. These insertion losses are measured separately at room temperature around 0.64 dB between 2–4 GHz. 1) Measurement Results at 295 K: The best mixer noise temperature measured at room temperature is 2660 46 K at 865.8 GHz, with DSB mixer conversion losses of 9.08 0.2 dB. The best DSB mixer conversion losses measured at room temperature is 8.02 0.28 dB at 862.2 GHz, with corresponding DSB mixer noise temperature of 3201 50 K. If the mixer performances are corrected for IF external cable losses (0.64 dB), DSB mixer noise temperature and conversion losses drops to 2330 K at 865.8 GHz and 7.38 dB at 862.2 GHz, respectively. DSB mixer noise temperature and conversion losses are below 4000 K and 10.5 dB, respectively, from 845 to 888 GHz. The optimum bias conditions for most of the band are a bias voltage between 1.3–1.45 V and total current between 300-400 A. These currents are consistent with previous reported values for optimal mixing [34]. In some specific frequencies, the bias voltage has to be decreased to 1.27 V to keep similar current and not over-pump the mixer. At room temperature, we estimate that the mixer requires about 1 mW for optimum pumping. With

the current LO source, we have also observed frequency points where the LO power over-pumps the mixer, thus degrading the noise performance. The mixer has also been tested with a lower power source that puts out about 0.3–0.6 mW of output power. With less than optimum LO power, the mixer performance degrades and the DSB noise temperature ranges from 3000 K up to 10 000 K. 2) Measurement Results at 120 K: The best DSB mixer noise temperature measured is 1910 29 K at 877.5 GHz, with DSB mixer conversion losses of 8.84 0.14 dB. The best DSB mixer conversion losses observed is 8.44 0.17 dB at 864 GHz, with corresponding DSB mixer noise temperature of 2213 33 K. DSB mixer noise temperature and conversion losses are below 3000 K and 10.5 dB, respectively, from 847 to 890 GHz. The optimum bias conditions for most of the band are a bias voltage between 1.5–1.6 V and total current between 200-400 A. 3) Comparison With Simulations: The predicted performance of the mixer are computed for the conversion losses and mixer noise temperature and are shown along with the measurement in Fig. 3. Flat LO input power of 1 mW for the simulations at room temperature. For a 120 K operating tem25 , peratures, the following parameters are assumed: 1.5, 0.95 V, 2.10 A, flat LO input power of 1.6 mW, and bias voltage of 1.5 V. These parameters are partly computed from temperature-dependent formulas such as saturation current and barrier potential, partly extrapolated from literature references such as the series resistance and ideality factor [19], [35]. Zero voltage capacitance is kept constant. The predicted performance of the mixer use the same nonlinear model of the Schottky barrier as for room temperature but with

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the modified electrical parameters listed above. As illustrated in Fig. 4, the simulations agree globally to within 1 dB of the measurements for both the DSB conversion losses and DSB noise figure at room temperature between 844–888 GHz. At 120 K, the simulations predict a drop in mixer noise temperature of approximately 600 K, which is comparable to 775 K in average for the measurements. The simulated DSB mixer conversion losses are consistent with the measurements at room temperature and 1 dB lower than expected at 120 K. This can be partly explained by the fact that the electrical characteristics of the Schottky diodes considered during the simulations are only estimated and have not been measured at this temperature. Uncertainties in the series resistance, ideality factor, and saturation current might lead to an optimistic value of the simulated conversion losses. Moreover, the device performance based on simulation show a broader operating bandwidth than what is measured. Below 845 GHz, this discrepancy can be explained by the fact that a constant LO power is considered in simulation for all frequencies, whereas a decrease in coupling efficiency of the mixer (refer to Section III) combined to a monotonic decrease in power available from the LO source adds up to starve the mixer in pump power. Above 890 GHz, additional simulations have shown that a shift of 10 m of the circuit inside the RF waveguide would lead to a degradation of the performances at the high end of the designed band. Machining tolerances of the block added to mounting tolerances inside the block of the chip can be estimated to at least 10 m and, therefore, could explain the degradation of the performances above 890 GHz. 4) Comparison With an 874-GHz Subharmonic Mixer: An 874-GHz MMIC subharmonic mixer developed previously using the same process give DSB mixer noise temperatures of approximately 4000 K and DSB conversion losses of 12 dB at room temperature (deduced from [21]). However, a direct comparison with this device cannot be made as such due to the fact that the subharmonic and fundamental MMIC devices have different doping densities and that the subharmonic mixer does not have any IF matching circuit included inside the block. The power consumption is significantly higher for the FBM channel (approximately 5 W) compared with the subharmonic mixer channel (approximately 2 W). This mainly due to the amount of power that has to be generated at the -band (500 mW for the FBM instead of 150 mW for the subharmonic mixor) using power-combined amplifiers. The multipliers can be self-biased and should not influence significantly the total power budget. It is interesting to notice that, due to the amount of LO power available, the subharmonic mixer can be operated bias-less whereas the FBM needs to be biased externally and cannot be self-biased, adding the power consumption of a bias board to the total power consumption. The FBM performance obtained in this study is similar to the performance reported at a single frequency point on the best whisker-contacted corner-cubes single-ended mixer [6]. VI. CONCLUSION A broadband FBM working in the 835–900-GHz range based on membrane Schottky diodes has been demonstrated.

The mixer provides superior performance compared with subharmonic mixers in a similar frequency range. The LO source for the mixer is based on a multiplier chain and has shown to provide sufficient power to pump the mixer. This represents the first demonstration of a compact broadband room-temperature receiver in this frequency range with a balanced mixer design. Moreover, it is demonstrated that, by cooling the mixer to 120 K, a 2-dB improvement can be achieved in the receiver performance. The successful demonstration of this design methodology along with the availability of high-power sources in the 600–1200-GHz range now enable development of highly sensitive heterodyne receivers at room temperature in this frequency range. ACKNOWLEDGMENT The authors would like to thank Dr. P. Siegel, JPL, Pasadena, CA, for his continued support, encouragement, and discussions regarding terahertz technology. The authors would also like to acknowledge Dr. Boussaha, LERMA, Paris, France, for his help with dicing of the IF circuits and SAP-France for the highquality block manufacturing. The work was carried out at the JPL, California Institute of Technology, under a contract with NASA, and at Observatoire de Paris. REFERENCES [1] F. T. Barath et al., “The upper atmosphere research satellite Microwave Limb Sounder instrument,” J. Geophys. Res. Atmos., vol. 98, no. D6, pp. 10,751–10,762, Jun. 1993. [2] S. A. Buehler, “CIWSIR: A proposed ESA submillimetre mission to measure cloud ice,” in Proc. 5th ESA Workshop MM-Wave Tech Appl., Noordwijk, The Netherlands, May 18–20, 2009, pp. 547–554. [3] K. B. Cooper, R. J. Dengler, N. Llombart, T. Bryllert, G. Chattopadhyay, E. Schlecht, J. Gill, C. Lee, A. Skalare, I. Mehdi, and P. Siegel, “Penetrating 3-D imaging at 4- and 25-m range using a submillimeterwave radar,” IEEE Trans. Microw. Theory Tech., vol. 56, no. 12, pp. 2771–2778, Dec. 2008. [4] P. H. Siegel, R. P. Smith, M. C. Gaidis, and S. C. Martin, “2.5-THz GaAs monolithic membrane-diode mixer,” IEEE Trans. Microw. Theory Tech., vol. 47, no. 5, pp. 596–604, May 1999. [5] A. R. Kerr, “Low-noise room-temperature and cryogenic mixers for 80–120 GHz,” IEEE Trans. Microw. Theory Tech., vol. MTT-23, no. 10, pp. 781–787, Oct. 1975. [6] H. P. Roeser, H. W. Huebers, T. W. Crowe, and W. C. B. Peatman, “Nanostructure GaAs Schottky diodes for far-infrared heterodyne receivers,” Infrared Phys. Technolol., vol. 35, no. 2–3, pp. 451–462, Mar./ Apr. 1994. [7] T. Suzuki, T. Yasui, H. Fujishima, T. Nozokido, M. Araki, O. BoricLubecke, V. M. Lubecke, and K. Mizuno, “Reduced low-frequency noise Schottky barrier diodes for terahertz applications,” IEEE Trans. Microw. Theory Tech., vol. 47, no. 9, pp. 1649–1655, Sep. 1999. [8] J. Hesler, W. R. Hall, T. W. Crowe, R. M. Weikle, B. S. Deaver, Jr, R. F. Bradley, and S.-K. Pan, “Fix-tuned submillimeter wavelength waveguide mixers using planar Schottky-barrier diodes,” IEEE Trans. Microw. Theory Tech., vol. 45, no. 5, pp. 653–658, May 1997. [9] E. Schlecht, J. Gill, R. Dengler, R. Lin, R. Tsang, and I. Mehdi, “A unique 520–590 GHz biased subharmonically-pumped Schottky mixer,” IEEE Microw. Wireless Compon. Lett., vol. 17, no. 12, pp. 879–881, Dec. 2007. [10] B. Thomas, A. Maestrini, D. Matheson, I. Mehdi, and P. de Maagt, “Design of an 874 GHz biasable sub-harmonic mixer based on MMIC membrane planar Schottky diodes,” in Proc. 33rd Int. Conf. IR, Millimeter Terahertz Waves, Pasadena, CA, Sep. 2008, Paper W4G3.1437. [11] A. R. Kerr, “Noise and loss in balanced and subharmonically pumped mixers: Part II-application,” IEEE Trans. Microw. Theory Tech., vol. MTT-27, no. 12, pp. 944–950, Dec. 1979. [12] J. A. Wells, N. J. Cronin, and P. H. Reece, “Rugged 94 GHz crossbar balanced mixer,” Proc. Inst. Elect. Eng., vol. 137, no. 4, pt. H, pp. 235–237, Aug. 1990.

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[13] E. Schlecht, J. Gill, R. Dengler, R. Lin, R. Tsang, and I. Mehdi, “First wideband 520–590 GHz balanced fundamental Schottky mixer,” in Proc. 18th Int. Symp. Space Terahertz Technol., Pasadena, CA, Mar. 2007, 296 pp. [14] N. R. Erickson and T. M. Goyette, “Terahertz Schottky-diode balanced mixers,” in Proc. SPIE Conf., Feb. 2009, vol. 7215, pp. 1–5. [15] B. Thomas, A. Maestrini, and G. Beaudin, “A low-noise fixed-tuned 300–360-GHz sub-harmonic mixer using planar Schottky diodes,” IEEE Microw. Wireless Compon. Lett., vol. 15, no. 12, pp. 865–867, Dec. 2005. [16] D. W. Porterfield, T. W. Crowe, R. F. Bradley, and N. R. Erickson, “A high-power fixed-tuned millimeter-wave balanced frequency doubler,” IEEE Trans. Microw. Theory Tech., vol. 47, no. 4, pp. 419–425, Apr. 1999. [17] “Advanced Design System,” Agilent Technol., Palo Alto, CA, 2009. [18] “High Frequency Simulation Software,” Ansoft Corporation, Pittsburgh, PA, V11.2. [19] A. Maestrini, J. S. Ward, J. J. Gill, H. S. Javadi, E. Schlecht, C. TriponCanseliet, G. Chattopadhyay, and I. Mehdi, “A 540–640-GHz highfrequency four-anode frequency tripler,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 9, pp. 2835–2843, Sep. 2005. [20] B. Thomas, “Etude et réalisation d’une tête de réception hétérodyne en ondes sub-millimétriques pour l’étude des atmosphères et surfaces de planètes” Ph.D. dissertation, Lab. d’Etude du Rayonnement et de la Mat. en Astrophys., Observatoire de Paris, Paris, France, 2004 [Online]. Available: http://hal.archivesouvertes.fr/docs/00/39/22/39/PDF/ These_doctorat_Thomas_2004.pdf [21] B. Thomas, A. Maestrini, J. Ward, E. Schlecht, J. Gill, C. Lee, R. Lin, and I. Mehdi, “Terahertz cooled sub-harmonic Schottky mixers for planetary atmospheres,” in Proc. 5th ESA Workshop Millimetre Wave Technol. Appl., Noordwijk, The Netherlands, May 2009, pp. 101–108. [22] B. Thomas, A. Maestrini, J. C. Orlhac, J. Goutoule, and G. Beaudin, “Numerical analysis of a 330 GHz sub-harmonic mixer with planar Schottky diodes,” in Proc. 3rd ESA Workshop Millimetre-Wave Technol. Tech., Espoo, Finland, May 2003, pp. P1–18. [23] T. W. Crowe and R. J. Mattauch, “Analysis and optimization of millimeter- and submillimeter-wavelength mixer diodes,” IEEE Trans. Microw. Theory Tech., vol. MTT-35, no. 2, pp. 159–168, Feb. 1987. [24] J. Heiermann and H.-P. Roeser, “Semiclassical description of Schottky diode mixer properties at THz frequenices,” in Proc. 16th Int. Symp. Space Terahertz Technol., Göteborg, Sweden, May 2005, pp. 483–485. [25] G. E. Stillman and C. M. Wolfe, “Electrical characterization of epitaxial layers,” Thin Solid Films, vol. 31, pp. 69–88, 1976. [26] L. T. Yuan, “Design and performance analysis of an octave bandwidth waveguide mixer,” IEEE Trans. Microw. Theory Tech., vol. MTT-25, no. 12, pp. 1048–1054, Dec. 1977. [27] S. Martin, B. Nakamura, A. Fung, P. Smith, J. Bruston, A. Maestrini, F. Maiwald, P. Siegel, E. Schlecht, and I. Mehdi, “Fabrication of 200 to 2700 GHz multiplier devices using GaAs and metal membranes,” in IEEE MTT-S Int. Microw. Symp. Dig., 2001, vol. 3, pp. 1641–1644. [28] C. Risacher, V. Vassilev, A. Pavolotsky, and V. Belitsky, “Waveguide-to-microstrip transition with integrated bias-T,” IEEE Microw. Wireless Compon. Lett., vol. 13, pp. 262–264, 2003. [29] J. W. Kooi, G. Chattopadhyay, S. Withington, F. Rice, J. Zmuidzinas, C. Walker, and G. Yassin, “A full-height waveguide to thin-film transition with exceptional RF bandwidth and coupling efficiency,” Int. J. Infrared Millimeter Waves, vol. 24, no. 3, pp. 261–284, Mar. 2003. [30] J. Bruston, A. Maestrini, D. Pukala, S. Martin, B. Nakamura, and I. Mehdi, “A 1.2 THz planar tripler using GaAs membrane based chips,” in Proc. 12th Int. Symp. Space Terahertz Technol., San Diego, CA, Feb. 2001, pp. 310–319. [31] J. Johansson and N. D. Whyborn, “The diagonal horn as a submillimeter wave antenna,” IEEE Trans. Microw. Theory Tech., vol. 40, no. 5, pp. 795–800, May 1992. [32] A. Maestrini, J. S. Ward, J. J. Gill, C. Lee, B. Thomas, R. H. Lin, G. Chattopadhyay, and I. Mehdi, “A 0.9 THz frequency multiplied source with milliwatts of power,” IEEE Trans. Microw. Theory Tech., to be published. [33] J. Treuttel, B. Thomas, A. Maestrini, H. Wang, B. Alderman, J. V. Siles, S. Davies, and T. Narhi, “A 380 GHz sub-harmonic mixer using MMIC foundry based Schottky diodes transferred onto quartz substrate,” in Proc. 20th Int. Symp. Space Terahertz Technol., Charlottesville, VA, Apr. 2009, pp. 251–254. [34] H. P. Roeser, R. U. Titz, G. W. Schwaab, and M. F. Kimmitt, “Current-frequency characteristics of submicrometer GaAs Schottky barrier diodes with femtofarad capacitance,” J. Appl. Phys., vol. 72, no. 7, pp. 3194–3197, Oct. 1992.

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[35] P. H. Siegel, I. Mehdi, and J. East, “Improved millimeter-wave mixer performance analysis at cryogenic temperatures,” IEEE Microw. Guided Wave Lett., vol. 1, no. 6, pp. 129–131, Jun. 1991.

Bertrand Thomas received the M.Sc. degree in radio-communication and microwave engineering jointly from ESIEE-Paris, Paris, France, and Université Marne-la-Vallée, Marne-la-Vallée, France, in 1999, and the Ph.D. degree in astrophysics and space instrumentation jointly from University Paris-VI, Paris, France, and Observatoire de Paris, Paris, France, in 2004. From 1999 to 2001, he was with the Receiver Group, IRAM 30-m Radio-Relescope, Granada, Spain. From 2001 to 2004, he was with the LERMA Department, Observatoire de Paris, Paris, France. From 2005 to 2008, he was a Research Engineer with the Rutherford Appleton Laboratory, Oxfordshire, U.K. In 2008, he joined the Submillimeter-Wave Advanced Technology Group, Jet Propulsion Laboratory (JPL), California Institute of Technology, Pasadena, as a National Aeronautics and Space Administration (NASA) Postdoctoral Program Fellow. His current research interests are the design and development of semiconductor devices for terahertz heterodyne receivers for planetary science and astrophysics. Dr. Thomas was the recipient of the 2009 JPL Outstanding Postdoctoral Research Award from NASA.

Alain Maestrini (M’05) received the M.S. degree in telecommunications and electrical engineering from the ENST de Bretagne, Bretagne, France, in 1993, and the Ph.D. degree in electronics jointly from the Université de Bretagne Occidentale, Bretagne, France, and the Observatoire de Paris, Paris, France, in 1999. From 1993 to 1995, he was an Engineer with the Receiver Group, IRAM 30-m Telescope, Granada, Spain. In 1999, he joined the Submillimeter-Wave Advanced Technology Group, Jet Propulsion Laboratory (JPL), California Institute of Technology, Pasadena, to work on solid-sate terahertz LO development for the heterodyne instrument of the Herschel Space Observatory. He returned to the Observatoire de Paris in 2002 and in 2003 joined the Laboratoire des Instruments et Systèmes d’Ile de France, Université Pierre et Marie Curie, Paris, as an Assistant Professor in electronics and microwaves. Since January 2008, he has been an Associate of LERMA, Observatoire de Paris, and a Technical Advisor for JPL. His current research interests are in the design of integrated millimeter- and submillimeter-wave electronics for radio astronomy and planetary science. Dr. Maestrini was the recipient of the Arago Prize from the French Academy of Science in 2009.

John Gill received the B.S. and M.S. degrees in mechanical engineering and Ph.D. degree microelectromechanical systems (MEMS) from the University of California at Los Angeles (UCLA), in 1997 and 2001, respectively. From 1997 to 1998, he was with the Jet Propulsion Laboratory (JPL), California Institute of Technology, Pasadena, where he was involved in developing the quantum-well infrared photodetector. Currently, he is back with JPL working on developing microwave devices. In 2001, he became involved with Herschel, a joint flight project with the European Space Agency (ESA), where he is leading the high-frequency cutting-edge multiplier and mixer device development effort. His research interests include design, fabrication, and characterization of microelectronic devices using conventional integrated circuit, MEMS, and nanoelectromechanical systems (NEMS) technologies for space and industrial applications.

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Choonsup Lee received the B.S. degree in electrical engineering from Kyungpook National University, Daegu, Korea, in 1996, and the M.S. and Ph.D. degrees in electrical engineering and computer science from the Korea Advanced Institute of Science and Technology (KAIST), Seoul, Korea, in 1998 and 2002, respectively. He is currently a Member of the Technical Staff with the Jet Propulsion Laboratory (JPL), California Institute of Technology, Pasadena. He has extensive experiences in the design and characterization of microelectromechanical systems/nano devices. He is currently working on GaAsbased frequency sources and mixers in the terahertz region. He has authored or coauthored 17 international journal papers and 32 international conference papers.

Robert Lin received the B.S. and M.S. degrees in electrical engineering from the California Institute of Technology, Pasadena, in 1997 and 2002, respectively. Since 1997, he has been a part of the Submillimeter-Wave Advanced Technology Group, Jet Propulsion Laboratory (JPL), California Institute of Technology, Pasadena, CA, where he has helped to assemble, build, and test submillimeter-wave and terahertz amplifiers, multipliers, and mixers for planetary, astrophysics, and earth-based applications.

Imran Mehdi (S’85–M’91–SM’05–F’10) received the three-year Certificate in Letters and Science from Calvin College, Grand Rapids, MI, in 1983, and the B.S.E.E., M.S.E.E., and Ph.D. (E.E.) degrees from the University of Michigan at Ann Arbor, in 1984, 1985, and 1990, respectively. In 1990, he joined the Jet Propulsion Laboratory (JPL), California Institute of Technology, Pasadena, where his responsibilities included the design and fabrication of low-parasitic planar Schottky diodes for mixers in the terahertz range. Since 1999, he has led the effort of developing broadband solid-state sources from 200 to 2500 GHz for the heterodyne instrument on the Herschel Space Observatory, a cornerstone European Space Agency (ESA) mission. Currently, he is a Principal Member of Engineering Staff with JPL and is responsible for developing terahertz technology for future National Aeronautics and Space Administration (NASA) missions. His interests include millimeter- and submillimeter-wave devices, high-frequency instrumentation, and heterodyne receiver systems.

Peter de Maagt (S’88–M’88–SM’02–F’08) was born in Pauluspolder, The Netherlands, in 1964. He received the M.Sc. and Ph.D. degrees from the Eindhoven University of Technology, Eindhoven, The Netherlands, in 1988 and 1992, respectively, both in electrical engineering. From 1992 to 1993, he was a Station Manager and Scientist with an INTELSAT propagation project, Surabaya, Indonesia. He is currently with the European Space Research and Technology Centre (ESTEC), European Space Agency (ESA), Noordwijk, The Netherlands. His research interests are in the area of millimeter and submillimeter-wave reflector and planar integrated antennas, quasi-optics, electromagnetic-bandgap antennas, and millimeter- and submillimeter-wave components. Dr. de Maagt serves as an associate editor for the IEEE TRANSACTION ON ANTENNAS AND PROPAGATION and was coguest editor of the November 2007 Special Issue on Optical and Terahertz Antenna Technology. He was corecipient of the H. A. Wheeler Award of the IEEE Antennas and Propagation Society (IEEE AP-S) for the Best Applications Paper of 2001 and 2008. He was granted an ESA Award for Innovation in 2002. He was corecipient of Best Paper Awards at the Loughborough Antennas Propagation Conference (LAPC) 2006 and the International Workshop on Antenna Technology IWAT) 2007.

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A Frequency-Multiplied Source With More Than 1 mW of Power Across the 840–900-GHz Band Alain Maestrini, Member, IEEE, John S. Ward, Member, IEEE, John J. Gill, Choonsup Lee, Bertrand Thomas, Robert H. Lin, Goutam Chattopadhyay, Senior Member, IEEE, and Imran Mehdi, Fellow, IEEE

Abstract—We report on the design, fabrication, and characterization of an 840–900-GHz frequency multiplier chain that delivers more than 1 mW across the band at room temperature with a record peak power of 1.4 mW at 875 GHz. When cooled to 120 K, the chain delivers up to 2 mW at 882 GHz. The chain consists of a power amplifier module that drives two cascaded frequency triplers. This unprecedented output power from an electronic source is achieved by utilizing in-phase power-combining techniques. The first stage tripler uses four power-combined chips while the last stage tripler utilizes two power-combined chips. The source output was analyzed with a Fourrer transform spectrometer to verify signal purity. Index Terms—Frequency multiplier, frequency tripler, local oscillator, planar diode, power combining, Schottky diode, submillimeter wavelengths, varactor.

I. INTRODUCTION

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ACK OF tunable, broadband, robust, and reliable power sources in the submillimeter-wave frequency range has been a major limiting factor in developing applications in this part of the spectrum. The range from 0.3 THz, where transistors show only limited gain, to about 10 THz, where solid-state lasers become available, continues to be of significant scientific interest where sources are much needed [1]–[4]. Photonic solutions to coherent generation at terahertz frequencies have dominated the field for decades starting with far-infrared lasers able to produce tens of milliwatts of coherent power, to femtosecond infrared lasers and photoconductors that enable broadband terahertz sources suited for numerous spectro-imagery applications [5]. Photomixers are also an attractive solution for generating coherent terahertz continuous waves (CWs) thanks to their wide frequency tunability [6], [7]. Recently, quantum Manuscript received October 12, 2009; revised February 21, 2010; accepted March 30, 2010. Date of publication June 07, 2010; date of current version July 14, 2010. The research presented in this paper was carried out at the Jet Propulsion Laboratory (JPL), California Institute of Technology, under a contract with the National Aeronautics and Space Administration (NASA), Université Pierre et Marie Curie-Paris 6, and Observatoire de Paris. The work of B. Thomas was supported by the Oak Ridge Associated University under the NASA Postdoctoral Program. A. Maestrini is with the Laboratoire d’Etude du Rayonnement et de la Matière en Astrophysique, Université Pierre et Marie Curie–Paris 6, 75005 Paris, France, and also with the Observatoire de Paris, LERMA, 75014 Paris, France (e-mail: [email protected]). J. S. Ward was with the Jet Propulsion Laboratory (JPL), Pasadena, CA 91109 USA. He is now with the Raytheon Company, Fort Wayne, IN 46808-4106 USA. J. J. Gill, C. Lee, B. Thomas, R. H. Lin, G. Chattopadhyay, and I. Mehdi are with the Jet Propulsion Laboratory (JPL), California Institute of Technology, Pasadena, CA 91109 USA (e-mail: [email protected]) Digital Object Identifier 10.1109/TMTT.2010.2050171

cascade lasers have made incursions into the sub-terahertz domain and are routinely delivering milliwatts or tens of milliwatts in the 1–4-THz range [8], [9] albeit at cryogenic temperatures and with limited bandwidth. These lasers have been successfully phase locked and used to build the local oscillator of a heterodyne receiver based on a super-conducting hot-electron-bolometer (HEB) mixer working at 2.8 THz [10]. In contrast, electronic sources in the terahertz region are scarce; if we put aside non solid-state sources like the power-hungry and heavy backward-wave oscillators (BWOs) that can work to about 1.2 THz, there is indeed only one proven solution: frequency multiplier chains from the microwave region to the terahertz [1], [11]. With current terahertz frequency multipliers, power is measured in microwatts rather than milliwatts. The current state-of-the-art at room temperature is 3 W at 1.9 THz [12], 15–20 W at 1.5–1.6 THz [13], [14], and 100 W at 1.2 THz [15]. As predicted in [16], these powers improve dramatically upon cooling: the same sources produce, respectively, 30, 100, and 200 W at 120 K. Despite relatively low output power levels, frequency-multiplied sources have some decisive advantages that make them the technology of choice for building the local oscillators of heterodyne receivers: firstly, they are inherently phase lockable and frequency agile, secondly, they work at room temperature, or at moderate cryogenic temperatures for enhance performance; thirdly, multiplier sources are robust enough, compact enough, and use a sufficiently low level of dc power to claim several years of heritage in the selective world of space technologies. From AURA [17] to the Herschel Space Observatory [18], frequency multipliers have demonstrated their real-word operability and are proposed for even more challenging missions to the outer planets [19]. The prospect of having a milliwatt-level broadband terahertz frequency-multiplied source would have seemed far fetched just a few years ago. This work will present a 0.9-THz frequency tripler that delivers more than 1 mW at room temperature when pumped with a fully solid-state source. This level of power has already enabled the demonstration of an 840–900-GHz fundamental balanced Schottky receiver that exhibits state-of-the-art noise and conversion loss [20]. It can also enhance terahertz imaging applications by driving frequency multipliers to even higher frequencies [21]–[23], such as the 2.5–2.7-THz band. Considering these new results, as well as recent advances in thermal management of frequency multipliers [24], the continuous progress of power amplifiers around or above 0.1 THz [25], and the prospect of high-breakdown-voltage GaN Schottky diodes for submillimeter-wave multipliers [26], [27], it is clear that electronic coherent sources have the potential to deliver

0018-9480/$26.00 © 2010 IEEE

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Fig. 1. Photograph of the bottom half of the power-combined 900-GHz frequency tripler showing device #1 (top view). Close-up view of the output combiner, device #1 and the dc capacitor (bottom left view.) Close-up view of device #1 with labels for diodes #1–#4 (bottom right view.). The tripler chip is approximately 300-m long and 100-m wide.

milliwatts of tunable single-mode power well into the terahertz range. The present approach, however, is based on the concept of power combining demonstrated recently at 300 GHz [28] and on the technological heritage of the past few years in planar GaAs Schottky diode multipliers. The source that will be presented is based on a power amplifier module at -band that pumps two frequency triplers that are cascaded. The first stage tripler utilizes four devices, while the second tripler is based on two devices and will be the focus of this paper. This unprecedented approach enables compact broadband sources with milliwatts of output power near 1 THz. II. DESIGN AND SIMULATIONS A. Design The power-combined 900-GHz tripler is based on two identical chips that are power combined in-phase in a single waveguide block using a Y-junction divider at the input waveguide and a Y-junction combiner at the output waveguide. The chip was first used for a single device version of the 900-GHz tripler before being employed in the current design. Fig. 1 shows an overall photograph of the tripler including the input matching circuit and two different close-ups of the device area. The tripler uses a symmetrical split-block waveguide design with one device mounted in each half block. The input

waveguide is split in two by a compact Y-junction to evenly feed the devices that are mounted in a channel that runs between their respective input and output waveguides. The two reduced-height output waveguides are combined by a Y-junction that is seen by each branch of the circuit as a simple waveguide step. Each device features four Schottky varactor diodes monolithically integrated on a 3- m thin GaAs membrane in a balanced configuration and biased in series. Each anode has an intrinsic zero bias capacitance of about 4 fF. An -plane probe located in the input waveguide couples the signal at the input frequency to a suspended microstrip line. This line has two sections of high impedance (about 130 at 900 GHz) and one section of medium-low impedance (about 50 at 900 GHz) to prevent the third harmonic from leaking into the input. The third harmonic produced by the diodes is coupled to a short section of a high-impedance line and then to the output waveguide by a second -plane probe. As for the 300-GHz tripler, the dimensions of both the channel and circuit are chosen to cut off the TE mode at two-third of the highest frequency of the desired band to insure that the second harmonic of the input signal is trapped in a virtual loop, i.e., the diode loop. This condition is necessary, though not sufficient, to balance the circuit [29]. The balancing has to be precise if the multiplier is to achieve high conversion efficiency from the fundamental frequency to

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Fig. 2. 3-D view of the inner part of the 900-GHz in-phase power-combined frequency tripler as modeled with Ansys HFSS for simulations at the output frequency. The two chips, part of the input waveguides, the output waveguides, and the output combiner are represented.

the third harmonic [29]. This is helped by the use of fewer pairs of diodes with small mesas. However, high-power frequency multipliers require the use of as many diodes as possible [30], [31]. The multiplier presented in this paper was designed for 40 mW of input power and can handle up to 60 mW. To increase the spectral purity of the 900-GHz frequency multiplier chain, the dimensions of the output waveguide has been chosen to cut off any second harmonic leakage that could result from circuit unbalance. In addition, the balanced geometry of the circuits ensures that power at the fourth harmonic of the input is strongly suppressed. The closest harmonic that can leak is the fifth at 1500 GHz, but, given the capacitance of the diodes, no significant power is expected at this frequency. As seen later in this paper, experimental results show that the chain achieves an excellent spectral purity at all the frequencies of the design band. As mentioned in [29], to extend the bandwidth, the input matching network includes several sections of waveguide of different heights and lengths. B. Simulations Predicted performance of the multiplier were obtained using the same method as in [28] and [29]. Our diode model was adjusted for the actual anode size (1.2 m ) and for the epilayer doping 5 10 cm . The multiplier structure was decomposed in several blocks that were analyzed separately with a 3-D electromagnetic field solver (Ansys High Frequency Structure Simulator (HFSS)1). Fig. 2 shows one of the sub-circuits used for simulating the linear response of the multiplier at the output frequency. The different blocks were then assembled in a circuit simulator (Agilent Advanced Design System (ADS)2) to perform harmonic-balance simulations of the whole circuit and to determine a number of parameters related to the performance of the multiplier. Among them, the balancing of the diode at the input frequency was investigated in detail to avoid the risk of overdriving a diode. The top graph of Fig. 3 shows the input coupling efficiency of each diode of one of the chips in the 775–950-GHz band for a flat input power of 45 mW and a reverse bias voltage 1HFSS, 2ADS,

Ansys Inc., Pittsburgh, PA. Agilent Technologies, Palo Alto, CA.

Fig. 3. Simulated response of the 900-GHz in-phase power-combined frequency tripler when pumped with 45 mW of input power and a fixed bias of 2 V (for four diodes in series per chip): the top graph shows the input coupling efficiency of the four diodes of one of the chips, and the bottom graph shows the power produced by each diode of the same chip.

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of 2 V. All simulations include waveguide losses and assume that the multiplier circuit is symmetrical; therefore, the second chip behaves exactly the same (no study on the effects of mechanical and electrical asymmetries between the chips has been pursued for this study). According to these simulations, the balancing at the input frequency is better than 2% for diodes #1, #2, and #4 with only diode #3 receiving less than 10% more power than the other three (see Fig. 1 to locate each diode on the chip). The bottom graph of Fig. 3 shows the power produced by the same diodes at the output frequency. The balancing is significantly degraded, but remains within 15% at the center of the band. It is notable that diode #4, which receives less input power than diode #2, does actually produce more power at the output frequency. No detailed investigation have been pursued to explain this, however, other simulations on this particular circuit, or simulations performed on similar circuits at other frequencies, suggest that such reversal in the input and output balance is related to the proximity of the diodes to the channel opening into the output waveguide. Depending on the position of the output backshort, this reversal can be observed or not, showing that the output backshort has an asymmetrical impact on the diodes (pushing the diodes further back inside the channel does reduce this asymmetrical impact, but at the expense of the multiplier performance). Fig. 4 shows the output power and the output coupling efficiency, which is defined as the ratio of the output power by the sum of the power produced individually by the diodes. All simulations do include the effects of the waveguide losses and are performed with a flat 45 mW of input power and a bias voltage of 2 V. From 775 to 865 GHz the output power rises from almost zero to 1.3 mW and then stays flat up to about 905 GHz

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Fig. 4. Simulated response of the 900-GHz in-phase power-combined frequency tripler when pumped with 45 mW of input power and a fixed bias of 2 V (for four diodes in series per chip): the top curve (dashed line) shows the output coupling efficiency and the bottom curve (solid line) shows the output power.

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before declining to almost zero at 950 GHz. The 3-dB bandwidth extends from approximately 820 to 930 GHz. The output power efficiency, however, declines slowly from 87% to 75% from 775 to 940 GHz, and then drops to 70% at 950 GHz. From Figs. 3 and 4, it clearly appears that the multiplier bandwidth is limited by the matching at the input frequency. III. MEASUREMENTS We assembled and tested several tripler blocks. Assembly was a bit more complex as for our dual-chip 300-GHz tripler, essentially due to bended shape of the dc line. The output power and the conversion efficiency of the 900-GHz power-combined frequency tripler were measured at room and cryogenic temperatures. A. Driver Stage The driver chain of the 900-GHz in-phase power-combined frequency tripler is constituted by a -band synthesizer fol-band amplifier lowed by a high power power-combined module, and a power-combined 300-GHz frequency tripler based on [28]. The power delivered by the driver stage at 300 GHz was measured using a waveguide Erickson Instruments power meter [32] and a 1-in-long WR10–WR3 waveguide transition to match the multiplier output waveguide. When pumped with 330–500 mW, this tripler delivers 29–48 mW in the 276–321-GHz band (see top graph of Fig. 5). The maximum power that can be handled by this multiplier is based on thermal modeling of the chip. B. Frequency Sweeps at 295 K—Comparison With Simulations At room temperature, the output power of the 900-GHz tripler was measured using an Erickson Instruments power meter and a 1-in-long WR10–WR1 waveguide transition to match the multiplier output waveguide. As for the calibration of the input power, the measurements of the output power of the 900-GHz tripler were not corrected for waveguide transition losses. The 900-GHz tripler output power was measured in the 826–950-GHz band every 1.8 GHz. The two bias voltages of the 900-GHz tripler were optimized independently at each frequency. The biases range between 2.5 V to 1 V for four

Fig. 5. Input power (top graph with square open markers), output power (bottom graph, bottom curve with round filled markers), and conversion efficiency (bottom graph, top curve with thin line and no markers) at 295 K of the in-phase power-combined 900-GHz frequency tripler measured with an Erickson Instrument power meter and a matched waveguide transition. The losses of the transition are not taken into account. The bias voltages were optimized at each frequency point and the structure in the measured plot can be due to interaction between the two triplers. The measurements were made using a power amplifier that delivers 330–500 mW from 92.0 to 93.0 GHz (828–837-GHz multiplier chain output frequency) and a fixed 500 mW from 93.0 to 105.5 GHz (837–950-GHz multiplier chain output frequency).

diodes in series at dc, and the rectified currents do not exceed 1.2 mA. Conversion efficiencies were calculated by dividing the power levels recorded at the output of the 900-GHz chain by the power levels recorded at the output of the driver stage. As there is no isolator between the two stages, the actual value of the efficiency may differ due to a possible interaction between the two triplers. Fig. 5 shows that the 900-GHz power-combined frequency tripler produces over 1 mW from 849.6 to 898.2 GHz at room temperature with a peak power of 1.2 mW at 857 GHz. The conversion efficiency is in the range of 2.1% to 2.5% in the same frequency range. Between 900–950 GHz, the tripler output power and efficiency decrease from 1 to 0.2 mW and from 2.4% to 0.3%, respectively. Fig. 6 shows a comparison of the measured conversion efficiency with the predicted efficiency when taken into account the measured values of the 900-GHz tripler input power. Therefore, these simulations differ from those presented in Fig. 4 where a flat 45 mW of input power was assumed. Fig. 6 shows a good agreement between the measurements and the simulations, except at the high end of the band where the roll-offs have a different slope. C. Frequency and Power Sweeps at 120 K The chain was tested at cryogenic temperature in a different setup. The -band power amplifier was replaced with a slightly different one and was left outside the cryostat, while the 900-GHz tripler and its driver were mounted inside. A corrugated horn directly attached to the output flange of the

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Fig. 6. Predicted (dashed line) and measured (solid line) tripler conversion efficiency of the in-phase power-combined 900-GHz frequency tripler. The measured values of the 900-GHz tripler available input power were used for the simulations.

900-GHz tripler and a mirror were used to focus the beam to the window of the Thomas Keating power meter. The modulation of the output beam was achieved by the -band synthesizer at about 23 Hz to avoid the use of an optical chopper. The cryostat window was made with a 25- m-thick Mylar film that introduced limited RF losses, in the range of 9%–17%. These losses were measured at each frequency point and taken into account, contrary to the losses of the corrugated horn, which were not measured, and consequently, not taken into account. The temperature was measured on top of the 900-GHz chain near the input flange of the 900-GHz tripler. As the cryostat uses an active cooling that can reach 15 K, heaters had to be used to maintain the temperature of the chain at 120 K within 2 K. Fig. 7 shows a comparison of the frequency response of the 900-GHz multiplier chain when cooling from an ambient temperature of 295 to 120 K from 837 to 937 GHz with a frequency step of 4.5 GHz. The power at -band does not change with the temperature and is limited to 500 mW since only the 900-GHz tripler and its driver stage are cooled. The improvement in performance depends strongly on the frequency. In the center of the band, between 835–900 GHz, the improvement varies between 20% at 846 GHz and 90% at 900 GHz. At 928 GHz, the improvement is about 100%. At an ambient temperature of 120 K, with a power at -band limited at 500 mW, the output power peaks at 1.9 mW at 886.5 GHz, and at 1.8 mW at 900 GHz. It is also noticeable that the power measured with the Thomas Keating power meter at room temperature in Fig. 7 matches the power measured with the Erickson Instruments power meter in Fig. 5 with a difference lower than 20%, or 0.75 dB, in the band where the -band amplifiers deliver the same amount of power to the 900-GHz multiplier chain. Given the difference of setup and the fact that no power standard exists in this band, this discrepancy can be considered as very limited. At 120-K ambient temperature, the power delivered by the -band amplifier that drives the 900-GHz multiplier chain was swept from 200 to 550 mW. Fig. 8 shows the output power of the 900-GHz chain versus input power at -band. A record output power of 2 mW was measured at 882 GHz for an input power of 550 mW. At this frequency, the output power increases almost linearly for input power ranging from 200 to 500 mW. Some saturation starts to occur at 500 mW of input power. At 900 GHz, the chain behaves almost the same as at 882 GHz, but starts to saturate at 450 mW.

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Fig. 7. Output power at 120 K (top curve with open markers) and at 295 K (bottom curve with filled markers) of the in-phase power-combined 900-GHz frequency tripler measured with a Thomas Keating power meter and a matched corrugated feed-horn. The measurements were not corrected for the losses of the horn. The bias voltages were optimized at each frequency. The measurements were made using a slightly different amplifier than for the measurements presented in Fig. 5. The amplifier delivers 390–500 mW from 93.0 to 94.5 GHz (837–850.5-GHz multiplier chain output frequency), a fixed 500 mW from 94.5 to 101.5 GHz (850–913.5-GHz multiplier chain output frequency) and 500–395 mW from 101.5 to 103.0 GHz (913.5–927-GHz multiplier chain output frequency).

Fig. 8. Power sweep at an ambient temperature of 120 K of the 900-GHz frequency multiplier chain at 882.0 GHz (top curve with open markers) and at 900.0 GHz (bottom curve with filled markers).

D. Fourier Transform Spectrometer (FTS) Scans The spectral purity of the 900-GHz frequency multiplier chain was checked from 0.15 to 2.1 THz using an FTS with 100-MHz resolution. Scans at different frequencies across the band have been performed. The scans where performed at room temperature. Fig. 9 shows the measured response at four frequencies covering the center of the band and its edges. The chain spectral purity is remarkably good with spurious or undesired harmonic below 27 dB with respect to the main signal, except at the high end of the band where the second harmonic of the 900-GHz tripler pump signal can be detected at a level of 10 dB below the third harmonic. Although the 100-MHz resolution of the FTS does not allow resolving low-frequency spurious signals around the main carrier, nor determine the level of phase noise, extensive tests of such multiplier chains have been done in the past and have shown that spurious signals and phase noise do not relate to the frequency multipliers themselves, but rather to the quality of the power supplies, to the fact that the power amplifiers are saturated or not, and to the phase noise of the synthesizer itself. Fig. 9 shows that a

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Fig. 9. FTS scans with 100-MHz resolution of the 900-GHz frequency multiplier chain at 830.0 GHz (top left), 891.0 GHz (top right), 918.0 GHz (bottom left), and 950.4 GHz (bottom right). For each scan, the graph is normalized to the peak power that corresponds to the ninth harmonic of the input frequency F at W -band. It can be seen that the chain has an excellent spectral purity for the design band with spurious or undesired harmonic below 27 dB with respect to the main signal. At the edge of the band (950.4 GHz), the sixth harmonic of the last stage tripler starts to be significant with a recorded relative level of 10 dB with respect to the main signal. The cutoff frequency of the second stage is 633 GHz, and thus, at the band edge, this signal starts to leak through the multiplier. Note that the FTS graphs show a strong signal at exactly twice the frequency of the main signal: it is actually an artifact (aliasing) due to the FTS itself. The twelfth harmonic is detected, but is very weak, as expected. The fifteenth harmonic is detected only at 891 and 950.4 GHz and is even weaker than the twelfth harmonic. A line at 1421 GHz is detected in all the scans and cannot be explained. Lines at 187, 214, and 245.5 GHz are detected for, respectively, the RF frequencies of 891, 918, and 950.4 GHz. These lines are at frequencies well below the cutoff frequency of the 900-GHz tripler output waveguide and are, respectively, 11.3, 12.6, and 14.0 times the synthesizer frequency that generates the pump signal at W -band. The synthesizer frequency is one-sixth of F or one fifty-forth of the output frequency. Other signals with unexplained origins are also detected in some scans.

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cascade of two balance triplers designed to suppress unwanted harmonics can actually achieve that goal at about 1 THz. IV. CONCLUSION A broadband solid-state source with more than 1 mW of output power across the 840–900-GHz band has been demonstrated. When cooled to 120 K, the output power increases to a peak of 2 mW. These power levels were made possible by the use of in-phase power combining of frequency multiplier chips. This source will be used to drive a third frequency tripler currently under development for use as the local oscillator of a 2.5–2.7-THz heterodyne receiver. While no systematic reliability study has been done on this source, it should be pointed out that the chips used are based on a space-qualified technology that has been designed for reliability. ACKNOWLEDGMENT The authors wish to thank Dr. P. Siegel, JPL, for many fruitful discussions regarding terahertz sources. The authors also acknowledge the superb waveguide fabrication work by the JPL

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Space Instruments Shop and P. Bruneau for his dedication and unwavering enthusiasm for building high-frequency waveguide components. Helpful discussions and help with the FTS measurements were provided by Dr. J. Pearson, Dr. B. Drouin, and T. Crawford. REFERENCES [1] P. H. Siegel, “Terahertz technology,” IEEE Trans. Microw. Theory Tech., vol. 50, no. 3, pp. 910–928, Mar. 2002. [2] P. H. Siegel, “Terahertz technology in biology and medicine,” IEEE Trans. Microw. Theory Tech., vol. 52, no. 10, pp. 2438–2447, Oct. 2004. [3] D. Mittleman, , D. Mittleman, Ed., “Terahertz imaging,” in Sensing With Terahertz Radiation. Berlin, Germany: Springer-Verlag, 2003, pp. 117–153. [4] D. L. Woolard, E. Brown, M. Pepper, and M. Kemp, “Terahertz frequency sensing and imaging: A time of reckoning future applications?,” Proc. IEEE, vol. 93, no. 10, pp. 1722–1743, Oct. 2005. [5] M. Tonouchi, “Cutting-edge terahertz technology,,” Nature Photon., vol. 1, pp. 97–105, Feb. 2007. [6] H. Ito, F. Nakajima, T. Furuta, and T. Ishibashi, “Continuous THzwave generation using antenna-integrated uni-travelling-carrier photodiodes.,” Semicond. Sci. Technol. 20, pp. S192–S198, 2005.

MAESTRINI et al.: FREQUENCY-MULTIPLIED SOURCE WITH MORE THAN 1 mW OF POWER

[7] B. Sartorius, M. Schlak, D. Stanze, H. Roehle, H. Künzel, D. Schmidt, H.-G. Bach, R. Kunkel, and M. Schell, “Continuous wave terahertz systems exploiting 1.5 m telecom technologies,” Opt. Exp., vol. 17, no. 17, pp. 15001–15007, Aug. 2009. [8] B. S. Williams, “Terahertz quantum-cascade lasers,” Nature Photon., vol. 1, pp. 517–525, 2007. [9] M. A. Belkin, J. A. Fan, S. Hormoz, F. Capasso, S. P. Khanna, M. Lachab, A. G. Davies, and E. H. Linfield, “Terahertz quantum cascade lasers with copper metal-metal waveguides operating up to 178 K,” Opt. Exp., vol. 16, no. 5, pp. 3242–3248, Mar. 2008. [10] J. R. Gao, J. N. Hovenier, Z. Q. Yang, J. J. A. Baselmans, A. Baryshev, M. Hajenius, T. M. Klapwijk, A. J. L. Adam, T. O. Klaassen, B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “Terahertz heterodyne receiver based on a quantum cascade laser and a superconducting bolometer,” Appl. Phys. Lett., vol. 86, 2005, Art. ID 244104. [11] T. W. Crowe, T. C. Grein, R. Zimmermann, and P. Zimmermann, “Progress toward solid-state local oscillators at 1 THz,” IEEE Microw. Guided Wave Lett., vol. 6, no. 5, pp. 207–208, May 1996. [12] A. Maestrini, J. Ward, J. Gill, H. Javadi, E. Schlecht, G. Chattopadhyay, F. Maiwald, N. R. Erickson, and I. Mehdi, “A 1.7 to 1.9 THz local oscillator source,” IEEE Microw. Wireless Compon. Lett., vol. 14, no. 6, pp. 253–255, Jun. 2004. [13] G. Chattopadhyay, E. Schlecht, J. Ward, J. Gill, H. Javadi, F. Maiwald, and I. Mehdi, “An all solid-state broadband frequency multiplier chain at 1500 GHz,” IEEE Trans. Microw. Theory Tech., vol. 52, no. 5, pp. 1538–1547, May 2004. [14] A. Maestrini, J. S. Ward, H. Javadi, C. Tripon-Canseliet, J. Gill, G. Chattopadhyay, E. Schlecht, and I. Mehdi, “Local oscillator chain for 1.55 to 1.75 THz with 100 W peak power,” IEEE Microw. Wireless Compon. Lett., vol. 15, no. 12, pp. 871–873, Dec. 2005. [15] F. Maiwald, E. Schlecht, A. Maestrini, G. Chattopadhyay, J. C. Pearson, D. Pukala, and I. Mehdi, “THz frequency multiplier chains based on planar Schottky diodes,” in Proc. SPIE: Astronom. Telescopes Instrum. Int. Conf., Waikoloa, HI, Aug. 22–28, 2002, vol. 4855, pp. 447–458. [16] J. T. Louhi, A. V. Raisanen, and N. R. Erickson, “Cooled Schottky varactor frequency multipliers at submillimeter wavelengths,” IEEE Trans. Microw. Theory Tech., vol. 41, no. 4, pp. 565–571, Apr. 1993. [17] F. T. Barath et al., “The upper atmosphere research satellite microwave limb sounder instrument,” J. Geophys. Res. Atmospheres, vol. 98, no. D6, pp. 10 751–10 762, Jun. 1993. [18] T. de Graauw, N. Whyborn, E. Caux, T. Phillips, J. Stutzki, A. Tielens, R. Güsten, F. Helmich, W. Luinge, J. Martin-Pintado, J. Pearson, P. Planesas, P. Roelfsema, P. Saraceno, R. Schieder, K. Wildeman, and K. Wafelbakker, “The Herschel-heterodyne instrument for the far-infrared (HIFI),” EAS Pub. Series, vol. 34, pp. 3–20, 2009. [19] P. Hartogh et al., “Submillimeter wave instrument for EJSM,” presented at the Europa Jupiter Syst. Mission Instrum. Workshop, Laurel, MD, Jul. 15–17, 2009 [Online]. Available: http://opfm.jpl.nasa.gov [20] B. Thomas, A. Maestrini, J. Gill, C. Lee, R. Lin, I. Mehdi, and P. de Maagt, “A broadband 835–900 GHz fundamental balanced mixer based on monolithic GaAs membrane Schottky diodes,” IEEE Trans. Microw. Theory Tech., vol. 58, no. 7, pp. 1917–1924, Jul. 2010. [21] R. Appleby and H. B. Wallace, “Standoff detection of weapons and contraband in the 100 GHz to 1 THz region,” IEEE Trans. Antennas Propag., vol. 55, no. 11, pp. 2944–2956, Nov. 2007. [22] K. B. Cooper, R. J. Dengler, G. Chattopadhyay, E. Schlecht, J. Gill, A. Skalare, I. Mehdi, and P. H. Siegel, “A high-resolution imaging radar at 580 GHz,” IEEE Microw. Wireless Compon. Lett., vol. 18, no. 1, pp. 64–66, Jan. 2008. [23] I. Mehdi, J. Ward, A. Maestrini, G. Chattopadhyay, E. Schlecht, B. Thomas, R. Lin, C. Lee, and J. Gill, “Boradband sources in the 1–3 THz range,” in Proc. 34th Int. Infrared, Millimeter, Terahertz Waves Conf., Busan, Korea, Sep. 2009, pp. 1–2. [24] C. Lee, J. Ward, R. Lin, E. Schlecht, G. Chattopadhyay, J. Gill, B. Thomas, A. Maestrini, I. Mehdi, and P. Siegel, “A wafer-level diamond bonding process to improve power handling capability of submillimeter-wave schottky diode frequency multipliers,” in IEEE MTT-S Int. Microw. Symp. Dig., Boston, MA, Jun. 7–12, 2009, pp. 957–960. [25] D. Pukala, L. Samoska, T. Gaier, A. Fung, X. B. Mei, W. Yoshida, J. Lee, J. Uyeda, P. H. Liu, W. R. Deal, V. Radisic, and R. Lai, “Submillimeter-wave InP MMIC amplifiers from 300–345 GHz,” IEEE Microw. Wireless Compon. Lett., vol. 18, no. 1, pp. 61–63, Jan. 2008. [26] F. Schwierz, “An electron mobility model for wurtzite GaN,” Solid State Electron., vol. 48, no. 6, pp. 889–895, Jun. 2005.

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[27] J. V. Siles and J. Grajal, “Capabilities of GaN Schottky multipliers for LO power generation at millimeter-wave bands,” in 19th Int. Space Terahertz Technol. Symp., Apr. 2008, pp. 504–507. [28] A. Maestrini, J. S. Ward, C. Tripon-Canseliet, J. J. Gill, C. Lee, H. Javadi, G. Chattopadhyay, and I. Mehdi, “In-phase power-combined frequency triplers at 300 GHz,” IEEE Microw. Wireless Compon. Lett., vol. 18, no. 3, pp. 218–220, Mar. 2008. [29] A. Maestrini, J. Ward, J. Gill, H. Javadi, E. Schlecht, C. TriponCanseliet, G. Chattopadhyay, and I. Mehdi, “A 540–640-GHz high efficiency four anode frequency tripler,” IEEE Trans. Microw. Theory Tech, vol. 53, no. 9, pp. 2835–284, Sep. 2005. [30] J. Tuovinen and N. R. Erickson, “Analysis of a 170 GHz frequency doubler with an array of planar diodes,” IEEE Trans. Microw. Theory Tech., vol. 43, no. 4, pp. 962–968, Apr. 1995. [31] D. Porterfield, “High-efficiency terahertz frequency triplers,” in IEEE MTT-S Int. Microw. Symp. Dig., Honolulu, HI, Jun. 3–8, 2007, pp. 337–340. [32] N. R. Erickson, “A fast and sensitive submillimeter waveguide power sensor,” in Proc. 10th Int. Space Terahertz Technol. Symp., Charlottesville, VA, 1999, pp. 501–507, available from Erickson Instruments LLC, Amherst, MA.

Alain Maestrini (M’05) received the M.S. degree in telecommunications and electrical engineering from the Ecole Nationale Supérieure des Télécommunications (ENST) de Bretagne, Bretagne, France, in 1993, and the Ph.D. degree in electronics jointly from the Université de Bretagne Occidentale and the Observatoire de Paris, Paris, France, in 1999. From 1993 to 1995, he was an Engineer with the Receiver Group, IRAM 30-m Telescope, Granada, Spain. In 1999, he joined the Submillimeter-Wave Advanced Technology Group, Jet Propulsion Laboratory (JPL), California Institute of Technology, Pasadena, where he was involved with solid-sate terahertz local oscillator development for the heterodyne instrument of the Herschel Space Observatory. In 2002, he returned to the Observatoire de Paris. In 2003, he joined the Laboratoire des Instruments et Systèmes d’Ile de France, Université Pierre et Marie Curie–Paris, Paris, France, as an Assistant Professor in electronics and microwaves. Since January 2008, he has been a member of the Laboratoire d’Etude du Rayonnement et de la Matière en Astrophysique, Université Pierre et Marie Curie and Observatoire de Paris, Paris, France. His current research interests are in the design of integrated millimeter- and submillimeter-wave electronics for radio astronomy and planetary science.

John S. Ward (M’08) received the Ph.D. degree in physics from the California Institute of Technology, Pasadena, in 2002. His doctoral research included the development of a 600–700-GHz superconductor–insulator–superconductor (SIS) receiver that he used to study molecular gas in astronomical sources, as well as the development of software tools for designing and optimizing submillimeter-wave heterodyne receivers. He was a Senior Member of the Engineering Staff with the Jet Propulsion Laboratory (JPL), Pasadena, CA, where he led a team in the development of local oscillators up to 1.9 THz for the heterodyne instrument on the Herschel Space Observatory. He is currently a Senior Principal Engineer with the Raytheon Company, Fort Wayne, IN. John J. Gill received the B.S. and M.S. degrees in mechanical engineering and Ph.D. degree in microelectromechanical systems (MEMS from the University of California at Los Angeles (UCLA), in 1997, 1997, and 2001, respectively. From 1997 to 1998, he was with the Jet Propulsion Laboratory (JPL), Pasadena, CA, where he was involved in the development of the quantum-well infrared photodetector. Following the earning of his doctoral degree, he returned to the JPL where he was involved in the development of microwave devices. In 2001, he became involved with Herschel, a joint flight project with

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the European Space Agency (ESA), where he leads the high-frequency cutting-edge multiplier and mixer device development effort. His research interests include design, fabrication, and characterization of microelectronic devices using conventional integrated circuit (IC), MEMS and nanoelectromechanical systems (NEMS) technologies for space and industrial applications. Choonsup Lee received the B.S. degree in electrical engineering from Kyungpook National University, Daegu, Korea, in 1996, and the M.S. and Ph.D. degrees in electrical engineering and computer science from the Korea Advanced Institute of Science and Technology (KAIST), Daejeon, Korea, in 1998 and 2002, respectively. He is currently a Member of the Technical Staff with the Jet Propulsion Laboratory (JPL), Pasadena, CA. He possesses extensive experiences in the design and characterization of MEMS/nano devices. He is currently involved with GaAs-based frequency sources and mixers in the terahertz region. He has authored or coauthored 17 international journal papers and 32 international conference papers. Bertrand Thomas was born in Suresnes, France, in 1976. He received the M.Sc. degree in radio-communication and microwave engineering from the École Supérieure d’Ingénieurs en Électronique et Électrotechnique (ESIEE)–Paris, Noisy-le-Grand, France, and Université Marne-la-Vallée, Noisy-Champs, France, in 1999, and the Ph.D. degree in astrophysics and space instrumentation from Université Pierre and Marie Curie, Paris-VI, Paris, France and Observatoire de Paris, Paris, France, in 2004. From 1999 to 2001, he was a Civil Servant with the Receiver Group, IRAM 30-m Radio-Telescope, Granada, Spain. From 2005 to 2008, he was a Research Engineer with the Rutherford Appleton Laboratory, Oxfordshire, U.K. In 2008, he joined the Submillimeter-Wave Advanced Technology group, Jet Propulsion Laboratory (JPL), Pasadena, CA, as a National Aeronautics and Space Administration (NASA) Postdoctoral Program Fellow. His current research interests are the design and development of semiconductor devices for terahertz heterodyne receivers, array architectures, and micromachining techniques for planetary science and astrophysics. Robert H. Lin received the B.S. and M.S. degrees in electrical engineering from the California Institute of Technology, Pasadena, in 1997 and 2002, respectively. Since 1997, he has been with the Submillimeter-Wave Advanced Technology Group, Jet Propulsion Laboratory (JPL), Pasadena, CA, where he has helped to assemble, build, and test submillimeter-wave and terahertz amplifiers, multipliers, and mixers for planetary, astrophysics, and earth-based applications.

Goutam Chattopadhyay (S’93–M’99–SM’01) received the B.E. degree in electronics and telecommunication engineering from Bengal Engineering College, Calcutta University, Calcutta, India, in 1987, the M.S. degree in electrical engineering from the University of Virginia, Charlottesville, in 1994, and the Ph.D. degree in electrical engineering from the California Institute of Technology, Pasadena, in 1999. His doctoral dissertation described the development of low-noise dual-polarized and balanced receivers at submillimeter wavelengths. From 1987 to 1992, he was a Design Engineer with the Tata Institute of Fundamental Research (TIFR), Pune, India, where he designed local oscillator systems for the Giant Meterwave Radio Telescope (GMRT) project. In January 1993, he joined the University of Virginia. In September 1994, he joined the California Institute of Technology. He is currently a Senior Member of the Technical Staff with the Jet Propulsion Laboratory (JPL), California Institute of Technology. His research interests include microwave, millimeter-, and submillimeter-wave heterodyne and direct detector receivers, frequency sources and mixers in the terahertz region, antennas, SIS mixer technology, and direct detector bolometer instruments. Dr. Chattopadhyay is a member of the IEEE Microwave Theory and Techniques Society (IEEE MTT-S) and Eta Kappa Nu. He was the recipient of the 1987 Best Undergraduate Gold Medal from the University of Calcutta, the 1992 Jawaharlal Nehru Fellowship Award from the Government of India, the 1997 IEEE MTT-S Graduate Fellowship Award, and the 2001 and 2003 Award of Excellence from the JPL. Imran Mehdi (S’85–M’91–SM’05–F’09) received the three-year Certificate in Letters and Science from Calvin College, Grand Rapids, MI, in 1983, and the B.S.E.E., M.S.E.E., and Ph.D. (E.E.) degrees from The University of Michigan at Ann Arbor, in 1984, 1985, and 1990, respectively. His doctoral dissertation concerned the use of resonant tunneling devices for high-frequency applications. In 1990, he joined t the Jet Propulsion Laboratory (JPL), California Institute of Technology, Pasadena, where his responsibilities included the design and fabrication of low-parasitic planar Schottky diodes for mixers in the terahertz range. This technology was developed for NASA’s earth remote-sensing applications and is being utilized for the Microwave Limb Sounder on the Aura spacecraft. Since 1999, he has led the effort of developing broadband solid-state sources from 200 to 2500 GHz for the Heterodyne Instrument on the Herschel Space Observatory (launched 2009). He is currently a Principal Member of Engineering Staff with the JPL, where he is responsible for the development of terahertz technology for future NASA missions. His research interests include millimeter- and submillimeter-wave devices, high-frequency instrumentation, and heterodyne receiver systems.

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Physics-Based Design and Optimization of Schottky Diode Frequency Multipliers for Terahertz Applications José V. Siles, Member, IEEE, and Jesús Grajal

Abstract—Planar Schottky diode frequency multipliers are by far the most employed devices for local oscillator (LO) power generation at terahertz frequencies. In order to push up to the limit the available LO power at terahertz frequencies, the use of accurate physics-based simulation tools is highly necessary to develop multiplier circuits with the highest performance. This paper investigates the potential capabilities of Schottky multipliers for LO power generation up to 2.4 THz by means of an in-house computer-aided design tool that combines harmonic balance techniques with an accurate physics-based numerical model of the semiconductor device. According to numerical simulation results, a 32- W LO power could be theoretically achieved with a 2.4-THz LO chain at room temperature from a 150-mW -band solid-state LO source. This demonstrates that there is still a broad margin for the improvement of state-of-the-art terahertz LO power sources. Index Terms—Frequency multipliers, harmonic balance, local oscillator (LO) sources, Schottky diode modeling, terahertz technology.

I. INTRODUCTION

HE BIG scientific interest in the terahertz region of the electromagnetic (EM) spectrum, not only in traditional fields like molecular spectroscopy and radioastronomy, but also for terrestrial applications such as security, terrain mapping, pollution monitoring, disease detection, and DNA sequencing among others [1], has greatly encouraged the development of broadband heterodyne receivers up to 2–3 THz. Hence, there is a major need to produce all-solid-state sources able to deliver high enough local oscillator (LO) power to guarantee high-sensitivity detection at submillimeter-wave bands [2]. Multiplier chains formed with cascaded Schottky doublers and/or triplers have been broadly used in the last two decades to upconvert the signal provided by the available solid-state sources at 100–150 GHz [2]–[26]. The provided LO power at room

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Manuscript received October 01, 2009; revised March 16, 2010; accepted March 16, 2010. Date of publication June 03, 2010; date of current version July 14, 2010. This work was supported by the European Space Agency (ESA) under Contract 15293/01/NL/FM-RIDER1 and by the Spanish National Research and Development Program under Project TEC2008-02148 and Project TeraSense (Consolider-Ingenio 2010, CSD2008-00068). The authors are with the Department of Signals, Systems and Radiocommunications, Technical University of Madrid, E.T.S.I. Telecomunicación, Ciudad Universitaria, 28040 Madrid, Spain (e-mail: [email protected]; jesus@gmr. ssr.upm.es). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2010.2050103

temperature by Schottky multipliers ranges from 30–35 mW @ 200 GHz [13] to 1–3 W @ 1800–1900 GHz [24] and 0.1 W @ 2.55 THz [27]. Multiplier performances are substantially better when the devices are cooled: at 120 K, output powers of 100 W at 1645 GHz [22] and 10–20 W at 1900 GHz [2] have been measured. The current generation of frequency multipliers were designed assuming limited available millimeter-wave input power from Gunn oscillators (typically 100–150 mW @ 100 GHz), and therefore, maximizing conversion efficiency was the key design goal for these circuits [26]. The low output power levels obtained beyond 1.5 THz so far are due to the technological difficulty in obtaining precise, uniform, and electrically identical Schottky contacts as a consequence of the small anode dimensions required for high-frequency multipliers [2]. Moreover, the use of simplified analytical electric models for the semiconductor device [19] can also have an impact in the low efficiencies obtained at high frequencies since important physical effects such as the carrier velocity saturation are not considered in the multiplier optimization process. The next generation of Schottky multipliers will take advantage of the high power already available from driver amplifiers based on InP high electron-mobility transistors (HEMTs), providing up to 500 mW in the 70–113-GHz band [26], [28]. Recently, InP-HEMPT power amplifier modules have been demonstrated up to 330 GHz with provided output powers of 10 mW [29]. The latest advances in power amplifier technology, which will soon produce several watts of continuous-wave power above 100 GHz [30], together with recent progress in chip fabrication technologies [2] enable the possibility to increase the output frequency to at least 3 THz [26]. The use of power-combining strategies consisting in using several chips on a single waveguide multiplier block will be essential to handle such amount of LO power [25], [31]. Furthermore, Schottky diodes based on wide-bandgap semiconductors might be employed for the first multiplication stages of terahertz LO chains in order to increase its power-handling capabilities. For example, GaN Schottky multipliers featuring two or four diodes could easily handle a 1-W input power at 100 GHz with conversion efficiencies around a 25% lower than those achieved with GaAs Schottky diodes [32]. The high operation temperature of Schottky multipliers derived from the increased input power can be greatly reduced by using substrates with high-thermal conductivity like SiC or diamond [33]. Thus, the use of accurate physical device models with adequate boundary conditions able to account for the limiting physical mechanisms occurring at high frequencies will be necessary

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Fig. 1. General circuit scheme of the multiplier CAD tool.

to develop terahertz LO sources with the best possible performance [34]. In this context, this work investigates the performance limit of Schottky multipliers for LO power generation up to terahertz frequencies by means of a computer-aided design (CAD) tool that combines an accurate physics-based numerical model of the semiconductor device with an external circuit simulator by means of harmonic-balance techniques [35]. The key aspect of this philosophy lies in the possibility to perform a simultaneous optimization of the external circuit and the device structure in a self-consistent way without either equivalent circuits or empirical adjustment parameters. It will be shown that LO power levels up to 32 W @ 2.4 THz could be theoretically achieved at room temperature with the current generation of Schottky multipliers (150 mW of input power @ 100 GHz) by means of a proper optimization of the different design parameters, in particular the structure of the diodes employed for the high-frequency multiplication stages. A brief description of our simulation tool is provided in Section II. The viability of this tool for the design of Schottky diode multipliers is shown in Section III through the comparison between simulations and measurement results for a number of multiplier circuits designed and fabricated at the National Astronautical and Space Administration’s (NASA)’s Jet Propulsion Laboratory (JPL), Pasadena, CA, in the frame of the Herschel project. In Section IV, we present the design and optimization of a 2.4-THz LO chain with two different configurations: X2X2X2X3 and X2X2X3X2. The goal of this section is to study the maximum achievable efficiency at 2.4 THz by a proper selection of all the design parameters. The results are compared with state-of-the-art multipliers in order to demonstrate that there is still a margin for improvement regarding LO power generation at terahertz frequencies. To conclude, future challenges for terahertz CAD tools are outlined in Section V. II. DESCRIPTION OF THE SIMULATION TOOL The multiplier design tool employed herein (see Fig. 1) integrates harmonic-balance techniques together with an accurate physics-based 1-D drift-diffusion (DD) numerical device simulator [36] and a self-consistent incorporation of image-force barrier lowering and tunneling transport unlike other models presented in the literature [37]–[39]. This philosophy accounts for the device-circuit interaction and provides another degree of freedom to improve the circuit performance since it can be designed from both a device and circuit point-of-view [35]. Furthermore, we have recently introduced an improved DD model with an enhanced definition of the recombination velocity and mobility-field characteristics in the flat-band regime in order

Fig. 2. Comparison between MC and DD results for the RF current response of a Schottky diode to a sinusoidal stimulus at 1200 GHz). The epilayer thickness is 90 nm.

to extend the validity of traditional DD semiconductor models to submicrometer devices [40]. For example, electron velocity overshoot is allowed with the improved DD model [40]. The simulator also features and efficient algorithm to obtain the optimum embedding impedances for the multiplier circuit. Impedances at the input frequency are automatically matched for each input power in all the simulations performed during the design process. Likewise, the output impedance (second harmonic for doublers and third harmonic for triplers) is optimized for the considered input power. Parasitic elements may be introduced in the analysis by means of a parasitics network, as shown in Fig. 1. Furthermore, it is possible to account for the most important limiting mechanisms of Schottky diodes at high frequency and high power operation, which are determined by forward and reverse conduction, and by the carrier velocity saturation [35]. Recently, we have successfully extended our CAD tool to mixer design using appropriate multitone harmonic-balance techniques [40], [41]. The current version of the simulator also offers the possibility to design frequency multipliers based on GaN Schottky diodes [32] and heterostructure barrier varactors (HBVs) [42]. Apart from the diode structure and barrier height, the only input data for our numerical DD model is the mobility-field characteristics of the material, which can be easily found in the literature [43]. This represents a clear advantage over analytical device models based on equivalent circuits generally included in commercial simulators such as Agilent Technologies’ Advanced Design System (ADS), where some empirical adjustments are often necessary for submillimeter-wave circuit design [44]. Note that these models assume that the capacitance and current are function of the present value of the internal voltage. For Schottky diodes, this quasi-static approach has been proved to be valid only up to a few hundred gigahertz [45]. III. COMPARISON BETWEEN EXPERIMENTAL DATA AND PHYSICS-BASED SIMULATIONS A comparison between experimental data and physics-based simulations was already presented in previous publications by comparing simulated device and circuit characteristics at dc with experimental results obtained for a number of Schottky diodes fabricated at the Technical University of Darmstadt, Darmstadt, Germany [35]. Some intial RF comparison results

SILES AND GRAJAL: PHYSICS-BASED DESIGN AND OPTIMIZATION OF SCHOTTKY DIODE FREQUENCY MULTIPLIERS FOR TERAHERTZ APPLICATIONS

TABLE I PERFORMANCE COMPARISON BETWEEN MEASUREMENTS AND SIMULATION RESULTS FROM JPL MULTIPLIER CHAINS AT ROOM TEMPERATURE (T DATA FROM SIMULATIONS ARE REFERRED TO A SINGLE-DIODE EQUIVALENT CIRCUIT. MEASUREMENT DATA OBTAINED FROM [2], [7]–[9], [12], [13], AND [19] (*ANODE AREA FOR THE 600-GHz TRIPLER HAS BEEN ASSUMED EQUAL TO THAT OF THE 400-GHz DOUBLER SINCE ITS VALUE IS NOT PROVIDED IN THE LITERATURE)

up to 200 GHz were also shown in [35] for doubler circuits fabricated at the University of Virginia, Charlottesville. The enhanced DD model recently included in our simulator has been tested up to 2.4 THz (output frequency) by means of a Monte Carlo (MC) simulator developed at the University of Rome “Tor Vergata,” Rome, Italy [46] for a wide range of epilayer thicknesses, doping levels and operation frequencies. As shown in Fig. 2, both the MC and DD models predict very similar current responses for an n-doped GaAs Schottky diode pumped with a sinusoidal voltage excitation at 1.2 THz. This is a very good representative case because it analyzes the response of a very short device with a high doping level to a voltage excitation approximately covering the whole range between breakdown and forward conduction. In the last decade, Schottky diode technology has reached maturity, and for the first time, a large amount of data can be found in the literature for a wide range of operation frequencies regarding Schottky frequency doublers and triplers fabricated with similar technology and foundry. These data enable us to demonstrate that our CAD tool can be trusted to design real multipliers up to terahertz frequencies. For this purpose, we present in this section an extensive comparison between physics-based simulations and measurement results corresponding to different doubler and triplers designed and fabricated at JPL in the frame of the Herschel project. For comparative purposes, real design parameter values provided in literature for JPL circuits, such as nominal input power, , and epilayer dopings zero-voltage junction capacitance have been employed in the simulations. In some cases, employed in the numerical simulations have the anode areas been slightly modified with respect to the nominal values provided in the literature so that the zero-voltage junction capacitances for both measurement and simulations coincide. In those cases where the junction capacitance is not provided, nominal anode areas have been employed. The data found in the literature describing the characteristics of JPL multipliers and the corresponding parameters considered for the physics-based numerical simulations are compiled in Table I. Note that series

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= 300 K).

values are given only for the simulation results resistance due to the lack of information in the literature with regard to the measured series resistance of the diodes.

A. Results for 200–1.5-GHz Doublers Fig. 3(a) presents simulations and measurements for a 200-GHz doubler at room temperature. This doubler consists of a balanced structure featuring a six-diode array with a 150-mW total input power [7], [8]. Fig. 3(b) displays the results for a 400-GHz doubler at room temperature designed in a balanced configuration of four diodes [8]. Fig. 3(c) and (d) shows, respectively, the results for a two-diode balanced 800-GHz doubler [9] and a 1500-GHz doubler [13]. For the physics-based simulation of these doublers, some circuit and device characteristics such as epitaxial layer thickness and bias voltage have been optimized to obtain the of the multiplier since they are not maximum efficiency provided in the literature (except for the 1500-GHz doubler [13]). Besides, an n -layer doping of 2 10 cm has been assumed. Output impedances have been optimized for the nominal freand have been kept constant in quency and input power the analyzed frequency band. Regarding the impedance at , two cases have been simulated. In the first one, this impedance is matched for each frequency so efficiency and output power do not experience great variation with frequency. In the second has been fixed to the optimum value case, the impedance at at the nominal frequency and output power. Obviously, there is a better agreement between measurements and simulations for the second situation. Except for the 200-GHz doubler, the input power for measurements is provided by the previous multiplication stage so it is not constant throughout the input bandwidth. However, a constant input power equal to that obtained at the nominal frequency from the previous stage was considered in the simulations. Constant input powers in simulations together

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Fig. 4. Comparison between experimental results for a 600-GHz tripler at 295 K (data reprinted from [19]) and physics-based simulations performed in this work (dashed–dotted color lines (in online version) assume perfect input coupling, dashed color lines (in online version) consider a 85% input coupling due to waveguide loss [19]).

with possible impedance mismatches between stages and waveguide losses can justify the observed discrepancies. B. Results for a 540–640-GHz Tripler

Fig. 3. Comparison between experimental data and physics-based simulations at 300 K. (a) 200-GHz doubler [8]. (b) 400-GHz doubler [8]. (c) 800-GHz doubler [9]. (d) 1500-GHz doubler [13].

Contrary to the previous comparisons, where only a few data from the real structure of the diodes were available in the literature, in this case all the characteristics of the 540–640-GHz tripler considered here can be found in [19]: 0.85-V barrier height, 6- m anode area, 500-nm epilayer thickness, 1 10 cm epilayer doping, 1.2- m n -layer thickness, 7 10 cm n -layer doping, 6 fF zero-voltage junction capacitance at dc and 295-K temperature. The tests of this tripler were carried out by tuning the bias voltage for each analyzed frequency within the band of 540–640 GHz. The bias voltage for each case is not provided in [19], but is indicated to be in the range from 1 to 12 V in total for the four diodes. It is also specified that a nominal bias voltage of 9 V was considered for the design. Hence, this value was employed in the numerical simulations for all analyzed frequencies within the considered bandwidth. Furthermore, a constant input power of 24 mW (6 mW per anode) has been assumed in the simulations, which is approximately equal to that provided for the previous 200-GHz doubler used in [19] to pump the 600-GHz tripler. The impedances at the fundamental frequency and second and third harmonics have been optimized at 600 GHz (output frequency) in the simulations. In practice, the input power provided by the 200-GHz doubler is not constant over the considered bandwidth, and also, possible mismatches in the interconnection of the two multiplier stages can lead to variations in the input power at 200 GHz. The results of the comparison between measurements and simulations are shown in Fig. 4. The key aspect of these results lies in the fact that our simulator predicts very well the tripler efficiency with any assumption or empirical adjustment. In contrast, the analytical Schottky diode model employed in [19] for circuit simulation necessitates an empirical adjustment of the series resistance to well determust be calmine the efficiency. The appropriate value of , which has to be derived culated from the product empirically from previous fabrication runs involving the same foundry technology [19].

SILES AND GRAJAL: PHYSICS-BASED DESIGN AND OPTIMIZATION OF SCHOTTKY DIODE FREQUENCY MULTIPLIERS FOR TERAHERTZ APPLICATIONS

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TABLE II RESULTS OF THE OPTIMIZATION OF A 200-GHz SCHOTTKY DOUBLER FOR DIFFERENT EPILAYER DOPING LEVELS AT 300 K (DATA REFERRED TO A SINGLE-DIODE EQUIVALENT CIRCUIT)

N = 3 10 cm (Z[3f ]) at 300 K.

Fig. 6. Sensitivity of the 200-GHz doubler ( impedance at second and third harmonic

(Z[2f ])

N = 1 10

Fig. 5. Bias optimization for a 1 cm epilayer doping at 300 K. Efficiency, output power, and dc current versus input power.

1

) to

N = 3 10

Fig. 7. Final results for the 200-GHz doubler design ( 1 cm ). Performance as a function of the temperature of the active region of the device (self-heating is not considered).

C. Final Remarks Results presented here show that our simulator provides very good results for a number of Schottky doublers and triplers designed by JPL for a big margin of operation frequencies ranging from 200 up to 1500 GHz. For the analyzed doublers, there is some uncertainty in the provided comparisons because some parameters were not provided in the literature and it was necessary to make some assumptions. Moreover, the specific Schottky diode technology and geometry employed in the real circuit might result in different values for the series resistances and zero junction capacitances with regard to those calculated with our physics-based simulator. Different foundry runs, presence of parasitics elements, waveguide losses, and impedance mismatches also add some uncertainty to the comparisons presented in this section. Possible parasitics elements have not been either considered in simulations herein since they must be derived from either measurements or EM simulation of the actual device geometry. Note that under no circumstances has our model been updated to account for the specific JPL diode technology. Nevertheless, the most remarkable aspect from these comparisons is the good agreement between simulations and experimental results in spite of the fact that the simulated results have to be evaluated within a certain margin of error due to these aspects. This is demonstrated for the 540–640-GHz tripler where

Fig. 8. Analyzed multiplication chains.

all the data on the structure of the employed diodes was available in the literature. In these case, the estimated value for circuit losses provided in [19] has allowed us to provide lower and upper limits for the simulated tripler performance. IV. PHYSICS-BASED OPTIMIZATION OF LO CHAINS UP TO TERAHERTZ FREQUENCIES All the design parameters play an important role during the optimization process and cannot be assumed independent since a variation in one parameter has an impact on the optimum values for the rest of parameters. Contrarily to other design methodologies where the optimization process is usually based on physical reasoning and previous empirical results [34], our method allows a self-consistent and concurrent optimization of all the design parameters (matching impedances, bias voltage,

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TABLE III SUMMARY OF OPTIMIZED MULTIPLIERS UP TO 2.4 THz AT ROOM TEMPERATURE (T

input power, epilayer thickness and doping, anode area, etc.). Thus, the theoretical limits of the Schottky technology for LO power generation can be well investigated. A. Design and Optimization Procedure The optimization of Schottky frequency multipliers is sometimes controlled by technological aspects (limited dimensions for the anode area, a fixed epilayer thickness and/or doping, ) or other design constraints (available input power, frequency bandwidth, ). In these particular cases, the design procedure has to be adapted to these design constraints. For example, it would be possible to maximize the output power at the expense of the conversion efficiency when enough input power is available. Nevertheless, the design process described here is general and will consist in finding the best achievable performance for a Schottky-based multiplier given a fixed input power. Primarily, a set of different doping levels for the device epilayer is defined. For each doping level, an optimization of the bias voltage is performed. At low frequencies, where enough input power is usually available, the starting point for the bias is and forward conducfixed halfway between breakdown tion. Therefore, greater capacitance modulation and efficiency are achieved. For high-frequency designs, when the available input power is not enough to guarantee a voltage swing from breakdown to forward conduction, better efficiencies will be obtained for bias voltages around 0 V due to the stronger nonlinearity of the diode capacitance around this operation point. Besides, bias voltage has an impact on the thickness of the space charge region, and thereby, on the optimum thickness for the epilayer. Hence, for a given doping, the optimization of the bias

= 300 K) ASSUMING A 150-mW INPUT POWER AT W -BAND

voltage and the epilayer thickness must be carried out simultaneously. Finally, the anode area is modified in order to locate the peak of efficiency at the desired input power per diode. Note that the number of diodes in the multiplier is connected to the power-handling capabilities of an individual diode. The larger the number of diodes, the lower the input power to be handled by each diode. However, a high number of diodes may not be affordable from a technological point of view due to the reduced dimensions of the transmission waveguide and the difficulty of manufacturing electrically identical Schottky diodes. To exemplify this procedure, the results of the design of a 200-GHz doubler are summarized in Table II, where the optimum values for the design parameters are shown as a function of the epitaxial layer doping. For this doubler, a six-diode balanced configuration has been considered with a total available input power of 150 mW. This topology has been widely used by JPL for the the first stages of the HIFI LO chains [7], [8], [13]. The simulated dc characteristics of the optimized devices (zero-voltage junction capacitance, series resistance, and breakdown voltage) are also compiled in Table II. In all the cases, a 2 10 cm n -layer doping has been considered. These simulated performances have to be evaluated together with the series resistance of the devices since multiplier efficiency depends on the series resistance of the Schottky diodes. The lower the series resistance, the higher the efficiency. The minimum series resistance of a specific diode is affected by the technological process: Quality of ohmic contacts, possibility to use very thin and highly doped n -layers, etc. Several conclusions can be extracted from the analysis of these results. On the one hand, the optimum thickness of the

SILES AND GRAJAL: PHYSICS-BASED DESIGN AND OPTIMIZATION OF SCHOTTKY DIODE FREQUENCY MULTIPLIERS FOR TERAHERTZ APPLICATIONS

epilayer becomes shorter as the doping level is increased due to the fact that the space charge region is inversely proportional to the doping level [43]. Note that epitaxial layer must be fully depleted in order to minimize the series resistance. However, if the epilayer is excessively short, physical simulations predict a decrease in the multiplier efficiency because the thickness of the depletion region is limited by the n -layer resulting in a lower capacitance modulation [47]. For doublers, the best conversion efficiencies are obtained when full depletion occurs for the maximum voltage swing in the diode, whenever enough input power is available. For triplers, the epilayer thickness should be selected so that it is fully depleted at the bias voltage in order to favor signal generation at the third harmonic [48]. On the other hand, the restrictions imposed by the breakdown voltage lead us to use lower bias voltages as the doping is increased. Another important aspect of the design process is to guarantee a safe operation regime for the diodes. This is illustrated in cm epiFig. 5 for the 200-GHz doubler with a layer doping. The peak efficiencies are analogous for the three bias voltages analyzed in spite of the shift in the curves towards higher input power values as bias voltage becomes more negaV and 6 V, breakdown causes tive. However, for a noticeable increase in the reverse current for an input power of V, there around 14 and 15 dBm, respectively. For is also an important increase in the dc current beyond 18 dBm V, both breakdown due to forward conduction. For and forward conduction are approximately reached for the same input power (16–17 dBm). Hence, a 5-V bias voltage is the most adequate option to guarantee a safe operation of the diodes in this particular case. With these data from physical simulations, the designer can take the most appropriate decision considering technological aspects as well. For example, the device is most resistive for bias voltages closer to forward conduction so better bandwidths may be achieved [47], [49]. However, there is a major risk for burnout problems since an excessive forward or reverse current can cause the GaAs/metal contact to degrade [50]. Note that, with these data provided by simulations and knowledge on the maximum forward current supported by the Schottky contacts, it would be possible to estimate the maximum power that can be handled by the designed device. Other design aspects as the influence of the impedance at the third harmonic for doublers, impedance at second harmonic for triplers, and the effect of the temperature can also be studied once the structure of the Schottky diode has been optimized. To exemplify this, Fig. 6 analyzes the sensitivity of the 200-GHz doubler to the input and output impedances. The analysis of the impact of possible mismatches in the real circuit is important since a very sensitive circuit may result in the impossibility of designing broadband matching networks. The effect of the device temperature on the 200-GHz multiplier performance is presented in Fig. 7. B. From Physics-Based Simulations to Multiplier Circuits Synthesis Today’s most widely employed balanced topologies for waveguide frequency multipliers at terahertz frequencies were

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Fig. 9. Efficiency improvement due to the optimization of 2.4-THz multiplier chains at 300 K. results are compiled in Table III (full optimized), Table III (area optimization), and Table I (reference data).

proposed by Erickson et al. [7] and Erickson [51]. For doublers, the diodes can be placed either in the input waveguide or in the output waveguide. In the equivalent electrical circuit of the former configuration, the two diode branches are antiseries connected at the input frequency and parallel connected at the output frequency [47]. In the latter case, the diodes are antiparallel connected at the input and series connected at the output [47]. For triplers, the diodes are placed within the channel waveguide between the input and output waveguides. In the equivalent circuit for triplers, the two diode branches are antiparallel connected for both input and output [47]. In this work, we have considered single-anode multiplier structures for the design and optimization process in order to speed up the time of simulation (see Fig. 1). Therefore, unless otherwise is specified, the obtained optimum impedances at the different harmonics are those seen from the diode terminals assuming a single-diode structure. These impedances can be easily converted to the real impedances of the desired topology by using the relations described in [47]. Once the optimum parameters for the Schottky diode have been determined, the embedding linear circuit has to be synthesized. This involves the definition and optimization of both the 3-D structure of the waveguide diode cell and the input and output matching networks. For this task, the method employed by most research groups consists of an iterative process involving commercial circuit simulations (e.g., with Agilent’s ADS) and 3-D EM simulations [e.g., with Ansoft Technologies’ High Frequency Structure Simulator (HFSS)] in order to obtain the desired efficiency and bandwidth. This method is described in [19]. The use of physics-based simulators like ours can greatly reduce the necessary iterations to converge to the final solution by a proper initial calculation of the optimum parameters of the semiconductor device. C. Potential Improvement of State-of-the-Art Multipliers The aim of this section is to investigate the theoretical limits of terahertz LO chains based on GaAs Schottky diode multipliers (see Fig. 8) by means of the design process described before. The optimization of each multiplier stage has been performed for the nominal frequencies indicated in Fig. 8. The embedding input and output impedances for each multiplier have

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Fig. 10. Performance comparison between room-temperature state-of-the-art measured LO chains (data from [7]–[10], [12], [13], [15], [16], [19], [22], [23], [26], and [27]) and simulation results in this work considering 150-mW input power at 100 GHz. (a) Efficiency (%). (b) Output power (in milliwatts).

been optimized for the nominal input power, which is the provided by the previous stage. A total input power of 150 mW at 100 GHz has been considered. Asastartingpoint,thecharacteristicsoftheSchottkyfrequency multipliers listed in Table I were considered as reference. Since possible losses or impedance mismatches between stages have not been taken into account, a perfect power coupling from the previous stage has been assumed for each multiplier. Hence, as a first step, the anode areas indicated in Table I were optimized so that the maximum efficiency of each stage is located at the available input power (output power from the previous stage). Results are summarized in Table III (area optimization case). The next step consists in performing a concurrent optimization of all the design parameters in order to analyze the performance limits of the analyzed LO chains. The results of the optimization process and the final characteristics of each multiplier stage are compiled in Table III (full optimization case). Fig. 9 compares the performance of the full optimized LO chain with those results corresponding to the preliminary case in which only the anode area was optimized. The most important conclusion that can be extracted from these results is the importance of a proper and joint optimization of all the design parameters in order to design Schottky multipliers with the highest performance. It can be seen that the global efficiency increases from 0.015% to 0.027% when a full optimization of the LO chain is carried out. A comparison between two possible alternatives for LO power generation at 2.4 THz (a X2X2X2X3 or X2X2X3X2 chain) is shown in Fig. 9. Note that the best performance is obtained for the former case, which exhibits an efficiency nearly two times higher than the latter. The possibility to study in advance the most appropriate configuration for LO power generation at a certain frequency is another interesting aspect of using these kinds of simulators. In order to have a good insight into these results, Fig. 10(a) and (b) shows a global perspective of the numerical simulation results corresponding to the optimized LO chains presented in this section and state-of-the-art efficiencies and output power levels from measured GaAs Schottky multipliers (results based on power-combining techniques are not included).

At the lower frequency range, the maximum efficiencies predicted by simulations after a full optimization of all the design parameters do not experience a significant improvement with regards to the experimental results. In fact, below 800 GHz, the , which deoutput power is approximately proportional to fines the theoretical limit for the performance of Schottky multipliers. Beyond 800 GHz, output power cannot follow this slope since performance of Schottky multipliers is limited by the carrier velocity saturation [52]. Nevertheless, simulation results corresponding to the optimized multiplier stages presented in this work predict slopes in the output power nearly proportional . Consequently, there is still an important margin for the to improvement of multipliers efficiency at the higher frequency range since measured output power beyond 1 THz drops at rates . higher than According to simulation results, a 32- W output power could be theoretically achieved from a 150-mW -band solid-state reference LO source at room temperature. Obviously, the predicted output power may be lower in practice due to possible mismatches between stages, waveguide losses, etc. However, with knowledge on these factors, the different multiplication stages might be re-optimized with our simulator in order to maximize the multiplier efficiency for the resultant effective power delivered to the diodes in the presence of these additional losses. Besides, losses may be compensated with the higher LO power levels now available at -band. V. FUTURE CHALLENGES Despite the good accuracy of our millimeter- and submillimeter-wave circuit simulator shown in this work, more efforts are still necessary towards global terahertz CAD tools with the capability to simulate both the semiconductor devices and the passive elements/circuitry in a coupled and self-consistent way. Physical models for different devices (Schottky diodes, HBV, HEB, SIS, etc.) that account for thermal and noise aspects together with a full-wave 3-D EM analysis of the complete structure must be included. In this context, new features are currently being added to improve the capabilities of our CAD tool. As mentioned in Section II, we have recently improved our DD model to well reproduce the device behavior under flat-band conditions. The

SILES AND GRAJAL: PHYSICS-BASED DESIGN AND OPTIMIZATION OF SCHOTTKY DIODE FREQUENCY MULTIPLIERS FOR TERAHERTZ APPLICATIONS

use of MC simulators has been essential for this task [40]. MC simulation is also being employed as well to investigate the inclusion of noise analysis in our CAD tool since noise is inherent to MC semiconductor models [53]. A 2-D DD model for Schottky diodes is already available [54] and will be included soon in the harmonic-balance simulator. The use of 2-D models make it possible to better account for the real geometry of the device within the harmonic-balance analysis, but it increases considerably the time of computation. Self-heating may also be a significant performance limiting factor for frequency multipliers and mixers. In this sense, we are working on the inclusion of electrothermal models (physical semiconductor models coupled with heat transport equation) in order to accurately predict the actual temperature of the junctions [55]. Although the results presented in this work assume identical diodes, our simulator offers the possibility to simulate multianode balanced structures in parallel/antiparallel configuration (support for series connection will be added soon). The structure of each diode can be defined separately in order to account for possible diode imbalances that may appear during manufacturing. The possibility to perform a more accurate analysis, consisting in introducing in our simulator the -parameter matrixes obtained from EM simulation of the real embedding circuit, is now being added. VI. CONCLUSION This work has focused on the physics-based optimization of millimeter- and submillimeter-wave frequency multipliers by means of a numerical CAD tool that performs a joint optimization of both the external circuit and the internal structure of the semiconductor device. The design method employed herein is self-consistent and no empirical adjustment is necessary for the device model. The presented results predict that there is still and important margin for performance improvement of Schottky multipliers beyond 1 THz. This improvement might be possible in practice by combining the potential of a physics-based CAD tool like the one employed in this work together with commercial simulators for matching network synthesis and the very precise nanofabrication processes now available. Moreover, simulation results exhibits a very good agreement with measurements results for a number of Schottky multipliers designed and fabricated by JPL in the frame of the Herschel project. This demonstrates that our simulator might be reliably employed for high-frequency circuit design. REFERENCES [1] P. H. Siegel, “THz technology: An overview,” Int. J. High Speed Electron. Syst., vol. 13, no. 2, pp. 351–394, 2003. [2] I. Mehdi, G. Chattopadhyay, E. Schlecht, J. Ward, J. Gill, F. Maiwald, and A. Maestrini, “Terahertz multiplier circuits,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2006, pp. 341–344. [3] A. Maestrini, D. Pukala, F. Maiwald, E. Schlecht, G. Chattopadhyay, and I. Mehdi, “Cryogenic operation of GaAs based multiplier chains to 400 GHz,” in 8th Int. Terahertz Conf., Sep. 2000, 4 pp. [4] A. Maestrini, J. Bruston, D. Pukala, S. Martin, and I. Mehdi, “Performance of a 1.2 THz frequency tripler using GaAs frameless membrane monolithic circuit,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2001, pp. 1657–1660. [5] E. Schlecht, G. Chattopadhyay, A. Maestrini, S. Martin, J. Bruston, and I. Mehdi, “200, 400 and 800 GHz Schottky diode “substrateless” multipliers: Design and results,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2001, pp. 1649–1652.

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[6] S. Martin, B. Nakamura, A. Fung, P. Smith, J. Bruston, A. Maestrini, F. Maiwald, P. Siegel, E. Schlecht, and I. Mehdi, “Fabrication of 200 to 2700 GHz multiplier devices using GaAs and metal membranes,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2001, pp. 1641–1644. [7] N. Erickson, G. Narayanan, R. Grosslein, G. Chattopadhyay, A. Maestrini, and E. Schlecht, “1500 GHz tunable source using cascaded planar frequency doublers,” in Proc. 13th Int. Space Terahertz Technol. Symp., Mar. 2002, pp. 177–185. [8] F. Maiwald, E. Schlecht, A. Maestrini, G. Chattopadhyay, J. Pearson, D. Pukala, and I. Mehdi, “THz frequency multiplier chains based on planar Schottky diodes,” in Proc. SPIE Int. Astronom. Telescopes Instrum. Confe., Aug. 2002, vol. 4855, pp. 447–458. [9] G. Chattopadhyay, E. Schlecht, J. Gill, S. Martin, A. Maestrini, D. Pukala, F. Maiwald, and I. Mehdi, “A broadband 800 GHz Schottky balanced doubler,” IEEE Microw. Wireless Compon. Lett., vol. 12, no. 4, pp. 117–118, Apr. 2002. [10] J. Ward, F. Maiwald, E. Schlecht, A. Maestrini, G. Chattopadhyay, J. Gill, and I. Mehdi, “1400–1900 GHz local oscillators for the Herschel space observatory,” in Proc. 14th Int. Space Terahertz Technol. Symp., Apr. 2003, pp. 94–101. [11] A. Maestrini, J. Ward, J. G. , G. Chattopadhyay, F. Maiwald, K. Ellis, H. Javadi, and I. Mehdi, “A planar-diode frequency tripler at 1.9 THz,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2003, pp. 747–750. [12] J. Ward, G. Chattopadhyay, A. Maestrini, E. Schlecht, J. Gill, H. Javadi, D. Pukala, F. Maiwald, and I. Mehdi, “Tunable all-solid-state local local oscillators to 1900 GHz,” in Proc. 15th Int. Space Terahertz Technol. Symp., Apr. 2004, pp. 120–127. [13] G. Chattopadhyay, E. Schlecht, J. Ward, J. Gill, H. Javadi, F. Maiwald, and I. Mehdi, “An all-solid-state broad-band frequency multiplier chain at 1500 GHz,” IEEE Trans. Microw. Theory Tech., vol. 52, no. 5, pp. 1538–1547, May 2004. [14] A. Maestrini, C. Tripon-Canseliet, and I. Mehdi, “Design of a wideband 6-anode frequency tripler at 300 GHz with optimum balance,” in Joint 29th Int. Infrared Milimeter Waves Conf. /12th Int. Terahertz Electron. Conf., Oct. 2004, pp. 203–204. [15] J. Ward, E. Schlecht, G. Chattopadhyay, A. Maestrini, J. Gill, F. Maiwald, H. Javadi, and I. Mehdi, “Capability of THz sources based on Schottky diode frequency multiplier chains,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2004, pp. 1587–1590. [16] A. Maestrini, J. Ward, J. Gill, H. Javadi, E. Schlecht, G. Chattopadhyay, F. Maiwald, N. R. Erickson, and I. Mehdi, “A 1.7-1.9 THz local oscillator source,” IEEE Microw. Wireless Compon. Lett., vol. 14, no. 6, pp. 253–255, Jun. 2004. [17] C. Tripon-Canseliet, A. Maestrini, and I. Mehdi, “Design of a wideband 900 GHz balanced frequency tripler for radioastronomy,” in Joint 29th Int. Infrared Milimeter Waves Conf./12th Int. Terahertz Electron. Conf., Oct. 2004, pp. 583–584. [18] J. Ward, E. Schlecht, G. Chattopadhyay, H. Javadi, J. Gill, I. Mehdi, A. Maestrini, and C. Tripon-Canseliet, “Local oscillators from 1.4 to 1.9 THz,” in Proc. 16th Int. Space Terahertz Technol. Symp., May 2005, pp. 374–377. [19] A. Maestrini, J. S. Ward, J. J. Gill, H. S. Javadi, E. Schlecht, C. TriponCanseliet, G. Chattopadhyay, and I. Mehdi, “A 540–640 GHz highefficiency four-anode frequency tripler,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 9, pp. 2835–2843, Sep. 2005. [20] T. W. Crowe, W. L. Bishop, D. W. Porterfield, J. L. Hesler, and R. M. WeikleII, “Opening the terahertz window with integrated diode circuits,” IEEE J. Solid-State Circuits, vol. 40, no. 10, pp. 2104–2110, Oct. 2005. [21] G. Chattopadhyay, “Heterodyne arrays at submillimeter wavelengths,” presented at the 28th Gen. Assembly URSI, Oct. 2005. [22] A. Maestrini, J. S. Ward, H. Javadi, C. Tripon-Canseliet, J. Gill, G. Chattopadhyay, E. Schlecht, and I. Mehdi, “Local oscillator chain for 1.55 to 1.75 THz with 100-w peak power,” IEEE Microw. Wireless Compon. Lett., vol. 15, no. 12, pp. 871–873, Dec. 2005. [23] D. W. Porterfield, “High-efficiency terahertz frequency triplers,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2007, pp. 337–340. [24] T. W. Crowe, J. L. Hesler, D. W. Porterfield, D. S. Kurtz, and K. Hui, “Development of multiplier based sources for up to 2 THz,” in Joint 32nd Int. Infrared Millimeter-Waves Conf. /15th Int. Terahertz Electron. Conf., Sep. 2007, pp. 621–622. [25] A. Maestrini, J. Ward, C. Tripon-Canseliet, J. Gill, C. Lee, H. Javadi, G. Chattopadhyay, and I. Mehdi, “In-phase power-combined frequency triplers at 300 GHz,” IEEE Microw. Wireless Compon. Lett., vol. 18, no. 3, pp. 218–220, Mar. 2008.

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[26] J. S. Ward, G. Chattopadhyay, J. Gill, H. Javadi, C. Lee, R. Lin, A. Maestrini, F. Maiwald, I. Mehdi, E. Schlecht, and P. Siegel, “Tunable broadband frequency-multiplied terahertz sources,” in 33rd Int. Infrared, Millimeter, Terahertz Waves Conf., Sep. 2008, 3 pp. [27] F. Maiwald, S. Martin, J. Bruston, A. Maestrini, T. Crawford, and P. Siegel, “2.7 THz tripler using monolithic membrane diodes,” in IEEE MTT-S Int. Microw. Symp. Dig., 2001, vol. 3, pp. 1637–1640. [28] L. Samoska, “Towards terahertz MMIC amplifiers: Present status and trends,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2006, pp. 333–336. [29] R. Lai, W. R. Deal, V. Radisic, K. Leong, X. B. Mei, S. Sarkozy, T. Gaier, L. Samoska, and A. Fung, “Sub-MMW active integrated circuits based on 35 nm InP HEMT technology,” in IEEE Int. Indium Phosphide Rel. Mater. Conf., 2009, pp. 185–187. [30] M. Micovic, A. Kurdoghlian, P. Hashimoto, M. Hu, M. Antcliffe, P. J. Willadsen, W. S. Wong, R. Bowen, I. Milosavljevic, A. Schmitz, M. Wetxel, and D. H. Chow, “GaN HFET for -band power applications,” in Int. Electron Devices Meeting, Dec. 2006, pp. 1–3. [31] J. V. Siles, A. Maestrini, B. Alderman, S. Davies, and H. Wang, “A novel dual-chip single-waveguide power combining scheme for millimeter-wave frequency multipliers,” in 20th Int. Space Terahertz Technol. Symp., Apr. 2009, pp. 205–209. [32] J. V. Siles and J. Grajal, “Capabilities of GaN Schottky multipliers for LO power generation at millimeter-wave bands,” in Proc. 19th Int. Space Terahertz Technol. Symp., Apr. 2008, pp. 504–507. [33] C. Lee, J. Ward, R. Lin, E. Schlecht, G. Chattopadhyay, J. Gill, B. Thomas, A. Maestrini, I. Mehdi, and P. Siegel, “A wafer-level diamond bonding process to improve power handling capability of submillimeter-wave Schottky diode frequency multipliers,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2009, pp. 957–960. [34] T. W. Crowe, T. C. Grein, R. Zimmermann, and P. Zimmermann, “Progress towards solid-state local oscillators at 1 THz,” IEEE Microw. Guided Wave Lett., vol. 6, no. 5, pp. 207–208, May 1996. [35] J. Grajal, V. Krozer, E. Gonzalez, F. Maldonado, and J. Gismero, “Modelling and design aspects of millimeter-wave and submillimeter-wave Schottky diode varactor frequency multipliers,” IEEE Trans. Microw. Theory Tech., vol. 48, no. 4, pp. 700–711, Apr. 2000. [36] S. Selberherr, Analysis and Simulation of Semiconductor Devices. New York: Springer-Verlag, 1984. [37] H. Hjelmgren, “Numerical modeling of hot electrons in n-GaAs Shottky-barrier diodes,” IEEE Trans. Electron Devices, vol. 37, no. 5, pp. 1228–1234, May 1990. [38] J. R. Jones, G. B. Tait, S. H. Jones, and D. S. Katzer, “DC and large signal time-dependent electron transport in heterostructure devices: An investigation of the heterostructure barrier varactor,” IEEE Trans. Electron Devices, vol. 42, no. 6, pp. 1070–1080, Jun. 1995. [39] S. F. Guo, “A simple model for computer simulation of Schottky-barrier diodes,” Solid State Electron., vol. 27, no. 6, pp. 537–543, Jun. 1984. [40] J. V. Siles and J. Grajal, “Design of submillimeter Schottky mixers under flat-band conditions using an improved drift-diffusion model,” IEEE Microw. Wireless Compon. Lett., vol. 19, no. 3, pp. 167–169, Mar. 2009. [41] J. V. Siles, J. Grajal, V. Krozer, and B. Leone, “A CAD tool for the design and optimization of Schottky diodes mixers up to THz frequencies,” in Proc. 16th Int. Space Terahertz Technol. Symp., May 2005, pp. 477–482. [42] V. Bernaldo, J. Grajal, and J. V. Siles, “Design of heterostructure barrier varactor frequency multipliers at millimetre-wave bands,” in Proc. 17th Int. Space Terahertz Technol. Symp., May 2006, pp. 229–232. [43] S. M. Sze, Physics of Semiconductor Devices, 2nd ed. New York: Wiley, 1981.

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[44] N. Erickson, “Diode frequency multipliers for terahertz local-oscillator applications,” in Proc. SPIE Adv. Technol. MMW, Radio, Terahertz Telescopes, Mar. 1998, pp. 75–84. [45] S. A. Maas, Non-Linear Microwave Circuits. Boston, MA: ArtechHouse, Inc., 1993. [46] C. Jacoboni and P. Lugli, The Monte Carlo Method for Semiconductor Device. New York: Springer-Verlag, 1989. [47] M. T. Faber, J. Chramiec, and M. E. Adamski, Microwave and Millimeter-Wave Diode Frequency Multipliers. Norwood, MA: Artech House, 1995. [48] J. Grajal, C. Lin, P. Gonzalez, and V. Krozer, “Optimization of doping profiles in Schottky diodes for millimeter frequency multipliers,” in 7th IEEE Int. Terahertz Electron. Conf., 1999, 4 pp. [49] N. Erickson, G. Narayanan, R. P. Smith, S. C. Martin, T. W. Crowe, and W. L. Bishop, “Planar frequency doublers and triplers for FIRST,” in 11th Int. Space Terahertz Technol. Symp., May 2000, pp. 543–551. [50] F. Maiwald, E. Schlecht, J. Ward, R. Lin, R. Leon, J. Pearson, and I. Mehdi, “Design and operational considerations for robust planar GaAs varactors: A reliability study,” in Proc. 14th Int. Space Terahertz Technol. Symp., Apr. 2004, pp. 488–491. [51] N. R. Erickson, “High efficiency submillimeter frequency multipliers,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 1990, pp. 1301–1304. [52] E. L. Kollberg, T. J. Tolmunen, M. A. Frerking, and J. R. East, “Current saturation in submillimeter-wave varactors,” IEEE Trans. Microw. Theory Tech., vol. 40, no. 5, pp. 831–838, May 1992. [53] F. Bonani, S. D. Guerrieri, and G. Ghione, “Physics-based simulation techniques for small- and large-signal device noise analysis in RF applications,” IEEE Trans. Electron Devices, vol. 50, no. 3, pp. 633–644, Mar. 2003. [54] J. Grajal, D. Moreno, and V. Krozer, “2-D design of Schottky diodes,” in 8th IEEE Int. Terahertz Electron. Conf., Sep. 2000, pp. 73–76. [55] J. Stake, S. H. Jones, L. Dillner, S. Hollung, and E. Kollberg, “Heterostructure barrier varactor design,” IEEE Trans. Microw. Theory Tech., vol. 48, no. 4, pp. 677–682, Apr. 2000.

José V. Siles (S’05–M’09) received the M.S. and Ph.D. degrees in telecommunication engineering from the Technical University of Madrid, Madrid, Spain, in 2003 and 2008, respectively. In 2002, he joined the Signal, Systems, and Radiocommunications Department, Technical University of Madrid, where he has been a Research Fellow supported by a fellowship from the Spanish Ministry of Education and Science. In 2008, he was a Visiting Postdoctoral Fellow with the Observatory of Paris–LERMA. His research activities are in the area of physics-based modeling, design and test of semiconductor devices, and millimeter– and submillimeter-wave circuits. Jesús Grajal received the M.S. and Ph.D. degrees in telecommunication engineering from the Technical University of Madrid, Madrid, Spain, in 1992 and 1998, respectively. In 1993, he joined the Signal, Systems, and Radiocommunications Department, Technical University of Madrid, where he has been an Associate Professor since 1998. His research activities are in the area of semiconductor simulation and high-frequency circuit design.

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Integrated 585-GHz Hot-Electron Mixer Focal-Plane Arrays Based on Annular Slot Antennas for Imaging Applications Lei Liu, Member, IEEE, Haiyong Xu, Member, IEEE, Arthur W. Lichtenberger, and Robert M. Weikle II, Senior Member, IEEE

Abstract—We have developed 585-GHz quasi-optical mixers and focal-plane arrays (FPAs) comprised of planar annular slot antennas (ASAs) with integrated niobium hot-electron bolometers for imaging applications. In order to optimize the single-element mixer design, the embedding impedance of the single ASA presented to the bolometer is analyzed using the induced electromotive force (EMF) method by including the antenna feed contribution. This approach has been further expanded to analyze the ASA self-impedance and mutual impedance in an array by utilizing the even-odd mode analysis. In addition, the far-field radiation patterns of the ASAs mounted to an extended hemispherical high-resistivity silicon lens have been calculated using the ray-tracing techniques. The details of circuit design and fabrication are presented in this study. Single mixer element measurement results have shown that a conversion gain of 11.9 dB and a double-sideband (DSB) receiver noise temperature of 650 K have been achieved. Initial array imaging experiment results are presented and show excellent agreement with theory and simulation data. A spatial resolution of 2.75 mm has been demonstrated at 585 GHz for a 1-D mixer FPA that is capable of diffraction-limited imaging. -factor measurements show DSB mixer noise temperatures of 1675 and 3517 K with mixer conversion gains of 14.73 and 17.74 dB, respectively, have been obtained for two adjacent elements in a mixer array, which is comparable to the results reported in the literature. Index Terms—Annular slot antenna (ASA), focal-plane array (FPA), hot electron mixer.

bolometer,

I. INTRODUCTION STRONOMIC and atmospheric remote sensing and chemical spectroscopy in the submillimeter-wave and terahertz frequency range have driven the demand for highly sensitive mixers/receivers for imaging applications [1]–[3].

A

Manuscript received October 01, 2009; revised February 07, 2010; accepted March 04, 2010. Date of publication June 01, 2010; date of current version July 14, 2010. This work was supported by the National Science Foundation (NSF) under Grant AST-0242525 and by the U.S. Army National Ground Intelligence Center under Grant DASC01-01-C-0009. L. Liu is with the Department of Electrical Engineering and the Advanced Diagnositcs and Theroputics Initiative, University of Notre Dame, Notre Dame, IN 46556-5637 USA (e-mail: [email protected]). H. Xu, A. W. Lichtenberger, and R. M. Weikle II are with the School of Engineering and Applied Science, University of Virginia, Charlottesville, VA 229044743 USA (e-mail: [email protected]; [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2010.2050101

Superconducting hot-electron bolometers (HEBs) have received much attention in recent years owning to their merits such as high sensitivity, broad IF bandwidth, and frequency scalability [4]. These devices have been succesfully integrated into bow-tie antennas [5], double slot antennas [6], [7], and log-spiral antennas [8] for building single-element mixers and receivers. However, in many applications, only one pixel of object information from the receiver is insufficient. To effectively map the spatial distribution of radiation intensity, many pixels of imaging information are usually needed. Although mechanical scanning can be applied to a single-element mixer to fulfill the above requirement, in some cases, this is not feasible due to the long observing time required to form a complete image [9], [10]. Imaging mixer focal-plane arrays (FPAs) [11] are the best approach for these applications since they can greatly reduce observing and processing time by recording imaging information in parallel. FPAs for submillimeter-wave and terahertz imaging applications have been a continuing interest in both the astronomy and bio-spectroscopy communities. A number of researchers have put considerable effort into developing imaging arrays based on Schottky diodes or superconducting detectors [3], [12]–[15]. In 1982, Rutledge and Muha proposed a high-resolution imaging antenna array with a “reverse-microscope” optical configuration [2]. On the bases of this approach, a research group at the University of California at Davis has presented a 90-GHz Schottky diode mixer array with bow-tie antennas [3]. Bow-tie antennas, however, have a number of drawbacks for high-resolution imaging applications in the terahertz region since they are not compact for single imaging element design and exhibit antenna patterns with maximum off the antenna bore-sight [16]. The Jet Propulsion Laboratory (JPL), Pasadena, CA, has proposed a 1.6-THz 1-D array based on diagonal horns antennas [11]. However, 2-D arrays based on this scheme are difficult to realize. In recent years, another approach called the “fly’s-eye concept” has been investigated at the University of Massachusetts at Amherst [14]. A three-element HEB focal plane array based on this concept has also been reported recently demonstrating promising performance [15]. For this approach, each mixer element uses a separate imaging lens, which presents difficulties for design and fabrication, and hence, the imaging resolution of this system is limited. To date, few of the single-element mixer circuit designs, especially the antenna structures used have been suitable for terahertz imaging arrays. The annular slot antenna (ASA) provides

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a compact and symmetric structure, making itself an ideal candidate for this applications. Prior to developing a complicated mixer FPA, single-element HEB mixers have been designed, fabricated, and tested for performance evaluation and improvement. To optimize the receiver performance, efficient power coupling from the antenna structure and mixer is required, demanding accurate knowledge of the embedding impedance presented to the bolometer. This is particularly crucial for integrated planar arrays that contain no tuning elements for adjusting the impedance match between the antenna and detector. In this paper, an analysis of the ASA and array impedances based on the induced electromotive force (EMF) method [18] is presented. This approach permits the effect of the antenna feed to be included in a direct manner and, in essence, extends the analysis of Tong and Blundell [17] and Leung [19], both of which assume a point or “delta” feed for the antenna. For the proposed integrated mixer, the geometry near the antenna feed can have a significant effect on the embedding impedance and can be critical for determining the receiver performance. For diffraction-limited imaging with heterodyne detectors, a quasi-optical system using lenses to couple incident radiation onto a planar antenna array with integrated detection devices (so-called “reverse-microscope” configuration) has been proven to be successful [2]. In this configuration, an element spacing between adjacent antennas should be less than one wavelength (assuming unity f-number) [20]. However, at such a small element spacing, the mutual coupling between adjacent elements becomes an important consideration. To facilitate the design of an FPA with capability of diffraction-limited imaging, the EMF analysis has been applied to two-element ASA arrays by using the even–odd-mode analysis. In addition, the far-field radiation patterns of the ANA arrays mounted to an extended hemispherical high-resistivity silicon lens have been calculated using the ray-tracing techniques [21]. On the basis of the theoretic analysis and calculations, the design and measurement results of a 1-D linear HEB mixer array with four pixels are presented and discussed. This paper is organized as follows. Sections II and III present the EMF analysis of single-element ASAs, and ASA arrays, respectively. Section IV summarizes the details of the design, fabrication, and measurements of the 585-GHz HEB mixers and mixer FPAs based on ASAs. Finally, discussion and conclusion are given in Section V.

Fig. 1. Diagram of an ASA with radius of a, slot width of w , and feed width of g .

(2) and are the components of the wave vector along where the - and -directions, respectively, and . The geometry of the annular slot and coordinate system used here are shown in Fig. 1. For clarity, the analysis process described in [23] is summarized below. and magnetic current density First, the magnetic field in the slot are expanded in terms of the TE and TM basis vectors given in (1) and (2). By applying Poynting’s Theorem, the complex power radiated by the magnetic current in the slot can be determined by

(3) where is the expansion coefficients for the magand are the TE or TM wave impedances netic field, and - and -directions, respectively. looking in the Second, assume a current to flow across the antenna feed (of width ) and specify an azimuthally directed magnetic field . For a sufficiently narrow feed, the assumption of a uniform current across the feed is a reasonable approximation. Expand both the magnetic current in the slot, and the magnetic field in the feed as Fourier series in azimuthal modes, and apply Poynting’s Theorem to determine the total power radiated from the feed associated with the th azimuthal mode

II. SINGLE ARRAY ELEMENT EMBEDDING IMPEDANCE ANALYSIS The analysis described and presented here extends that developed by Tong and Blundell [17] by incorporating the effect of the ASA feed. The approach is based upon the induced EMF method of Carter [18] and follows the general technique first applied by Eisenhart and Khan to determine the driving point impedance of a common waveguide mount [22]. To facilitate the analysis, the electromagnetic fields and magnetic current distribution in the annular slot are expressed as linear combinations of TE and TM basis vectors. In Cartesian coordinates, these basis vectors are given by (1)

(4) represents the complex power flowing from the feed, where is the magnetic current expansion coefficient, describes the dependence of the magnetic current on radial distance , and is the voltage component across the feed associated with the th azimuthal mode. Third, determine the driving-point admittance, and hence, the driving-point impedance of the annular slot from (3) and (4), we

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have (5) (6) and (7) where is defined in [23] following the notation of Tong and Blundell [17]. Assuming the magnetic current to be uniform for , across the annular slot, we have (8)

resulting in (9) Using the above formulation, a numerical computer code was written to calculate the annular slot embedding impedance. To verify the EMF analysis, the calculated results are compared to experimental data provided in [17]. The results shown in Fig. 2(a) are for a freestanding ASA with radius of 36 m, m, and width of 2.24 m, feed width of THz. Normalized to this center center frequency of frequency, the calculated impedance and measured data from [17] are shown with excellent agreement. Fig. 2(b) shows the m, m) on a EMF analysis result of an ASA ( with GHz. This result silicon half-space will be used for design of the single imaging FPA element. The analysis was also performed with various feed gap sizes to . Over this range, the imaginary part of from the impedance varies as much as 19 and the real part varies up to 10 . Although these are relatively small variations compared with the antenna impedance, they can be significant compared to the typical impedance of a niobium bridge, which is on the order of 30 to 50 , and thus are taken into account in the mixer design. III. EMF ANALYSIS OF ASA ARRAYS For diffraction-limited imaging with heterodyne detectors using the “reverse-microscope” configuration, an element spacing of less than one wavelength is required (assuming unity f-number) [20]. However, at such a small element spacing, the mutual coupling between the adjacent elements in an array cannot be ignored. To facilitate the design of an FPA with capability of diffraction-limited imaging using ASAs, we further apply the EMF analysis described in Section II to a two-element ASA array.

= 36

Fig. 2. (a) EMF analysis results of a freestanding annular slot (a m, w : m,  ) compared to experimental data (cf. [17]). (b) EMF m, w : m) on a silicon analysis results of an annular slot (a : with f GHz. half-space 

= 2 24 =1 ( = 11 8)

= 36 = 585

= 26

To account for the feed point azimuthal position differences, the analysis begins with the four-port problem, as shown in Fig. 3(a). The annular slots under study have a radius of , a slot width of , and port width of . The centers of the two antennas are separated with a spacing of d along the -axis. By applying even–odd-mode analysis [24], the original four-port problem can be decomposed into two two-port single-antenna problems, as shown in Fig. 3(b). For the odd mode, the two antenna feed and with an elecpoints are located at trical-wall placed along the -axis (axis of symmetry), while for the even-mode, the ports are located at the same azimuthal locations with a magnetic-wall along the -axis. The EMF analysis is then applied separately to the even- and odd-modes structures by following the approach described in Section II. The even- and , , , and odd-mode impedances network are found from this analysis and the overall four-port impedance parameters of the two antenna network can be calculated using

(10) (11)

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(21) The EMF analysis of ASA arrays is significantly simplified by using (20) and (21). This step also makes the analysis expandable to 2-D arrays (e.g., 2 2 arrays) by exploiting the symmetric structure of these ASA arrays. Following the steps described in Section II and [23], the mod, , ified TE and TM magnetic current coefficients ( , and ) can be found and we define the parameter for the above four magnetic current coefficients

(22) Fig. 3. Even-odd mode analysis of two-element ASA arrays. (a) Original fourport problem. (b) Decomposed even- and odd-mode two-port problems with ASA centered at (d=2, 0).

(23) (12) (13)

Equations (6)–(8) still hold, resulting in driving-point impedances of (24)

Taking into account the boundary conditions imposed by the electric and magnetic walls in Fig. 3, the TE and TM basis vectors can be expressed in the form (14) (15) (16) (17) for the even- and odd mode, respectively. Recalling the previously defined plane wave basis vectors, and introducing another two sets of vectors

for the even mode and (25) for the odd mode respectively. Following Tong and Blundell’s results in [17], the mutual impedances for even and odd mode between port 1 and port 2 [see Fig. 3(b)] can be calculated simply by including the azimuthal phase difference between the port feeds (26) (27)

(18) (19) (14)–(17) can then be expressed in the form of combinations of these vectors in (1), (2), and (18), and (19) as

(20)

Substituting (24)–(27) into (10)–(13), the original four-port problem between two annular-slot antennas is then fully solved. Using the above formulations, numerical computation was performed to study the mutual coupling between two ASAs on a silicon half-space separated with distance . Each of the antenna is assumed to have a radius of 36 m and a slot width of 2.6 m. Initially, the case with the driving points on the two antennas located at different azimuthal position is studied, and the azimuthal coordinates for the feeds are and

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TABLE I 1-D ARRAY SELF-IMPEDANCE AND MUTUAL IMPEDANCE AT 585 GHz ( )

demonstrated that the mutual coupling is not negligible with small element spacing. To design an imaging array with acceptable performance, a tradeoff must be made between the imaging resolution and the crosstalk from adjacent elements. The EMF analysis results shown above have been compared to simulations using ADS Momentum. Discrepancies only arise at higher frequencies ( 500 GHz). This may be attributed partially to the coplanar waveguide (CPW) feeding structure used in ADS Momentum simulations. Although the phase caused by the CPW transmission line is de-embedded to the reference plane, a small section of the feed structure remains, introducing two effective capacitances between the feed gap and ground. The effect from these capacitances increases with frequency (or dielectric constant) and is difficult to be fully removed from the results, while the feed structure is not required for the EMF analysis. Moreover, the EMF analysis can solve the mutual impedance for two ports located anywhere on the annular slots. The antenna feeding structure required may cause some difficulties for ADS Momentum simulation in some cases. In addition, the EMF approach provided above can be applied to a 2-D annular-slot array. IV. DESIGN AND MEASUREMENT RESULTS A. Single Array Element Mixer Design and Measurement Fig. 4. (a) Annular-slot antenna array self-impedance for driving port 1 with separation distance of 0:52 ( is the wavelength in silicon). (b) Exemplary results for the mutual impedances between ports 1 and 4 (separation distance of 0:52 ), and ports 1 and 3 (separation distance of 0:8 ).

, respectively. All the feed gap sizes are taken to be , where is the antenna slot width. The calculated re( is the sults are plotted in Fig. 4. At a distance of is close to 100 at wavelength in silicon), the impedance 585 GHz, and the mutual impedance between port 1 and port 4 is approximately at 585 GHz and over the frequency range of 500–600 GHz, the magnitudes of the real part and imaginary part impedances can be as large as 30 , which is comparable to the antenna self-impedance. The case with the feeds on the two antennas located at the same azimuthal position is then studied and the results show that at , the mutual-impedance absolute value a distance of at 585 GHz is also in the range of 30 . With an increase in the element spacing, a corresponding decrease in the mutual , the muimpedance is expected. At a distance of tual-impedance magnitudes decrease significantly to less than 6 over the range of 500–600 GHz, specifically for at 585 GHz [see in Fig. 4(b)]. The self-impedance and mutual impedance for the cases with feedpoints on the same and opposite sides of the ring, analyzed using the EMF method, have been summarized in Table I. The EMF analysis has clearly

For operation at 585 GHz with a high-resistivity 1000 cm silicon substrate of 0.5 mm , the annular slot is designed to have a radius of 36 m and a slot width of 2.6 m. Since the superconducting niobium HEB bridge is a purely resistive device, the antenna is designed to operate at resonance where it has an impedance of 100 , according to the impedance analysis presented in Section II [see Fig. 2(b)]. To maximize power coupling to the bolometer, a quarter-wavelength impedance transformer based on a CPW structure is employed to match the bolometer normal-state impedance of 35–100 ). One square niobium HEB device is required since the sheet resistance of a 10-nm-thick Nb square. To reduce the footprint thin film is estimated at 35 of the single-element mixer circuit, a conventional high/low stepped-impedance low-pass filter (LPF) is integrated with the ASA on a single silicon chip. The LPF utilized has a cutoff frequency of 320 GHz and an RF signal (585 GHz) suppression of 18 dB. The mixer circuit was fabricated in the University of Virginia Microfabrication Laboratories (UVML), University of Virginia, Charlottesville, and the typical fabrication result is shown in Fig. 5. The one-square niobium bridge is integrated at the end of the quarter-wave impedance transformer using the e-beam lithography (EBL) process. The device length is 240 nm and the width is 237 nm, resulting in an HEB resistance close to 35 at the normal state. The mixer chip is mounted to an extended hemispherical silicon lens with radius of 4.5 mm. Analysis

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Fig. 5. Annular slot HEB mixer utilizing a quarter-wave impedance matching circuit. Fig. 7. Diagram of the Y -factor measurement setup for measuring the HEB mixer noise temperature.

Fig. 6. Measured and calculated ASA radiation patterns (with extended hemispherical silicon lens) at 585 GHz. The angular range measured for the pattern was limited by the window of the cryostat used in the measurement system.

of the far-field patterns of the lens-mounted antenna was done using the ray-tracing approach of Filipovic [21] and an extenmm was chosen to achieve the maximum sion length of antenna directivity while maintaining a Gaussian coupling efficiency of approximately 85%. DC measurements have demonstrated that the fabrication process has been successful. The resulting device resistances are in the range of 30–40 , which is a perfect matching to the antenna impedance with the quarter-wave transformer. The critical temperature of the Nb micro-bridge is 5.4 K with a transition width of 0.5 K. A quasi-optical mixer block has been fabricated and installed into the HD-3(8) Dewar system for cooling tests and RF measurements. The measured -plane radiation pattern of the receiver is shown in Fig. 6, and the main beam shows good agreement with the calculated antenna pattern obtained from ray-tracing [21]. Fig. 7 shows the diagram of the -factor measurement system. In this system, a VDI 576–640-GHz frequency extension module (courtesy of Virginia Diodes Inc., Charlottesville, VA) is employed to provide the local oscillator (LO) power. A hot/cold load (RF signal) is used to measure the system -factor. Both the LO and RF are coupled into the cryogenic

Dewar through a set of lenses and mirrors. Inside the Dewar, the quasi-optical mixer block is placed before a Teflon window and biased from a bias-T. Between the Teflon window and the mixer block, a 585-GHz mesh filter with a bandwidth of 100 GHz is placed to avoid the direct-detection effect reported by other groups [25]. The IF signal is output to an isolator and a low-noise amplifier (LNA) before being fed to an external IF chain for data processing. -factor measurements have been performed on the annular slot receiver with the HEB device dc biased at (0.8 mV, 47 A). The estimated LO power coupled in is approximately 150 nW. The IF output power (1.8 GHz) measured is 17.5 nw with a hot load (300 K), and 13.3 nW with a cold (77 K) load, respectively, resulting in a double-sideband (DSB) receiver noise temperature of 650 K, and a mixer conversion gain of 11.9 dB [23], [26]. This mixer will be utilized as an array element in PFAs presented in Section IV-B. B. HEB Mixer Array Design and Measurement On the basis of previous EMF analysis of ASA arrays, prototype 1-D ASA focal plane arrays incorporating niobium HEB mixers have been designed for operation at 585 GHz [26]. This approach follows the pioneering work in [2] and provides an architecture that is capable of diffraction-limited imaging in the terahertz region. Fig. 8(a) shows the diagram of the HEB imaging mixer array mounted on an extended hemispherical silicon lens. Each of the imaging elements incorporates a receiving antenna structure as the coupling component in which a superconducting niobium HEB microbridge is integrated. An input image signal is focused by an objective lens (not shown in this figure) onto the mixer array through the substrate lens. Images are then obtained by measuring the IF output signal from each element in the array. By utilizing the same material (high-resistivity silicon) for both the array substrate and extended hemispherical lens, trapped surface waves are eliminated [2]. For prototype demonstration, a 1-D array containing four ASAs is illustrated in Fig. 8(b). CPW transmission lines are

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Fig. 9. Off-axis element radiation patterns for the 1-D ASA array calculated using ray-tracing technique. Patterns are calculated with an element spacing of 1:0 .

Fig. 8. (a) Schematic of an HEB imaging mixer FPA mounted on an extended hemispherical silicon lens with radius R and extension length L. (b) Specific diagram of a 1-D four-pixel ASA array with element spacing of d. Each antenna has a radius a of 36 m and a slot width w of 2.24 m.

included at the feed points of the antennas, corresponding to the location where the HEB devices are to be fabricated. For operation at 585 GHz, each ASA has a radius of 36 m and of 2.6 m. High-resistivity silicon is chosen as a slot width the substrate due to its high dielectric constant, resulting in a high directive gain and antenna efficiency. The hemispherical silicon lens has a radius of 4.5 mm. According to the EMF analysis in Section III, the mutual impedances between the in Fig. 3(a)] are small and only have adjacent elements [ a minor effect to the array if the element spacing is larger . Thus, in this work, FPAs with element spacing than , , and have been studied. The far-field of off-axis radiation patterns of the annular-slot array mounted on the silicon lens have been calculated using the ray tracing technique of Filipovic [21]. Shown in Fig. 9 is the calculation . The element SRA pattern has a 3-dB result for beam width of approximately 3 with a sidelobe level less than 10 dB. The angular distance between adjacent beams are 4.0 , 5.0 , and 5.7 with a crossover power level of 7.2, 11.0, and 12.5 dB for antenna spacings of 0.8, 1.0, and , respectively. The relationship between the angular imaging resolution and corresponding ASA element spacing is

Fig. 10. Photograph of the mixer FPA chip mounted on a cryogenic circuit block. Four SMA IF outputs are connected to the four mixer elements separately.

also calculated. With decreasing element spacing, the imaging resolution increases nearly linearly. However, the imaging contrast degrades. Consequently, the choice of antenna element spacing results in a tradeoff between imaging resolution and contrast. The designed HEB mixer FPAs were fabricated at the UVML using the EBL process. The HEB device size is designed to be 250 nm 250 nm (one square), resulting in a 35- resistance at the normal state. To measure the array performance, a quasi-optical mixer array block has also been fabricated, as shown in Fig. 10. The array chip is first bonded to a silicon substrate ( 1.1-mm thick with four bended CPW transmission lines) using cryogenic epoxy, and an ultrasonic wire-bonding tool is used to electrically connect both the grounds and center conductors. Another silicon substrate with CPW transmission lines fabricated have been installed into the backside of the array block, and four subminiature A (SMA) connectors are utilized to output the IF signals. DC probe testing has shown that the HEB device resistances are in the range of 55–65 at 4.2 K. Compared to the designed value of 35 , the difference can be attributed to the focusing during the EBL processes.

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Fig. 11. Measured normalized response (square and circular dots) from two adjacent mixer elements (B and C) in the 1-D array. The solid and dotted lines are theoretical results by ray-tracing technique.

the basis of the “reverse-microscope” configuration provide a capability to realize diffraction-limited high-resolution FPAs in the terahertz frequency region. -factor measurements have been performed to each of the two array mixer elements (elements B and C) and the results show that DSB mixer noise temperatures of 1675 and 3517 K, with mixer conversion gain of 14.73 and 17.74 dB, respectively, have been obtained for the two adjacent elements in the 1-D focal-plane mixer array, which is comparable to the results reported in the literature. To the authors’ best knowledge, the HEB mixer focal plane array described in this paper is the first heterodyne FPA reported on the basis of the “reverse-microscope” architecture with the capability of diffraction-limited imaging. With this architecture, all the array antennas, HEB devices, and IF circuits are integrated onto one silicon wafer, thus providing an alternative way for developing large FPAs in the terahertz region. V. DISSCUSSION AND CONCLUSION

A close-cycled cryocooler has been employed in the mixer array RF measurements. Inside the cryocooler, a 585-GHz mesh filter ( 100-GHz bandwidth) is placed on the 40-K stage just in front of the Teflon window. On the 4.2-K stage, the mixer array block is installed with four outputs connected to four bias-T’s so that the four HEB devices can be dc biased separately. A Miteq four-way power combiner is followed to combine the IF signals. A Durado cryogenic isolator and a Miteq LNA are utilized before sending out the signal for external processing. During the HEB array operation, only one of the four HEB devices is dc biased at one time, and thus, each mixer can be measured separately. To measure the HEB mixer FPA imaging angular resolution, two adjacent elements (elements B and C with B in the upper position) in a 1-D array chip (see inset of Fig. 10, element spacing ) were dc biased and the responses were monitored. During the experiment, the VDI 585-GHz solid-state source is employed and the distance between the silicon lens and the source is nearly 50 mm for maximum response. The responses for elements B and C are normalized and plotted in Fig. 11 together with the off-axis antenna patterns (see Fig. 9) predicted using the ray-tracing technique. Again, reasonable agreement has been obtained. The discrepancies can be attributed to errors in source position measurement and the nonlinear relationship between the current response and the absorbed RF power. The vertical distance between the two maximum response position is 4.4 mm, resulting in an angular resolution of 5.04 , which is very close to the theoretical prediction (see Fig. 9). By using an optical lens as an objective lens, the system imaging resolution can be further improved. Experiments have been performed with a distance of 133.1 mm between the silicon lens and the 585-GHz solid-state source. The optical lens is placed 49.3 mm from the cryocooler window (86.3 mm from the silicon lens). The response peaks from elements B and C are measured at source displacement of 69.35 and 72.10 mm, corresponding to an imaging resolution of 2.75 mm. Compared to the results reported by the University of Massachusetts group [15] at 1.6 THz with a three-element HEB array based on the “fly’s-eye” concept, the integrated HEB mixer arrays on

The measurement results in Section IV-B are comparable to that reported in the literature [15]. However, the measured noise temperatures for elements in an array are not as good as that for a single-element HEB mixer presented in Section IV-A. Although further study needs to be done to fully understand this discrepancy, we attribute this to several possible reasons, which are: 1) the ASAs are off-axis positioned at the back side of the silicon lens and this could introduce as large as 10-dB coupling loss; 2) the array receiver system used in this research is not optimized. A four-way power combiner is utilized introducing 6-dB loss, which further increases the receiver noise level; and 3) the array assembly strategy is designed for prototype demonstration. A wire-bonding technique is used for electrical connection, which unavoidably deteriorates the IF performance of the mixer array circuits. In conclusion, prototype quasi-optical mixer FPAs comprised of ASAs integrated with HEBs have been developed for imaging applications at 585 GHz. The embedding impedance of the annular-slot antenna is analyzed using the induced EMF method by including the contribution of the antenna feed. This approach has been further applied to analyze the mutual impedances of the annular slots in a FPA by using the even–odd-mode analysis. In addition, the ray-tracing technique has been applied to determine the far-field antenna patterns of the ASA element and antenna arrays mounted to a high-resistive silicon lens. Measurement results of the single mixers element and preliminary results of the FPAs are also presented and discussed. The HEB mixer focal plane array described in this paper provides an promising architecture for developing FPAs that are capable of diffraction-limited imaging in the terahertz region. ACKNOWLEDGMENT The authors would like to thank all their colleagues with the University of Virginia Microfabrication Laboratories (UVML), Univeristy of Virginia, Charlottesville, and the Microwave Laboratory, University of Virginia. The authors are also grateful for the assistance and advice of Prof. A. Isin and Prof. B. S. Deaver, Jr., both with the Department of Physics, University of Virginia.

LIU et al.: INTEGRATED 585-GHz HOT-ELECTRON MIXER FPAs

REFERENCES [1] D. Mittleman, M. Gupta, R. Neelamani, R. Baraniuk, J. Rudd, and M. Koch, “Recent advances in terahertz imaging,” Appl. Phys. B, Lasers Opt., vol. 68, pp. 1085–1094, 1999. [2] D. B. Rutledge and M. S. Muha, “Imaging antenna arrays,” IEEE Trans. Antennas Propag., vol. AP-30, no. 4, pp. 535–540, Jul. 1982. [3] P. L. Hsu et al., “Millimeter-wave imaging array development for microwave reflectometry and ECE imaging,” Rev. Sci. Instrum., vol. 72, no. 1, pp. 364–367, Jan. 2001. [4] D. E. Probe, “Superconducting terahertz mixer using a transition-edge microbolometer,” Appl. Phys. Lett., vol. 62, pp. 2119–2121, 1993. [5] R. B. Bass, “Hot-electron bolometers on ultra-thin silicon chips with beam leads for a 585 GHz receiver,” Ph.D. dissertation, Dept. Elect. Comput. Eng., Univ. Virginia, Charlottesville, VA, 2004. [6] A. Skalare, W. R. McGrath, B. Bumble, and H. G. LeDuc, “Receiver measurements at 1267 GHz using a diffusion-cooled superconducting transition-dege bolometer,” IEEE Trans. Appl. Supercond., vol. 7, no. 2, pp. 3568–3571, Jun. 1997. [7] W. F. M. Ganzevles, L. R. Swart, J. R. Gao, P. A. J. de Korte, and T. M. Klapwijk, “Direct response of twin-slot antenna-coupled hotelectron bolometer mixers designed for 2.5 THz radiation detection,” Appl. Phys. Lett., vol. 76, no. 22, pp. 3304–3306, May 2000. [8] A. D. Semenov et al., “Terahertz performance of integrated lens antennas with a hot-electron bolometer,” IEEE Trans. Microw. Theory Tech., vol. 55, no. 2, pp. 239–247, Feb. 2007. [9] D. T. Hodges, F. B. Foote, E. E. Reber, and R. L. Schellenbaum, “Near millimeter wave radiometric imaging,” in 4th Int. Infrared Millim. Waves Appl. Conf., 1979, no. 79, pp. 51–52. [10] J. Waldman, H. R. Fetteman, P. E. Duffy, T. G. Bryant, and P. E. Tannenwald, “Submillimeter model measurements and their applications to millimeter radar systems,” in 4th Int. Infrared Millim. Waves Appl. Conf., 1979, no. 79, pp. 49–50. [11] G. Chattopadhyay, I. Mehdi, J. S. Ward, E. Schlecht, A. Skalare, and P. H. Siegel, “Development of multi-pixel heterodyne array instruments at submillimeter wavelength,” in IEEE Asia–Pacific Microw. Conf., 2004. [12] P. P. Tong, D. P. Neikirk, D. Psaltis, D. B. Rutledge, K. Wagner, and P. E. Yong, “Tracking antenna arrays for near-millimeter waves,” IEEE Trans. Antennas Propag., vol. AP-31, no. 3, pp. 512–515, May 1983. [13] E. N. Grossman and A. J. Miller, “Active millimeter-wave imaging for concealed weapons detection,” Proc. SPIE, vol. 5077, pp. 62–70, 2003. [14] K. S. Yngvesson et al., “New results on THz HEB low-noise receivers and focal plane arrays,” Proc. SPIE, vol. 4111, p. 152, 2000. [15] F. Rodriguez-Morales et al., “A terahertz focal plane array using HEB superconducting mixers and MMIC IF amplifiers,” IEEE Microw. Wireless Compon. Lett., vol. 15, no. 4, pp. 199–201, Apr. 2005. [16] D. B. Rutledge, D. P. Neikirk, and D. P. Kasilingham, “Integrated circuit antennas,” in Infrared and Millimeter Waves, K. J. Button, Ed. New York: Academic, 1983, vol. 10, pp. 1–90. [17] C. E. Tong and R. Blundell, “An annular slot antenna on a dielectric half-space,” IEEE Trans. Antennas Propag., vol. 42, no. 7, pp. 967–974, Jul. 1994. [18] P. S. Carter, “Circuit relations in radiating systems and applications to antenna problems,” Proc. IRE, vol. 20, no. 6, pp. 1004–1041, Jun. 1932. [19] K. W. Leung, “Efficient and accurate computation of an annular slot on a dielectric half-space,” IEEE Trans. Antennas Propag., vol. 48, no. 3, pp. 467–468, Mar. 2000. [20] C. E. Shannon, “Communication in the presence of noise,” Proc. IRE, vol. 37, no. 1, pp. 10–21, Jan. 1949. [21] D. F. Filipovic, S. S. Gearhart, and G. M. Rebeiz, “Double-slot antennas on extended hemispherical and elliptical silicon dielectric lenses,” IEEE Trans. Microw. Theory Tech., vol. 41, no. 10, pp. 1738–1749, Oct. 1993. [22] R. L. Eisenhart and P. J. Khan, “Theoretical and experimental analysis of a waveguide mounting Structure,” IEEE Trans. Microw. Theory Tech., vol. MTT-19, no. 8, pp. 706–719, Aug. 1971. [23] L. Liu, Q. Xiao, A. W. Lichtenberger, and R. M. Weikle II, “Integrated 585 GHz hot-electron mixers based on annular slot antennas,” in IEEE MTT-S Int. Microw. Symp. Dig., Honolulu, HI, Jun. 2007, pp. 1153–1156. [24] R. Mongia, I. Bahl, and P. Bhartia, RF and Microwave Coupled-Line Circuits. Boston, MA: Artech House, 1990. [25] J. J. A. Baselmans, A. Baryshev, S. F. Reker, M. Hajenius, J. R. Gao, T. M. Klapwijk, Y. Vachtomin, S. Maslennikov, S. Antipov, and G. Gol’tsman, “Direct detection effect in small volume hot electron bolometer mixers,” Appl. Phys. Lett., vol. 86, 2005, Art. ID 163503.

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[26] L. Liu, Q. Xiao, H. Xu, J. C. Schultz, A. W. Lichtenberger, and R. M. Weikle II, “Design, fabrication and characterization of a submillimeter-wave niobium HEB mixer imaging array based on the ‘reversemicroscope’ concept,” IEEE Trans. Appl. Supercond., vol. 17, no. 2, pp. 407–411, Jun. 2007. Lei Liu (S’99–M’07) was born in Shuyang, China, in 1977. He received the B.S. and M.S. degrees in electrical engineering from Nanjing University, Nanjing, China, in 1998 and 2001, respectively, and the Ph.D. degree in electrical engineering from the University of Virginia, Charlottesville, in 2007. From 2007 to 2009, he was a Post-Doctoral Research Associate with the Department of Electrical and Computer Engineering, University of Virginia. In September 2009, he joined the faculty of the University of Notre Dame, Notre Dame, IN, as a Research Assistant Professor of electrical engineering. He is also a Research Faculty Fellow with the Advanced Diagnostics and Therapeutics Initiative (AD&T), University of Notre Dame. His research interests include millimeter- and submillimeter-wave device and circuit design, modeling, and testing, quasi-optical techniques, terahertz detectors for imaging and spectroscopy, novel microwave materials and devices, superconducting electronics, microfabrication, and processing.

Haiyong Xu (S’00–M’06) received the B.S. and M.S. degrees from the University of Science and Technology of China, Hefei, China, in 1995 and 1998, respectively, the M.Eng. degree from the National University of Singapore, Singapore, in 2001, and the Ph.D. degree in electrical and computer engineering from the University of Virginia, Charlottesville, in 2005. He is currently a Research Scientist with the Charles L. Brown Department of Electrical and Computer Engineering, University of Virginia. His current research interests include microwave and millimeter-wave circuit analysis and design, novel device development, and system testing.

Arthur W. Lichtenberger was born in Plainfield, NJ, in 1958. He received the B.A. degree in physics from Amherst College, Amherst, MA, in 1980, and the M.S. and Ph.D. degrees in electrical engineering from the University of Virginia, Charlottesville, in 1985 and 1987, respectively. In 1987, he joined the faculty of the University of Virginia, where he is currently a Research Professor with the Department of Electrical and Computer Engineering and Director of the University of Virginia Microfabrication Laboratories (UVML). His current research interests include superconducting materials, devices and circuits in conjunction with submillimeter electronics, high-frequency instrumentation, and metrology.

Robert M. Weikle II (S’90–M’91–SM’05) was born in Tacoma, WA, in 1963. He received the B.S. degree in electrical engineering and physics from Rice University, Houston, TX, in 1986, and the M.S. and Ph.D. degrees in electrical engineering from the California Institute of Technology, Pasadena, in 1987 and 1992, respectively. During 1992, he was a Post-Doctoral Research Scientist with the Department of Applied Electron Physics, Chalmers University of Technology, Göteborg, Sweden. In 1993, he joined the faculty of the University of Virginia, Charlottesville, where he is currently a Professor of electrical engineering. His current research interests include submillimeter electronics, high-frequency instrumentation and measurement systems, and quasi-optical techniques for millimeter-wave power combining, imaging, and beam forming.

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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 58, NO. 7, JULY 2010

A Global Approach for Modeling and Analysis of Edge-Coupled Traveling-Wave Terahertz Photoconductive Sources Mohammad Neshat, Member, IEEE, Daryoosh Saeedkia, Leila Rezaee, Member, IEEE, and Safieddin Safavi-Naeini, Member, IEEE

Abstract—In this paper, a global and geometry-independent approach is proposed for accurate analysis of edge-coupled continuous wave (CW) traveling-wave terahertz photomixer sources. All major physical phenomena involved in the operation of such devices are included in three interconnected solvers, which are combined as a unified analysis tool. A photonic solver is developed to find the optical intensity across the fast photoabsorbing region from which the carrier generation rate is determined. A semiconductor solver is used to study the charge carrier transport inside the photoconductive region through drift-diffusion model, and to predict the generated photocurrent with the beat frequency of two CW lasers. An electromagnetic solver is introduced to rigorously calculate the coupled terahertz signal into the guiding transmission line through a Lorentz reciprocity theorem. Theoretical formulation behind each solver is discussed in detail, and numerical results from each solver are presented. The proposed approach is a powerful tool for global optimization of the photoconductive sources, especially for maximizing the optical-to-terahertz power conversion. Index Terms—Carrier transport, edge coupled, photomixer, reciprocity theorem, terahertz source, traveling wave.

I. INTRODUCTION

I

N RECENT years, various applications of terahertz technology have become feasible due to the advancement of terahertz generation and detection techniques. Among different terahertz generation techniques, photoconductive sources have shown great promise as they are potentially compact, low power consuming, coherent, widely tunable, and cost effective with room-temperature operation [1]. Photomixing is a heterodyne scheme in which the outputs of two single-mode lasers or the output modes of a dual-mode laser, with the frequency difference falling in the terahertz range, mix in a nonlinear medium such as photoconductor or superconductor [2], [3]. High-performance photomixer design requires the combination of both microwave and photonic techniques.

Manuscript received September 30, 2009; revised February 04, 2010; accepted February 23, 2010. Date of publication June 10, 2010; date of current version July 14, 2010. This work was supported by the Natural Science and Engineering Research Council of Canada (NSERC) and by the Research in Motion (RIM) Industrial Research Chair Program. The authors are with the Electrical and Computer Engineering Department, University of Waterloo, Waterloo, ON, Canada N2L 3G1 (e-mail: [email protected]; [email protected]; [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2010.2050379

In conventional small area photomixer structures [4], laser beams illuminate the photoconductor at a small gap between feeding points of an antenna, whereas in a traveling-wave photomixer [5], the laser beams interact with the photoconductor in a relatively large area. In fact, in a traveling-wave photomixer, a microwave waveguide or transmission line is combined with an optical waveguide on the same multilayer guiding structure. Therefore, the propagation characteristics of the two waveguides, as well as carrier dynamics in the photoabsorbing region, determine the overall behavior of the device. The advantage of the traveling-wave scheme is that even for relatively high-power lasers, the power density inside the semiconductor remains below the damage threshold, resulting in the increased terahertz power. Moreover, the RC frequency roll-off, associated with lumped element gap capacitance and the load resistance, is avoided in a distributed scheme. Recently, some performance characteristics of traveling-wave photomixers are experimentally demonstrated in [6]–[8]. In an edge-coupled photomixer configuration, two frequency detuned laser beams are gradually absorbed inside an ultrafast photoabsorbing layer while propagating along the optical waveguide. Due to the photocarrier generation, upon applying a dc-bias field, a traveling-wave current with the beat frequency of two lasers flow inside the photoabsorbing layer. The traveling-wave photocurrent acts as an impressed source for terahertz radiation [9]. When a microwave transmission line such as a coplanar stripline (CPS) or coplanar waveguide (CPW) is integrated with the photomixer structure, the terahertz radiation is coupled into it as guided wave. Modeling of traveling-wave terahertz photomixer sources demands a global approach. Rigorous analysis of such sources is a multifacet problem encompassing three fields of photonics, semiconductor physics, and electromagnetics. The involved interconnected physical processes require each topic to be addressed on more than an individual basis. Thus far, most of the works that have been reported on modeling of photoconductive terahertz devices deal in detail with one part of the problem while making simplistic assumptions about other aspects of the problem. For example, some research focuses on the details of the electromagnetic part while using simple models of materials and photo-induced charge carrier dynamics [10], or some others concentrate on the details of the materials and charge transport, but apply simple models of the electromagnetic fields inside the system, and use equivalent circuits to represent the external system [11].

0018-9480/$26.00 © 2010 IEEE

NESHAT et al.: GLOBAL APPROACH FOR MODELING AND ANALYSIS OF EDGE-COUPLED TRAVELING-WAVE TERAHERTZ PHOTOCONDUCTIVE SOURCES

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Fig. 2. CS of the proposed optical waveguide for an edge-coupled terahertz photomixer. Fig. 1. Combining various solvers for analysis of terahertz photoconductive devices.

Our attempt in this paper is to incorporate all important physical phenomena that contribute to the operation of a travelingwave terahertz photomixer to raise the analytical accuracy, and yet keep the complexity at a reasonable level. Fig. 1 shows the combination of various solvers and their relative connections, which we have developed for comprehensive analysis of a terahertz photoconductive device. In Fig. 1, a photonic solver is basically an optical mode solver, which provides the optical intensity distribution across the optical waveguide as its output. The semiconductor solver takes the optical intensity as the excitation, and solves the coupled partial differential equations governing the charge transport inside the photoconductor. As the output, the semiconductor solver calculates the photocurrent distribution inside the photoconductor. Finally, the electromagnetic solver is used to find the coupled and radiated terahertz signal generated from the previously calculated photocurrent. Our goal in developing these three solvers is to make a balance between the accuracy and complexity of the techniques and models. In subsequent sections, the theory behind each solver is discussed in detail. II. OPTICAL WAVEGUIDE DESIGN AND ANALYSIS (PHOTONIC SOLVER) In this section, an optical waveguide structure for a traveling-wave photomixer is proposed and its design considerations are discussed. The optical waveguide structure being presented here is inspired from a multilayer dielectric slab waveguide previously proposed in [12] for traveling-wave terahertz photomixers. Fig. 2 shows the cross section (CS) of the proposed six-layer ridge waveguide structure with refractive . indices, which satisfy inequality relation Layer I is made of an ultrafast photoabsorbing material such as low-temperature-grown GaAs (LTG GaAs). LTG-GaAs has been widely used in terahertz photomixers working at optical wavelengths around 800 nm. To use LTG-GaAs as the fast phoAs will be the compatible material for toabsorber, Al Ga other layers, which are epitaxially grown over semi-insulating GaAs substrate. By selecting an appropriate range for aluAs layers, the absorption minium mole fraction in Al Ga

of the optical pump signal is prevented in all layers, except the LTG-GaAs layer. Moreover, the aluminium mole fraction are chosen so that there exists a desired refraction contrast between low index cladding layers and the higher index core layer. and for core and cladding, respecChoosing tively, an Al Ga As layer with the refractive index [13] is grown as region IV (see Fig. 2) over a semi-insulating GaAs substrate followed by an Al Ga As layer with as region III, followed by the refractive index another Al Ga As layer as region II, and the LTG-GaAs as region I. Growing layer with the refractive index another layer of Al Ga As on top of the photoabsorber and using etching techniques can provide sufficient etch depth, as shown in Fig. 2, for lateral optical confinement in the ridge region. As is The energy bandgap for Al Ga and eV for , , and , respectively [14]. Hence, applying lasers with wavelength eV, and the around 780 nm results in photon energy optical power absorption takes place only inside the LTG-GaAs layer. Considering the structure in Fig. 2, the design parameters are the thickness of the lower cladding , the core , the upper cladding , the photoabsorber layer , and the ridge , and and the etch depth . The effective also the ridge width index method (EIM) is used to find an initial value for these parameters, and the whole design is fine tuned using the semivectorial beam propagation method (BPM). A few design parameters can be initialized to reduce the degrees of freedom in the design space. For example, to prevent interaction of the optical mode with the semi-insulating substrate, the lower cladding layer with the thickness of must be sufficiently thick. In practice, a cladding layer with the thickm effectively isolates the mode from the ness of substrate. However, for modeling purposes, the lower cladding layer is assumed to be infinitely thick. The LTG-GaAs photoabm . This is due sorber layer should also be thin to the fact that thin layers reduce the photoabsorber fill factor (FF), and consequently, the optical power inside the photoabsorber layer remains below the damage threshold. Moreover, the responsivity per unit length of LTG-GaAs photomixers is

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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 58, NO. 7, JULY 2010

Fig. 3. 1-D phototabsorber FF (solid line) and absorption length (dashed line) with respect to the upper cladding thickness. Other parameters were selected m, h : m, h : m, and  cm for as h LTG-GaAs at 780 nm.

=1

= 01

= 03

= 1 2 10

larger for a thin photoabsorber layer as the carrier collection effectively decreases with depth [11]. A single-mode condition sets an upper limit on the core thickness . Requiring the mode to be well confined, e.g., 65% of the power confined in the core layer, defines the lower limit on . The upper cladding thickness controls the field coupling to the LTG-GaAs, and is selected to give the desired photoabsorber FF. Field distribution across the optical waveguide, and consequently, the photoabsorber FF, can be found through EIM. The photoabsorber FF is defined as the fraction of the total power in the photoabsorber layer. The effective power absorpcan then be approximated by multiplying the tion coefficient photoabsorber FF by the bulk absorption coefficient of the absorbing material, as discussed in the Appendix. It is useful to as a length after which the optical define an absorption length . Knowing the bulk absorppower drops off by a factor of tion coefficient of LTG-GaAs and the photoabsorber FF, one from (35). can readily calculate the absorption length Using 1-D analysis of the six-layer slab in the central region in Fig. 2, the phototabsorber FF and the absorption length with respect to the upper cladding thickness is shown in Fig. 3. For distribution of the optical power over a large area, an appropriate value for the absorption length is first selected, and the corresponding thickness for the upper cladding can be extracted from Fig. 3. Shown in Fig. 4 are the modal field distribution in a 1-D multilayer optical waveguide with different upper cladding thicknesses and for TE modes. The photoabsorber FF and the effective absorption coefficient for even and odd modes are also compared in Table I. It should be noted that by choosing a proper value for , the effective loss for the odd mode can be much higher than that of the even mode. Therefore, the waveguide can be considered almost single mode. In the lateral direction, the designs with the widest singlemode ridge is desired, as the wider ridge permits more optical power being coupled into the guide, and also a larger absorber region being provided for better thermal load distribution in the

Fig. 4. Even (solid line) and odd (dashed line) modes in 1-D multilayer wave: m, (b) h : m, and (c) h : m. Other guide for: (a) h parameters: h m, h : m, and h : m. Vertical lines show the interfaces.

= 01 =1

=01

= 05

=03

= 07

absorber layer. The single-mode condition for the equivalent vertical slab in the EIM is given by (1)

NESHAT et al.: GLOBAL APPROACH FOR MODELING AND ANALYSIS OF EDGE-COUPLED TRAVELING-WAVE TERAHERTZ PHOTOCONDUCTIVE SOURCES

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TABLE I COMPARISON OF PHOTOABSORBER FF AND EFFECTIVE ABSORPTION COEFFICIENT BETWEEN EVEN AND ODD TE MODES. DESIGN m, h : m, PARAMETERS WERE CHOSEN AS h : m, AND  cm h

=03

=1 = 1 2 10

= 01

TABLE II CALCULATED EFFECTIVE INDICES AND MAXIMUM RIDGE WIDTH BASED ON EIM. DESIGN PARAMETERS WERE SELECTED m, h : m, h : m, AS h : m AND h

=1

= 01 = 1 05

= 03

Fig. 5. Cross-sectional profile of the TE field obtained from semi-vectorial BPM. TABLE III DESIGN PARAMETERS USED IN BPM SIMULATION FOR THE OPTICAL WAVEGUIDE SHOWN IN Fig. 2

TABLE IV COMPARISON BETWEEN EIM AND CM

Table II summarizes the calculated effective refractive index of the five-layer slab in the side regions and the six-layer of Fig. 2, along with the maximum slab in the center region ridge width, all with respect to the upper cladding thickness. The EIM can be considered as a fast analysis and design tool. However, more accurate mode solving techniques, such as the correlation method (CM) based on the BPM, should be deployed in the final stages of the design. In the CM, an arbitrary field is launched into the structure and propagated via a normal BPM. During the propagation, a correlation function between the input field and propagating field is computed [15]. The Fourier transform of the computed correlation function should then have a spectrum with peaks at the modal propagation constants. Finally, the corresponding modal fields can be obtained with a second propagation by beating the propagating field against the known propagation constants. Using the initial parameters from the EIM, we deploy the implemented CM in BeamPROB, a commercial software based on BPM [16], to find the modal field distribution and the effective absorption coefficient for the 2-D optical waveguide. There are several considerations that are required to be considered when computing mode eigenvalues and eigenfunctions via the CM. One must launch a field that excites all the possible modes, e.g., a Gaussian beam launched off the center by half the waveguide width. Second, since the eigenvalues are obtained by taking the fast Fourier transform (FFT) of the correlation function, the accuracy and bandwidth of the spectrum are determined by standard Fourier sampling. Namely, the narrowness of the peaks, which determines how closely spaced peaks can be resolved, is

determined by the propagation length; the longer the propagation, the better the resolution. Furthermore, the range of eigenvalues is determined by the sampling period; the shorter the sampling period, the wider the range of eigenvalues [16]. Fig. 5 shows the modal field distribution obtained from a semi-vectorial BPM for the TE mode of the structure shown in Fig. 2. The optical waveguide parameters are given in Table III. The modal analysis showed that the optical waveguide with the given parameters is single mode. The photoabsorber FF, calculated with 1-D analysis, assumes a uniform field distribution laterally, and therefore, it gives an upper limit on the achievable FF in a 2-D ridge waveguide for the same stack of dielectric layers in the ridge region. However, as seen in Fig. 5, the lateral confinement in the ridge is almost ten times smaller than that in the slab core. We observed the same order of difference in the FF calculated from BPM and 1-D calculations. Therefore, to have more accurate FF from 1-D calculation, we define a correction factor (CF) as the ratio of the ridge width to the lateral beam width in the core slab. The modified FF (or the absorption coefficient) calculated from 1-D analysis should then be multiplied by the CF to give more accurate results. Using 2-D analysis, Table IV compares the calculated effective indices and the effective absorption coefficient for several

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upper cladding thicknesses obtained from the EIM and CM. Other parameters are the same as those given in Table III. (3b) III. PHOTO-INDUCED CHARGE CARRIER TRANSPORT (SEMICONDUCTOR SOLVER) To study the charge carrier transport in semiconductor devices, various models including Monte Carlo [17], hydrodynamic [18], and drift-diffusion [19] have been used. Most of them are based on the solution of Poisson’s equation along with the Boltzmann transport equation. In choosing the proper analysis model, it is apparent that a tradeoff between accuracy and complexity should be performed. A. Drift-Diffusion Model We use the drift-diffusion model to calculate the generated photocurrent inside the fast photoconductive layers in the photomixer device. In this model, only the carrier continuity and carrier momentum conservation are included, whereas carrier energy conservation is left out. Despite this, a drift-diffusion model is able to describe the main physical processes inside the photoconductor such as optical generation of carriers and currents and field-screening effect. This model is also relatively simple in numerical implementation compared to other more rigorous models, leading to better convergence of the numerical algorithm and lower computational time. The set of basic drift-diffusion equations in the time domain consists of Poisson’s equation, continuity equations for electrons and holes, and current equations for electrons and holes as follows [20]: (2a) (2b) (2c) where subscripts and distinguish the parameters associated with electron and hole carriers, respectively, is the electric pois the carrier density, is the carrier tential, current density, and are carrier recombination is the net trap conand generation rates, respectively, is centration filled by the charge inside the semiconductor, is the carrier diffusion coefficient, the carrier mobility, is the vacuum permittivity, is the relative permittivity, and is the electron charge. It is important to note that when the cross-sectional dimensions of the device are comparable with the operating wavelength, Poisson’s equation may not give an accurate representation of the electric field in terms of the distributed time-varying charges, and instead the wave equation should be used. In this case, the basic drift-diffusion equations given in (2) are replaced by the following set of equations:

(3a)

(3c) where is the electric vector field, is the speed of light is the permeability of vacuum. It is to note in vacuum, and that higher accuracy is obtained at the expense of greater complexity in using system of equations in (3) instead of that in (2). The set of basic drift-diffusion equations given in (2) can be manipulated by substituting the current equation (2c) into the continuity equations (2b) to yield a system of three partial dif, and ferential equations with dependent variables , (4a) (4b) (4c) The compact system of the basic drift-diffusion equations given in (4) represents the basis of the numerical algorithm for calculation of the photocurrent. B. Generation-Recombination (GR) Process The carrier GR process makes a balance between the electron and hole concentrations inside the semiconductor crystal. Many GR processes have been discovered and explained thus far, among which the Shockley–Read–Hall (SRH) and Auger processes have the most important roles in terahertz photoconductive source modeling. The SRH GR is a phonon transition, which occurs due to trapping of the carriers in the trap states created by the defects in LTG-GaAs. LTG-GaAs is deposited by molecular beam epitaxy (MBE) at low substrate temperature 200 C in an As-rich environment, and then is annealed under an arsenic overpressure at higher temperature, e.g., 600 C for 10–30 min or 700 C or higher for 30 s or less [21]. In LTG-GaAs, because of the low substrate temperature and As-rich growth conditions, about 1% or less excess arsenic is incorporated into the GaAs matrix. During the annealing process, the arsenic precipitates in the form of clusters. The arsenic clusters in annealed LTG-GaAs results in a large trap density that consequently results in a high-re10 cm , large breakdown field 50 V m , sistivity and extremely short carrier lifetime ( 0.2 ps) [21]. In the LTG-GaAs photoconductor, the SRH GR process has a major role because of the existence of high density of trap states. There are four partial processes involved in the SRH GR process [20]. • Electron capture—an electron is transferred from the conduction band to a trap state, and fills up the trap state. • Hole capture—an electron is transferred from the trap state to the valence band and recombines with a hole. The trap state becomes empty. • Electron emission—an electron from the trap state is transferred to the conduction band, and the trap state becomes empty.

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• Hole emission—an electron from the valence band is transferred to a trap state, leaving a hole in the valence band. The trap state is filled up. Combining the above partial processes and assuming that each trap state has an energy level located in the energy bandgap (superscript distinguishes discrete levels), and denoted by the net recombination rate in the presence of electron traps is mathematically given by [20] (5) and is the intrinsic carrier concentration, the parameter accounts for degeneracy effects, and are electron and hole lifetimes, respectively. and For the analysis of electron trapping process based on the represent the trap density for the th level, SRH model, let and assume that the fraction of occupied traps at each energy (a maximum value of 1 for shows a level is denoted by completely full trap state). The dynamics of the trap state occupied by electrons at each level of trap energy can be expressed as where

,

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The Auger recombination rate can be mathematically expressed as [20]

(8) where and are the Auger capture coefficients for the electron and hole, respectively, and are obtained experimentally. C. Optical Generation Upon the optical excitation of the photoconductor, photo-induced electron–hole pairs are generated through absorption of photons. The optical generation rate is given by [12] (9) where is the optical power density, and is obtained from the photonic solver through the analysis discussed in is velocity of light in free Section II, is Plank’s constant, is the optical wavelength in free space, space, is the quantum efficiency, and is the optical absorption coefficient inside the photoabsorber layer. D. Boundary Conditions

(6) The differential equation given in (6) is an additional equation, which is solved along with the basic drift-diffusion system of equations. Equation (6) is coupled to the Poisson’s equation given in (4a) through the occupied trap concentration term (7) where and are densities of ionized deep-donor and represents the deep-acceptor traps, respectively, and density of occupied shallow traps at the trap energy level . The Auger GR is a second important process, which involves three particle transitions. The following four partial processes are involved. • Electron capture—an electron is transferred from the conduction band to the valance band, and recombines with a hole. The excess energy of the electron is released to another electron in the conduction band. • Hole capture—an electron is transferred from the conduction band to the valance band, and recombines with a hole. The excess energy of the electron is released to another hole in the valance band. • Electron emission—an electron from the valance band is transferred to the conduction band by consuming the energy of a high energetic electron in the conduction band. A hole is left in the valance band. • Hole emission—an electron from the valance band is transferred to the conduction band by consuming the energy of a high energetic hole in the valance band. A hole is left in the valance band edge.

Solving the system of partial differential equations given in (4) needs proper boundary conditions for the dependent vari, and . A set of boundary conditions for the ohmic ables , contacts and the interface between a semiconductor and an insulator are briefly discussed. 1) Ohmic Metallic Contacts: The boundary condition for ohmic contacts between a metal and semiconductor are characterized by vanishing total space charge in the semiconductor at the interface. Therefore, the impressed charge accumulation at the interface does not happen, and the incoming carriers to the boundary can move freely in both directions, depending on the applied potential. For ohmic contacts, the boundary conditions for electric potential and carrier concentrations are given by (10) (11) (12) where is the built-in potential due to the fixed charge distri, and is the bias potential applied to the bution metal contact. It is noted that an ohmic contact is characterized by Dirichlet boundary conditions. 2) Semiconductor–Insulator Interface: The boundary conditions for the interface between a semiconductor and an insulating material are given by (13) (14) (15)

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TABLE V PHYSICAL PARAMETERS OF THE MSM PHOTOMIXER WITH LTG-GaAs AS PHOTOABSORBER

Fig. 6. CS of a traveling-wave MSM photomixer.

where and arepermittivitiesof the semiconductor and insulating material, respectively, is the surface charge density at is the surface recombination rate, and is the the interface, unit normal vector at the boundary. It is good to point out that at the interface between the semiconductor and air, assuming no surfacecharges and vanishingsurface recombination velocities, conditions (13)–(15) transform into Neumann boundary conditions.

References:

[23],

[24]

E. Results and Discussion Fig. 6 shows the CS of a traveling-wave metal–semiconductor–metal (MSM) photomixer. It consist of an optical waveguide integrated with a CPS. The optical waveguide is the same as that discussed in Section II and with the physical and geometrical parameters given in Table III. The CPS consists of two metal strips with the width of and separation distance of . The metallic strips act as biasing electrodes, as well is applied as terahertz transmission line. A dc voltage between two electrodes to provide the necessary dc electric field for photocurrent excitation. The theory of photomixing has been very well established in the literature [22], [23], and here we only use the relevant results. Upon the excitation of the optical waveguide with two detuned laser whose frequency difference falls in the terahertz region, photo-induced electron–hole pairs are generated inside the photoabsorber. The density of carriers is modulated with the beat frequency, and terahertz photocurrent is excited inside the photoabsorber due to the applied dc voltage. The cross-sectional terahertz photocurrent is approximated by

Fig. 7. Carrier photogeneration inside the LTG-GaAs layer for the total optical power of 42 mW.

(16) where is the modulation index or grating contrast, is the time-averaged carrier current density calculated from is the angular terahertz frequency, and is the (2c), carrier recombination life time. To solve the basic drift-diffusion equations given in (4) along with the equation governing the dynamics of trap states in (6) at the CS of the MSM photomixer, Taurus Medici,1 a commercial 2-D device simulator was used. Using the parameters given in Table V, Fig. 7 shows the carrier photogeneration inside the LTG-GaAs layer for the total optical power of 42 mW. Fig. 8 shows the electrode dc photocurrent with respect to the applied voltage for the same total optical power. 1Taurus Medici, Synopsys, Parsippany, NJ, 2005. [Online]. Available: http:// www.synopsys.com

Fig. 8. Cross-sectional dc photocurrent of the MSM photomixer with total optical power of 42 mW.

It is known that, in the LTG-GaAs material, the carrier life time at a high dc electric field increases. A model presented in [24] for dependency of the carrier life time on the applied field was used to find the photocurrent presented in Fig. 8. The amplitude of the cross-sectional terahertz photocurrent versus beat frequency is illustrated in Fig. 9 for different dc voltages. The total optical power is assumed 42 mW. As expected, the

NESHAT et al.: GLOBAL APPROACH FOR MODELING AND ANALYSIS OF EDGE-COUPLED TRAVELING-WAVE TERAHERTZ PHOTOCONDUCTIVE SOURCES

Fig. 9. Cross-sectional terahertz photocurrent versus beat frequency for several dc voltages. The total optical power is assumed 42 mW.

Fig. 10. CS of a CPS.

frequency bandwidth of the photomixer decreases by increasing the applied dc voltage, as shown in Fig. 9. This is due to the increase of the carrier life time at higher dc electric fields. IV. ELECTROMAGNETIC MODELING OF ACTIVE REGION (ELECTROMAGNETIC SOLVER) In this section, the aim is to develop a rigorous analytical tool to determine the guided electromagnetic field generated by the photocurrent in the active region of the photomixer. To do so, it is convenient to express the field in terms of the modal fields in the structure. The main advantage of using modes is that they provide the field distribution over the whole space, once their amplitude are known on a given section. In fact, once modal amplitudes are known, it is sufficient to multiply each of them by the corresponding propagation factor to obtain the field at any given point. A. Modal Analysis of CPS The CS of a CPS is shown in Fig. 10. It consists of two metallic strips with the width of running in parallel on a dielectric substrate with the relative permittivity of and thickness of . The strips are separated with the distance . For modal analysis, it is assumed that the structure is uniform along the -direction, and also is infinite. CPS is an open waveguide and its complete spectra includes both discrete and continuous spectrum representing bound modes and radiation modes, respectively [25]. Bound modes falls into two categories; the guided modes, which propagates along the CPS, and their modal field distribution is mostly

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concentrated around the strips, and surface waves, which propagate in an angle away from the strips, and their modal field is distributed all over the dielectric substrate. On a uniform coplanar transmission line, it is expected for the dominant mode to be a purely guided mode, and this is true at the lower and middle ranges of frequency. However, as the frequency exceeds a critical value determined by the dielectric constant and the relative CS dimensions, the dominant mode wavenumber becomes complex and power leaks away into the substrate at an angle from the transmission line in the form of a surface wave. In fact, the CPS dominant mode will become leaky and lose energy by exciting surface waves once the dispersion curve for the lowest surface wave far from the CPS center electrodes crosses the dispersion curve for the dominant CPS mode [26]. The mode wavenumber becomes complex if the structure is infinite laterally; if it is finite on the sides, the wavenumber may remain real and the leaking power still spreads out, but is reflected from the sides [27]. In any case, power can be coupled to a neighboring line, resulting in undesired crosstalks. Shah et al. have used electrooptic sampling to measure photoconductively generated signals on CPSs [28]. They performed field measurements at positions laterally displaced from the center of the transmission line to demonstrate that the surface waves are indeed excited in the terahertz range. To avoid the excitation of surface waves, one way is to add a superstrate for elimination of the dielectric inhomogeneity encountered by the electric field [29]. However, tiny air gaps or an insufficient thickness of the superstrate layer will degrade the performance. A superior approach appears to be the reduction of the substrate thickness, as in the guiding structures demonstrated by Keil et al. [30], where the substrate material has been mostly etched away, leaving almost freestanding metal coplanar electrodes, or by Cheng et al. [31], where a CPS has been fabricated on a 1.4- m-thick membrane. From the design point of view, the thickness of the SI-GaAs substrate should be selected small enough in order to prevent the leakage of the guided mode into the surface waves on the one hand, but on the other hand, the chip should have enough rigidity and mechanical strength for handling and manipulation. To study all surface waves supported in a multilayer substrate, and to find the characteristic equation governing their propagation constants, the transverse resonance technique [32] was deployed, as it is straightforward and easy to implement. Fig. 11 shows the normalized propagation constant or the efversus frequency for all possible fective index surface waves supported in a symmetric dielectric slab wavem guide. Layer parameters were chosen as follow: m in Fig. 11(b). For this simulation, in Fig. 11(a) and and . For a symmetric dielectric slab waveguide, the cutoff fre, of the th-order surface wave is given quency, at which by (17) Therefore, by decreasing the slab thickness , the cutoff frequency inversely increases, and by choosing a proper thickness,

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boundary conditions should be solved using a numerical technique, e.g., the finite-element method (FEM) [33]. Since the FEM with finite size discretization elements are applicable only to close waveguide problems, its application to the analysis of open waveguides must be adapted to model an open infinite region. A simple approach is to enclose the waveguide in a large enough fictitious boundary. A zero boundary condition such as a perfect electric conductor (PEC) or perfect magnetic conductor (PMC) is then applied at the fictitious boundary to define the boundary-value problem uniquely. The drawback of this approach is that for a given accuracy, correct location of the fictitious boundary is unknown, although it can be determined iteratively at the expense of more computational efforts. The boundary must also be sufficiently far away from the waveguide and the distance between the boundary and waveguide must be increased as the propagation constant approaches cutoff (for open waveguide structures, cutoff is usually defined rather than as for closed waveguides [33]). as Since the asymptotic dependence of the fields in a transverse plane can be expressed as for

(20)

for where

Fig. 11. Normalized propagation constant versus frequency for a symmetric m and (b) d m. For this dielectric slab waveguide with: (a) d and  : . simulation, 

=1

= 12 9

= 150

= 20

all higher order surface waves are suppressed within a given frequency range of interest, as demonstrated in Fig. 11(b). It is and modes noted that since the cutoff frequency of is zero, they can exist at any given frequency. However, by choosing proper design values for , , and in Fig. 10, it is possible to make the propagation constant of the fundamental and guided mode of the CPS greater than that of the modes to prevent the leakage. Presence of the strips in the CPS structure produces transverse diffraction, which cannot be represented by TE or TM modes alone, and rigorously hybrid modes should be considered. Assuming that the infinite axis of the guide is along the -axis, as shown in Fig. 10, and the wave is propagating in the -direction, the guided modal fields can be expressed as (18) (19) where denotes the angular frequency and denotes the propand agation constant. To find eigenfunctions eigen value , a standard eigenvalue problem with appropriate

, the fields decay exponentially when , but propagate to infinity when . Therefore, this approach is suitable only when the propagation characteristics in the guided-wave region is concerned. In the region of , this approach could result in enormous errors since the fictitious PEC or PMC boundary conditions prevents the energy from traveling away from the waveguide, and completely reflects the incoming wave back into the computational domain. In order to overcome such deficiency, the so-called absorbing boundary conditions (ABCs) have been introduced. The ABCs simulate or replace the infinite space that surrounds a finite computational domain. It should be noted that the solution computed within an ABC is an estimate to the solution that would be computed within a really infinite domain. Moreover, the ABCs only absorb fields produced by sources located inside the surrounded domain, and they cannot be placed outside the ABCs. Over the years, various ABCs from the extrapolation [34] or the radiating boundary [35] to the perfectly matched layer (PML) [36] and the complementary operators method [37] have been developed. Among all ABCs, the PML has been proven to be advantageous in modal analysis [38]–[40], e.g., it can be placed closer to the guide. To make use of the PML in modal analysis, COMSOL Multiphysics, a commercial software based on the FEM [41], was deployed. Selecting the physical and geometrical parameters similar to those given in Table VI, Fig. 12 shows the results obtained from modal analysis. In Fig. 12(a), the normalized propagation constant of the CPS mode is compared with those of surface wave modes. A higher effective index of the CPS mode prevents any power leakage into the surface waves. In Fig. 12(b), the total loss due to the metallic and dielectric losses are shown with respect to the frequency. It should be noted that the metallic loss was dominant at all frequencies.

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TABLE VI CPS STRUCTURE PARAMETERS

Fig. 13. Arbitrary current distribution in an open waveguide.

on distributed-source transmission line theory [43]. Here, we apply a rigorous method to find the field radiated by an arbitrary impressed photocurrent distribution in an open guide. In this rigorous method, the radiated field is expanded in terms of a suitable set of orthogonal modes, and the amplitude coefficients in this expansion are determined by applying the Lorentz reciprocity theorem. This approach has been applied to the classic problem of the excitation of modes by a probe in closed cylindrical waveguides [44], and here it is extended to be used for open waveguides. Unlike closed waveguides that comprise an infinite numerable spectrum of discrete modes, open waveguides comprise a few discrete (guided) modes and a continuous (radiative) spectrum [45]. It is possible to apply reciprocity to an open waveguide as long as the mode of interest is confined and mode orthogonality can still be applied, which is usually the case if one chooses the expansion modes (discrete and continuous) properly. represents an arbitrary curWith reference to Fig. 13, let rent distribution in an open waveguide, e.g., it could be the generated photocurrent inside the photoabsorber layer in Fig. 6. Fields for the th guided mode propagating in the positive -direction are represented as follows: (21a) (21b) and for propagation along the negative -direction, the fields are then given by Fig. 12. (a) Normalized propagation constant versus frequency for CPS mode (dotted line), TE surface wave mode (solid line), and TM surface wave mode (dashed line). (b) Loss (dashed line) and power absorption length (dotted line). Structure parameters are given in Table VI.

Terahertz power absorption length is also shown in Fig. 12(b). Power absorption length is defined as the length after which the or 37%. terahertz power drops off by a factor of Modal analysis results obtained in this section will be used in the subsequent sections to calculate the generated terahertz signal coupled to the CPS. B. Calculation of the Generated Terahertz Signal Based on Lorentz Reciprocity Theorem Electromagnetic modeling of traveling-wave photomixers can be addressed through a semi-analytical approach based

(22a) (22b) and are transverse vector eigenIn (21) and (22), , functions dependent on the transverse coordinates, i.e., and are longitudinal vector functions of the whereas transverse coordinates. Discrete eigenfunctions are mutually orthonormal over the guide CS so that (23) where represents the Kronecker delta function. The above orthogonal property is also valid for degenerate modes [44].

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The response of the guide to a source involves excitation of the discrete (guided) modes of the CPS, as well as of a continuum of modes, which radiate transversally, and either propagate, or are evanescent along the guide axis . Such docontinuous modes can be seen as wave packets in the main [45]. Each packet corresponds to a fixed value of , the transverse wavenumber, which individually satisfy boundary and edge conditions on the strips, radiation at infinity, and continuity of the tangential fields at the interfaces between dielectrics. For a given , there is still the possibility of degeneracy, which is the existence of a number of different strip currents and field configurations satisfying all boundary and edge conditions, pertaining to the same value of , which are labeled by the discrete index . It can be shown that wave packets corresponding to difand of the discrete index are mutually ferent values of orthonormal over the cross section [25] as follows: (24)

and surface composed of the two cross-sectional planes , and a cylindrical sidewall, which expands to infinity, as in Fig. 13. There is no contribution to the surface integral arising and are from the sidewall since guided modal fields exponentially decaying, as seen from their asymptotic behavior given in (20), and they become zero on the sidewall, which is located at a transversally far away distance. When the expansion (25) and (26) for and on the cross sections are used along and with mode orthogonality, the amplitudes of the forward backward propagating waves of the th guided mode outside the active region are obtained as (28a) (28b) It should be noted that in (28), is the modal field of interest, which is obtained from the modal analysis discussed in Section IV-A, and also the integration is performed on the is distributed. volume where the current C. Results and Discussion

and . The orthogonality rewhere lation also exists between guided and radiative modes. Beside orthogonality, the completeness of the combined discrete and continuous spectra of an open waveguide has been proven in [25, Ch. 7]. Therefore, any field radiated in the positive -direction by the impressed current distribution can be expanded in terms of discrete and continuos eigenmodes as (25a)

(25b) and the field radiated in the negative -direction can be represented by

(26a)

The traveling-wave photocurrent and fundamental quasi-TEM mode of the CPS inside the active region can be expressed as (29a) (29b) (29c) where is the cross-sectional current distribution obis the effective optical power absorptained in Section III-E, tion calculated in Section II, is the angular difference freis the current phase quency of two lasers, and are the 2-D modal field dispropagation, and tribution and propagation constant of the quasi-TEM mode of CPS, respectively, obtained in Section IV-A. It should be noted is normalized according to (23). Substituting (29) that into (28), and assuming that the active region is distributed from to , the expansion coefficients of the forward and backward propagating waves of the quasi-TEM mode of CPS outside the active region are obtained as (30a)

(26b) In particular, the expansion (25) gives the radiated field on the cross-sectional plane , whereas (26) gives the radiated field , as shown in Fig. 13. on From Lorentz reciprocity theorem [44], (27)

(30b) where (31a) (31b)

where and are the total fields radiated by the current , surface encloses the current distribution , and has been chosen as the inward-directed normal to . We now choose the

(31c) (31d)

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Fig. 14. Amplitude of complex coefficient: (a) C ( ; K ) and (b) C ( ; K ) with respect to the terahertz mode propagation constant. Parameters are the optical absorption length 1= = 434:8 m, optical effective refractive index n = 3:49562, and beat frequency f = 500 GHz.

Fig. 15. Calculated terahertz mode power coupled in: (a) forward direction and (b) backward direction versus normalized active region length. Solid lines are for the case of unmatched phase velocity ( =K = 0:73) and dotted lines are for the matched phase velocity ( =K = 1). Parameters are the optical absorption length l = 434:8 m, total optical power 42 mW, optical effective refractive = 40 V. index n = 3:49562, beat frequency f = 500 GHz, and V

Shown in Fig. 14 are the amplitude of complex coefficients and with respect to the normalized terahertz mode propagation constant. In Fig. 14, it is assumed that the optical power absorption coefficient and the effective re, respectively, fractive index are 2300 m and as given in Table IV. The beat frequency is 500 GHz. From Fig. 14(a), it is evident that when phase velocity matching conbetween the traveling-wave photocurrent and dition the propagating mode occurs, maximum power is coupled in the forward direction. Moreover, by increasing the active region length up to a maximum length, the peak increases. Any length longer than about four times the optical absorption length does not effectively increase the terahertz mode power. This is due to the fact that the amplitude of the traveling-wave photocurrent approaches zero value. For the CPS structure parameters given in Table VI, the normalized terahertz mode propagation at 500 GHz. It is worth noting that constant is this ratio can approach unity by using, e.g., slow-wave transmission lines [46], or by confining the terahertz mode entirely in a dielectric waveguide with a refractive index close to that of the optical waveguide.

Fig. 15 shows the calculated terahertz mode power coupled and backward . Solid lines in the forward direction , are for the case of unmatched phase velocity whereas dotted lines show the matched phase velocity case . In Fig. 15, other parameters are selected as follow; m, total optical the optical absorption length , power 42 mW, optical effective refractive index beat frequency GHz, and V. In the unmatched phase velocity case, the forward mode power has a resonance behavior with respect to the length of the active region. Its peak value happens at a certain length around . In the matched phase velocity case, the forward mode power increases when the active region becomes longer and start to saturate beyond a length of about four times the optical absorption length. Comparing the graphs in Fig. 15(a) reveals that by satisfying the phase match condition and assuming the modal field and current distribution does not change, the coupled power will increase by a factor of around 2 for the equal length and by a factor of about 8 for the increased length. Moreover, by comparing Fig. 15(a) and (b), it is evident

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relates to the field attenuation constant. The power absorption coefficient is then obtained by doubling the field attenuation constant. To find the power absorption coefficient, the more rigorous approach is to use a complex dielectric permittivity for the photoabsorbing layer, and solve the effective index problem with complex numbers. Here, a second approach, which is much simpler with reasonable accuracy, is discussed. For illustration, consider a mode propagating in the -direction. The mode is partly in the absorbing region. Assuming the absorption is small such that the mode does not change substantially by propagating denotes the total a short incremental distance , and power at point , the total power at point is given by (32) Fig. 16. Maximum achievable mode power with respect to frequency for a traveling-wave MSM photomixer shown in Fig. 6. The optical, semiconductor, and electromagnetic parameters used for this simulation are give in Tables III, V, and VI, respectively.

that the power coupled in the backward direction is negligibly small compared to that coupled in the forward direction. Fig. 16 shows the maximum achievable mode power with respect to frequency for a traveling-wave MSM photomixer illustrated in Fig. 6. The optical, semiconductor, and electromagnetic parameters used for this simulation are given in Tables III, V, and VI, respectively. For the unmatched case, the peak power is selected at the resonance length, whereas in the matched case, it is assumed that the active region is long enough to get the maximum power. It should be noted that the calculated values for the level of the generated terahertz power are comparable with some of the experimental results reported in the literature [47]. V. CONCLUSION Rigorous analysis of CW traveling-wave terahertz photomixers demands for a global approach, which includes all the involved physical phenomena. The main aim of this paper was to establish such an approach by formulating an example structure. Moreover, several advancements have been introduced in the design and analysis of such terahertz sources. For example, a systematic method was proposed for the optical waveguide design. The main design parameter is the optical FF of the photoabsorbing region, which determines the absorption length and the optimum length of the active region. Moreover, in the drift-diffusion model, the trap charge dynamic was included in the formulation to increase the accuracy and to prevent nonphysical net charge creation. Additionally, by representing the total field in terms of the guided and radiated modes, a rigorous method was proposed to find the coupled terahertz power into any desired guided mode. The importance of phase velocity match was studied numerically. Finally, the proposed global analysis approach can be used for optimization of both material and geometry for increased optical-to-terahertz power conversion in terahertz photoconductive sources. APPENDIX In Fig. 2, since one of the layers are lossy, the effective refractive index becomes a complex number whose imaginary part

where is the photoabsorber FF, and is the bulk power absorption coefficient of the photoabsorbing material. Dividing both sides of (32) by , rearranging the terms and letting yields a first-order ordinary differential equation for as (33) Knowing the total optical power at , the total power at any other point along the propagation path is readily obtained from (34a) (34b) From (34), when a mode is partially confined in a photoabcan be sorbing region, the effective absorption coefficient determined by multiplying the bulk absorption coefficient of the photoabsorbing material and the mode’s FF in the photoabsorber. From the effective absorption coefficient, one can deas a length after which the optical fine the absorption length power drops off by a factor of

(35)

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[7] M. Mikulics, E. A. Michael, M. Marso, M. Lepsa, A. van der Hart, H. Lüth, A. Dewald, S. Stanˇcek, M. Mozolik, and P. Kordoˇs, “Travelingwave photomixers fabricated on high energy nitrogen-ion-implanted GaAs,” Appl. Phys. Lett., vol. 89, no. 7, Aug. 2006, Art. ID 071103. [8] M. Mikulics, E. A. Michael, R. Schieder, J. Stutzki, R. Güsten, M. Marso, A. van der Hart, H. P. Bochem, H. Lüth, and P. Kordoˇs, “Traveling-wave photomixer with recessed interdigitated contacts on lowtemperature-grown GaAs,” Appl. Phys. Lett., vol. 88, no. 4, Jan. 2006, Art. ID 041118. [9] D. Saeedkia, S. Safavi-Naeini, and R. R. Mansour, “The intraction of laser and photoconductor in a continuous-wave terahertz photomixer,” IEEE J. Quantum Electron., vol. 41, no. 9, pp. 1188–1196, Sep. 2005. [10] D. Pasqualini, A. Neto, and R. A. Wyss, “Distributed sources on coplanar waveguides: Application to photomixers for THz local oscillators,” Microw. Opt. Technol. Lett., vol. 33, no. 6, pp. 430–435, 2002. [11] E. R. Brown, “A photoconductive model for superior GaAs THz photomixer,” Appl. Phys. Lett., vol. 75, no. 6, pp. 769–771, 1999. [12] D. Saeedkia and S. Safavi-Naeini, “Modeling and analysis of a multilayer dielectric slab waveguide with applications in edge-coupled terahertz photomixer sources,” J. Lightw. Technol., vol. 25, no. 1, pp. 432–439, Jan. 2007. [13] Y. Kokubo and I. Ohta, “Refractive index as a function of photon energy for AlGaAs between 1.2 and 1.8 eV,” J. Appl. Phys., vol. 81, no. 4, pp. 2042–2043, Feb. 1997. [14] , T. Tamir, Ed., Guided-Wave Optoelectronics, 2nd ed. Berlin, Germany: Springer-Verlag, 1990, p. 321. [15] R. Scarmozzino, A. Gopinath, R. Pregla, and S. Helfert, “Numerical techniques for modeling guided-wave photonic devices,” IEEE J. Sel. Top. Quantum Electron., vol. 6, no. 1, pp. 150–162, Jan./Feb. 2000. [16] BeamPROP. Rsoft Design Group, Ossining, NY, 2003. [Online]. Available: http://www.rsoftdesign.com/ [17] A. Reklaitis, “Monte carlo analysis of terahertz oscillations of photoexcited carriers in GaAs p-i-n structures,” Phys. Rev. B, Condens. Matter, vol. 74, pp. 165 305-1–165 305-9, Oct. 2006. [18] A. W. Smith and K. F. Brennan, “Hydrodynamic simulation of semiconductor devices,” Prog. Quantum. Electron., vol. 21, no. 4, pp. 293–360, 1998. [19] D. Pasalic and R. Vahldieck, “A hybrid drift-diffusion-TLM analysis of traveling-wave photodetectors,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 9, pp. 2700–2706, Sep. 2005. [20] S. Selberherr, Analysis and Simulation of Semiconductor Devices. Wien, Austria: Springer-Verlag, 1984. [21] M. R. Melloeh, J. M. Woodall, E. S. Harmon, N. Otsuka, F. H. Pollak, D. D. Nolte, R. M. Feenstra, and M. A. Lutz, “Low-temperature grown III–V materials,” Annu. Rev. Mater. Sci., vol. 25, pp. 547–600, 1995. [22] E. Brown, “Terahertz generation by photomixing in ultrafast photoconductors,” in Terahertz Sensing Technology: Electronic Devices and Advanced Systems Technology. Singapore: World Sci., 2003, vol. 1. [23] D. Saeedkia, “Modeling and design of photoconductive and superconductive terahertz photomixer sources,” Ph.D. dissertation, Dept. Elect. Comput. Eng., Univ. Waterloo, Waterloo, ON, Canada, 2005. [24] N. Zamdmer, Q. Hu, K. A. McIntosh, and S. Verghese, “Increase in response time of low-temperature-grown GaAs photoconductive switches at high voltage bias,” Appl. Phys. Lett., vol. 75, no. 15, pp. 2313–2315, 1999. [25] T. Rozzi and M. Mongiardo, Open Electromagnetic Waveguides, ser. IEE Electromagn. Waves 43. London, U.K.: IEE Press, 1997. [26] Y. D. Lin, J. W. Sheen, and C. Y. Chang, “Surface-wave leakage properties of coplanar strips,” in IEEE MTT-S Int. Microw. Symp. Dig., May 1995, vol. 1, pp. 229–232. [27] H. Shigesawa, M. Tsuji, and A. A. Oliner, “Dominant mode power leakage from printed-circuit waveguides,” Radio Sci., vol. 26, no. 2, pp. 559–564, Mar.–Apr. 1991. [28] S. A. Shah, A. Zeng, M. K. Jackson, L. Pouliot, A. Lecours, and J. F. Currie, “Guided surface waves in photoconductive excitation,” IEEE Microw. Guided Wave Lett., vol. 6, no. 9, pp. 309–311, Sep. 1996. [29] J. Nees, S. Williamson, and G. Mourou, “100 GHz travelling-wave electro-optic phase modulator,” Appl. Phys. Lett., vol. 54, pp. 1962–1964, May 1989. [30] U. D. Keil, D. R. Dykaar, A. F. J. Levi, R. F. Kopf, L. N. Pfeiffer, S. B. Darack, and K. W. West, “High-speed coplanar transmission lines,” IEEE J. Quantum Electron., vol. 28, no. 10, pp. 2333–2342, Oct. 1992. [31] H. Cheng, J. F. Whitaker, T. M. Weller, and L. P. B. Katehi, “Terahertzbandwidth pulse propagation on a coplanar stripline fabricated on a thin membrane,” IEEE Microw. Guided Wave Lett., vol. 4, no. 3, pp. 89–91, Mar. 1994.

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[32] “Transverse resonance technique,” in Numerical Techniques for Microwave and Millimeter-Wave Passive Structure, T. Itoh, Ed. New York: Wiley, 1989. [33] J. Jin, The Finite Element Method in Electromagnetics, 2nd ed. New York: Wiley, 2002. [34] A. Taflove and M. E. Brodwin, “Numerical solution of steady-state electromagnetic scattering problems using the time-dependant Maxwell’s equations,” IEEE Trans. Microw. Theory Tech., vol. TMTT-23, no. 8, pp. 623–630, Aug. 1975. [35] R. Holland, “THREDE: A free-field EMP coupling and scattering code,” IEEE Trans. Nucl. Sci., vol. NS-24, no. 6, pp. 2416–2421, Dec. 1977. [36] J. P. Berenger, Perfectly Matched Layer (PML) for Computational Electromagnetics. San Rafael, CA: Morgan & Claypool, 2007. [37] O. M. Ramahi, “Complementary operators: A method to annihilate artificial reflections arising from the truncation of the computational domain in the solution of partial differential equations,” IEEE Trans. Antennas Propag., vol. 43, no. 7, pp. 697–704, Jul. 1995. [38] W. P. Huang, C. L. Xu, W. Lui, and K. Yokoyama, “The perfectly matched layer boundary condition for modal analysis of optical waveguides: Leaky mode calculations,” IEEE Photon. Technol. Lett., vol. 8, no. 5, pp. 652–654, May 1996. [39] S. Selleri, L. Vincetti, and M. Zoboli, “Truncation of finite-element mesh for modal analysis of dielectric waveguides,” Microw. Opt. Technol. Lett., vol. 32, no. 3, pp. 178–182, Dec. 2001. [40] H. E. Hernandez-Figueroa, F. A. Fernandez, and J. B. Davies, “Finite element approach for the modal analysis of open-boundary waveguides,” Electron. Lett., vol. 30, no. 24, pp. 2031–2032, Nov. 1994. [41] COMSOL 3.5a. COMSOL AB, Burlington, MA, 2008. [Online]. Available: http://www.comsol.com [42] M. Ordal, L. Long, R. Bell, S. Bell, R. Bell, R. Alexander, and C. Ward, “Optical properties of the metals Al, Co, Cu, Au, Fe, Pb, Ni, Pd, Pt, Ag, Ti, and W in the infrared and far infrared,” Appl. Opt., vol. 22, no. 7, pp. 1099–1120, Apr. 1983. [43] M. Neshat, D. Saeedkia, and S. Safavi-Naeini, “Semi-analytical calculation of terahertz signal generated from photocurrent radiation in traveling-wave photonic mixers,” Int. J. Infrared Millim. Waves, vol. 29, no. 9, pp. 809–822, Sep. 2008. [44] R. E. Collin, Field Theory of Guided Waves, 2nd ed. New York: IEEE Press, 1990. [45] T. Rozzi and G. Cerri, “Radiation modes of open microstrip with applications,” IEEE Trans. Microw. Theory Tech., vol. 43, no. 6, pp. 1364–1370, Jun. 1995. [46] E. Bottcher and D. Bimberg, “Millimeter wave distributed metal–semiconductor–metal photodetectors,” Appl. Phys. Lett., vol. 66, no. 26, pp. 3648–3650, Jun. 1995. [47] E. A. Michael, B. Vowinkel, R. Schieder, M. Mikulics, M. Marso, and P. Kordos, “Large-area traveling-wave photonic mixers for increased continuous terahertz power,” Appl. Phys. Lett., vol. 86, no. 11, pp. 111 120–111 123, 2005.

Mohammad Neshat (S’99–M’10) received the B.Sc. degree in electrical engineering from the Isfahan University of Technology, Isfahan, Iran, in 1998, the M.Sc. degree in electrical engineering from the Sharif University of Technology, Tehran, Iran, in 2000, and the Ph.D. degree in electrical engineering from the University of Waterloo, Waterloo, ON, Canada in 2009. His doctoral dissertation concerned resonance-based on-chip biosensing in terahertz range. From 2000 to 2005, he was a Research and Developement Engineer involved in the area of microwave engineering for several telecommunication companies in Tehran, Iran. He is currently a Postdoctoral Fellow with the Microwave and Terahertz Photonics Integrated System Laboratory (MISL), University of Waterloo. His current research interests include modeling of integrated terahertz and millimeter-wave devices, terahertz spectroscopy and imaging for biomedical applications, biochips based on terahertz technology, and electromagnetic modeling of bio-molecules in the terahertz region.

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Daryoosh Saeedkia received the B.Sc. and M.Sc. degrees in electrical engineering from the Sharif University of Technology, Tehran, Iran, in 1995 and 2001, respectively, and the Ph.D. degree in electrical and computer engineering (with outstanding achievement in graduate studies designation) from the University of Waterloo, Waterloo, ON, Canada, in 2005. From 1995 to 2001, he was with the Optical Fiber and Solar Cell Fabrication Company, Tehran, Iran, as a Head Engineer of the optical fiber production line. From 2005 to 2007, he was initially a Postdoctoral Fellow and then a Research Assistant Professor with the Electrical and Computer Engineering (ECE) Department, University of Waterloo. From 2007 to 2008, he was a Natural Sciences and Engineering Research Council of Canada (NSERC) Postdoctoral Fellow with the Engineering Physics Department, McMaster University, Hamilton, ON, Canada. In Summer 2008, he was a Visiting Faculty with the Division of Engineering and Applied Science, California Institute of Technology, Pasadena. From 2006 to January 2010, he was the Chief Technology Officer of T-Ray Science Inc. He is the developer and the coordinator of the Microwave and Terahertz Photonics Integrated System Laboratory (MISL) (a world-class terahertz photonics research laboratory), Department of Electrical and Computer Engineering, University of Waterloo. His research interests are in the areas of theoretical investigation and physical modeling of millimeter- and terahertz-wave photonics and opto-electronics devices and systems, study of the interaction of terahertz waves with biological, organic, and inorganic materials, as well as the interaction of terahertz waves with novel electromagnetic structures such as photonic bandgap, surface plasmon, and metamaterial structures for a variety of photonics and opto-electronics applications including terahertz system-on-chip applications, and device and system development for real-world terahertz applications with an emphasis on pharmaceutical and life sciences applications. Dr. Saeedkia was the recipient of the 2008 Douglas R. Colton Medal for Research Excellence in Canada, the 2007 Natural Science and Engineering Research Council of Canada (NSERC) Postdoctoral Fellowship Award, and the 2006 NSERC Innovation Challenge Award.

Leila Rezaee (S’06–M’09) received the M.Sc. degree in electrical engineering from the University of Tehran, Tehran, Iran, in 2001, and the Ph.D. degree from the University of Waterloo, Wateroo, ON, Canada, in 2008. From 1999 to 2002, she was with the Thin Film Laboratory (TFL), University of Tehran. Since 2003, she has been involved with the modeling and simulation of gate–oxide breakdown in sub-100-nm CMOS technology. She is currently a Researcher with the Microwave and Terahertz Photonics In-

tegrated System Laboratory (MISL), University of Waterloo, where she is focused on the modeling and characterization of photoconduction in terahertz devices. Her research interests and activities include the study of the reliability issues in MOSFETs, the physics of degradation and breakdown phenomena in gate–oxide films, the characterization and reliability of high-k materials, and modeling of nanoscale plasma silicon MOSFETs for terahertz detection. Dr. Rezaee was the recipient of the 2002 Silver Material Research Society (MRS) Student Award for her publications on low-temperature silicon crystallization on glass.

Safieddin Safavi-Naeini (M’79) received the BSc. degree in electrical engineering from the University of Tehran, Tehran, Iran, 1974, and the MSc. and Ph.D. degrees in electrical engineering from the University of Illinois at Urbana-Champaign, in 1975 and 1979, respectively. From 1980 to 1995, he was a Faculty Member with the School of Engineering, University of Tehran. In 1996, he joined the University of Waterloo, Waterloo, ON, Canada, where he is currently a Professor with the Department of Electrical and Computer Engineering. He holds the Research in Motion (RIM)/Natural Science and Engineering Research Council of Canada (NSERC) Industrial Research Chair in Intelligent Radio/Antenna and Photonics. He is also the Director of a newly established Center for Intelligent Antenna and Radio System (CIARS), University of Waterloo. He has led several international collaborative research programs with research institutes in Germany, Finland, Japan, China, Sweden, and the U.S. His research activities concern RF/microwave technologies, smart integrated antennas and radio systems, millimeter-wave/terahertz integrated technologies, nanoelectromagnetics and photonics, electromagnetics (EM) in health science and pharmaceutical engineering, antenna, wireless communications and sensor systems and networks, new EM materials, bioelectromagnetics, and computational methods.

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Tunable Subterahertz Wave Generation Based on Photonic Frequency Sextupling Using a Polarization Modulator and a Wavelength-Fixed Notch Filter Shilong Pan, Member, IEEE, and Jianping Yao, Senior Member, IEEE

Abstract—Optical frequency multiplication based on electrooptical modulation is an effective way to generate high-spectral-purity and frequency-tunable subterahertz waves. The previously demonstrated frequency-doubling and quadrupling techniques based on a Mach–Zehnder modulator have a low multiplication factor and suffer from bias drift problem and residual chirp. In this paper, a novel approach to achieving frequency sextupling using a polarization modulator and a wavelength-fixed optical notch filter is proposed and experimentally demonstrated. The method is free from bias drift problem and residual chirp, which can be used to generate high-spectral-purity subterahertz wave signals using relatively low-frequency electrical and optical devices. By using a narrow-bandwidth fiber Bragg grating as a wavelength-fixed optical notch filter, a high-spectral-purity microwave signal tunable from 18 to 27.6 GHz is generated when a microwave drive signal from 3 to 4.6 GHz is applied to the polarization modulator. The phase noise of the generated signal is measured as low as 107.57 dBc/Hz at a 10-kHz offset frequency. By replacing the narrow-bandwidth notch filter by an optical interleaver, a subterahertz wave tunable from 66 to 114 GHz is generated when the drive signal is tuned from 11 to 19 GHz. The distribution of the generated signal over optical fiber is investigated. The results show that the quality of the distributed subterahertz wave signal is maintained after transmission over a 40-km standard single-mode fiber. Index Terms—Microwave photonics, polarization modulator, terahertz generation.

I. INTRODUCTION

M

ILLIMETER waves and terahertz waves, covering a frequency range from 30 GHz to 10 THz, are very attractive for applications in spectroscopic sensing [1]–[3] and ultrabroadband wireless communications [4], [5]. A spectroscopic system using frequency-tunable continuous-wave (CW) terahertz sources is found to have a higher signal-to-noise ratio and spectral resolution as compared with a pulsed-terahertz-based system [6]. To generate high-frequency and frequency-tunable CW terahertz waves, the most promising method is to heterodyne two light waves at a photomixer or photodetector with a Manuscript received October 01, 2009; revised February 08, 2010; accepted March 11, 2010. Date of publication June 28, 2010; date of current version July 14, 2010. This work was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC). The authors are with the Microwave Photonics Research Laboratory, School of Information Technology and Engineering, University of Ottawa, Ottawa, ON, Canada K1N 6N5 (e-mail: [email protected]). Color versions of one or more figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2010.2050182

wavelength difference that falls in the terahertz range [7]. To generate a terahertz wave with high spectral purity, the two optical waves applied to the photomixer or photodetector for heterodyne must be phase correlated. A simple and cost-effective way to produce two optical waves is to employ a dual-wavelength single-longitudinal-mode laser source [8]–[12] or two free-running semiconductor lasers [13]. However, the generated terahertz wave has a large phase noise. To increase the phase correlation, an optical phase-locked loop (PLL) can be employed [14]–[16]. However, expensive electrical devices operating at high frequency are required to extract the phase information from the high-frequency beat signal, which makes the system complicated and costly. Two phase-correlated optical waves can also be generated by optical frequency multiplication of a low-frequency microwave reference signal, in which a single laser source is needed. Since the frequency multiplication is a nonlinear process, a nonlinear device must be used, which can be a highly nonlinear fiber (HNLF) or a semiconductor optical amplifier to achieve fourwave mixing (FWM) [17]–[19] leading to the generation of a frequency-tripled electrical signal. The major problem associated with the FWM effects is its ultralow conversion efficiency. Frequency multiplication can also be achieved using an optical modulator [20]–[29]. Compared with the use of a nonlinear optical device, the techniques using an optical modulator are of greater interest thanks to the simplicity, tunability, higher nonlinear efficiency, and better stability. For instance, an optical frequency comb consisting of multiple optical spectral lines was generated by phase modulation of an optical carrier at an electrooptic phase modulator [20]–[22]. With two narrowband optical filters to select two of these spectral lines, two phase-correlated light waves with a frequency spacing tunable from the ( can be larger than 50) times the reference frequency to reference frequency are obtained, which can be used to generate a low phase noise and continuously frequency-tunable subterahertz-wave signal. However, the two optical filters must be tunable to ensure the frequency tunability. To generate a frequency-tunable millimeter-wave signal without using tunable optical filters, Qi et al. proposed using a Mach–Zehnder modulator (MZM) that was biased at the maximum transmission point to eliminate the odd-order sidebands [23]. By using a wavelength-fixed optical notch filter to remove the optical carrier, a microwave or millimeter-wave signal with a frequency that is four times the frequency of the microwave drive signal was generated. The frequency tunability was achieved by simply tuning the frequency of the microwave

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drive signal. Other configurations that can be used to achieve frequency quadrupling include the use of two cascaded LiNbO MZMs that are biased at the minimum transmission points [24] and the use of a specially designed LiNbO MZM consisting of three sub-MZMs which are also biased at the minimum transmission points [25]. A disadvantage of the approaches in [23]–[25] is the bias drift of the MZMs. The bias drift of the MZMs which are biased at the minimum or maximum transmission points would significantly affect the spectral purity of the generated signal. Based on [30], a 2% drift of the dc bias can make the suppression ratio of the first-order sideband to the carrier drop by 30 dB. More impor% drift of the tant, the bias drift is intrinsic for a MZM; the dc bias may happen in several seconds, which makes the system unstable or a sophisticated control circuit is needed to stabilize the operation. In addition, it is difficult to achieve an ideal 50/50 splitting ratio in the Y-splitter of a MZM due to the fabrication tolerances, which would result in a residual chirp, leading to a poor suppression of the odd-order or even-order sidebands even when the bias of the MZM is carefully adjusted, which would degrade the spectral purity of the generated electrical signals. The situation would be more severe when the frequency of the drive signal is high, making the scheme only applicable for the generation of an electrical signal at a few tens of gigahertz. To avoid the above problems, an optical phase modulator may be used to replace the MZM [26], [27]. Again, by using a wavelength-fixed optical filter to remove the optical carrier, a frequency-doubled or quadrupled microwave signal could be generated. The major limitation of the approach using a phase modulator is that all sidebands are generated; therefore, if only the optical carrier is removed using a wavelength-fixed optical filter, at the output of the photodetector, an electrical signal consisting of a frequency-doubled and quadrupled frequency components will be generated. Recently, we have proposed a photonic microwave quadrupler using a polarization modulator [28]. Compared with the approaches in [23]–[27], the method is more attractive due to the higher spectral purity of the generated signal, better simplicity, and improved operation stability. In [23]–[28], the frequency multiplication factor is only four. To generate an electrical signal with a frequency up to the subterahertz range using relatively low-frequency electrical and electrooptic devices, a higher frequency multiplication factor is highly desirable. In this paper, we propose and experimentally demonstrate a novel method to generate a high-spectral-purity and frequencytunable subterahertz-wave signal using a photonic frequency sextupler. The proposed frequency sextupler consists of a polarization modulator and a wavelength-fixed optical notch filter. The key significance of using a polarization modulator is that the modulator is not biased, which eliminates the bias drift problem. In addition, the residual chirp can be adjusted to zero by tuning a polarization controller (PC) placed before the polarization modulator. A theoretical analysis on the frequency tuning range and harmonic suppression ratio under different phase-modulation indices and filter attenuations is performed, and an experiment to verify the analysis is carried out. A high-spectral-purity microwave signal tunable from 18 to 27.6 GHz is generated when a microwave drive signal from 3 to 4.6 GHz is applied to the

Fig. 1. (a) Block schematic diagram of the millimeter wave generation system. (b) Transmission spectrum of a wavelength-fixed notch filter showing a frequency tuning range from f to 3 f . LD: laser diode; RF: radio frequency; PC: polarization controller; PolM: polarization modulator; UTC-PD: unitraveling-carrier photodetector; EDFA: erbium-doped fiber amplifier; ESA: electrical spectrum analyzer; OSA: optical spectrum analyzer.

polarization modulator. The phase noise of the generated signal is measured as low as 107.57 dBc/Hz at a 10-kHz offset frequency. The generation of a stable electrical signal tunable from 66 to 114 GHz is also demonstrated by tuning the microwave drive signal from 11 to 19 GHz. The distribution of the generated subterahertz wave signal over optical fiber is investigated. II. ANALYSIS A. System Architecture The schematic of the proposed frequency sextupler is shown in Fig. 1(a). The system consists of a laser diode (LD), a polarization modulator, an optical polarizer, a wavelength-fixed optical notch filter, an erbium-doped fiber amplifier (EDFA), and a unitraveling-carrier photodetector (UTC-PD). A CW light wave from the LD is sent to the polarization modulator, which is driven by a microwave signal with a frequency of . The polarization modulator is a special phase modulator that can support both TE and TM modes with opposite phase-modulation indices [31]. When a linearly polarized incident light wave oriented with an angle of 45 to one principal axis of the polarization modulator is sent to the polarization modulator, a pair of complementary phase-modulated signals is generated along the two principal axes of the polarization modulator. Applying the two signals to the optical polarizer with its polarization axis aligned with an angle of 45 with respect to one principal axis of the polarization modulator, the phase-modulated signals will be combined to generate an intensity-modulated signal with the even-order sidebands including the optical carrier suppressed. A wavelength-fixed notch filter is then used to filter out the two first-order sidebands. As a result, two phase-correlated opare generated. tical waves with a wavelength spacing of 6 By beating the two optical waves at the photodetector, a millimeter-wave signal at six times the frequency of the electrical

PAN AND YAO: TUNABLE SUBTERAHERTZ WAVE GENERATION BASED ON PHOTONIC FREQUENCY SEXTUPLING

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tical notch filter is shown in Fig. 1(b). After the optical filtering, the optical signal can then be expressed as (3)

Fig. 2. Illustration of the operation principle. A, B, C, D: the optical spectra at different locations in the system shown in Fig. 1(a); E: the electrical spectrum at E.

drive signal is generated. Because no bias is needed for the polarization modulator, the system is free from bias drift, and a stable operation is guaranteed. In addition, the frequency of the generated millimeter-wave signal can be tuned by simply tuning the frequency of the electrical drive signal. B. Frequency-Sextupled Millimeter-Wave Signal Generation Fig. 2 shows the spectra at different locations in the system shown in Fig. 1(a). The CW light wave from the laser diode that is oriented with an angle of 45 to one principal axis of the polarization modulator is phase modulated in the polarization modulator along the - and -directions by a microwave drive . The norsignal with an angular frequency of malized optical field at the output of the polarization modulator along the - and -directions can be expressed as

(1) where is the angular frequency of the optical carrier and is the phase-modulation index of the polarization modulator. Applying the two signals to a polarizer with its principal axis aligned with an angle of 45 to one principal axis of the polarization modulator as shown in Fig. 1(a), we obtain

As a result, two optical sidebands separated by six times the frequency of the microwave drive signal are generated. Since the two sidebands originate from the same optical and microwave sources, a good phase correlation is maintained. Beating the two wavelengths at a photodetector, a high-spectral-purity frequency-sextupled microwave signal is generated. The photocurrent of the generated microwave signal is (4) where

is the responsibility of the photodetector.

C. Frequency Tunability In the system shown in Fig. 1(a), an optical notch filter is used to remove the two first-order sidebands. Ideally, the notch filter should have zero transmission over a certain range of frequency and 100% transmission elsewhere. This would support the frequency-sextupled microwave generator to be tunable in a certain frequency range, in which the two first-order sidebands are sufficiently suppressed by the optical notch filter while the two third-order sidebands are not attenuated. We assume that the optical notch filter has an isosceles-trapezoid-shaped transmission spectral profile with the spectral width and , redefined by the lower and upper limits denoted by spectively, as shown in Fig. 1(b). The assumption is justified in practice since the two slopes of the notch filter will not be used. Since the two first-order sidebands should be removed, the two sidebands must be located in the stopband of the notch filter, which gives a maximum spacing between the two first-order sidebands of . To ensure that the two third-order sidebands are not attenuated, the spacing of the two third-order sidebands must be larger than . As a result, the frequency of the proposed millimeter wave generator can be tuned in the range (5)

(2) is the th-order Bessel function of the first where kind. As can be seen only odd-order sidebands are present at the output of the polarizer. The amplitude distribution of the sidebands is a function of governed by the Bessel function. To generate optical sidebands up to the third order, should be prop. When this optical signal is fed erly controlled to be around to a photodetector, a frequency-doubled electrical signal and a frequency-sextupled electrical signal will be generated. To generate a frequency-sextupled electrical signal only, a wavelengthfixed optical notch filter to remove the two first-order sidebands is needed. The transmission spectrum of a wavelength-fixed op-

It should be noted that the optical carrier is always located at the center of the stopband. Therefore, the optical notch filter does not need to be tunable. This feature ensures that the proposed approach can generate a frequency-tunable millimeter wave signal by simply tuning the frequency of the microwave drive signal without the need to tune the optical filter. The highest frequency that can be generated by the system is limited by the bandwidth of the photodetector and the polarization modulator. So far, a photodetector based on the unitraveling carrier structure allows an effective detection of an optical microwave signal up to 914 GHz [32]. Meanwhile, a polarization modulator with a bandwidth in excess of 50 GHz has been developed [33]. Therefore, the maximum frequency of the generated millimeter-wave signal can be as high as 300 GHz, limited by the polarization modulator. D. Electrical Harmonic Suppression Assume that all of the even-order optical sidebands can be completely suppressed by carefully adjusting the polarization

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direction of the polarizer. Assume also that the two first sidebands are attenuated with an attenuation of dB by the optical notch filter. Based on the above assumptions, from (2), the optical signal at the output of the optical notch filter can be rewritten as

(6) where is related to by . For practical applications, the phase-modulation index is usually less than , due to the limited microwave power applied , the Bessel functo the polarization modulator. For tion for are all monotonically increasing with respect to and monotonically decreasing with respect to the order of Bessel function , and , and . Therefore, it is reasonable to ignore the optical sidebands with orders higher than 5 in our analysis. Thus, (6) can be simplified to

(7) Applying this optical signal to a photodetector, an electrical signal containing different orders of harmonics will be generated as

(8) where and are the powers of the second-, fourth-, sixth-, eighth-, and tenth-order electrical harmonics, given by (9) (10) (11) (12) (13) The power of the sixth-order harmonic and the harmonic and are plotted suppression ratios of in Fig. 3. From Fig. 3(a), we can see that the power is monotonically increasing for . Fig. 3(b) is calculated 60 dB. The harmonic suppression ratios of when and are monotonically decreasing and is mono. The ratio is generally tonically increasing for less than the ratios and with a peak value of . 23.5 dB at To evaluate the harmonic suppression performance of the generated electrical signals, we define a new term called global . For a given , the global suppression suppression ratio ratio is given by (14)

Fig. 3. Power and harmonic suppression ratios versus modulation index when  60 dB. (a) Powers of the sixth-order harmonic I . (b) Harmonic suppression ratios I =I ; I =I ; I =I and I =I .

=

From (9)–(13), we can see that is dependent on the attenuation of the optical notch filter and the phase-modulawould be tion index . For a given , a maximum value of achieved by controlling , which can be realized by adjusting the power of the microwave drive signal to the polarization modand the corulator. Fig. 4 shows the maximum value of responding as a function of . As can be seen, a larger attenuation of the optical notch filter leads to a larger global suppression ratio. However, the corresponding phase-modulation index is monotonically decreasing with , showing a decreasing output power of the sixth-order electrical harmonic. This problem can be solved at a low cost by using an EDFA to increase the optical power before photodetection. It should be noted that a lower modulation depth corresponds to a less power requirement for the microwave drive signal [23]. III. EXPERIMENT An experiment is performed based on the setup shown in Fig. 1(a). A light wave from a laser source is sent to the polarization modulator (Versawave Technologies) for complementary phase modulation. The polarization modulator is driven by a microwave signal from a microwave signal generator (Agilent E8254A). The phase modulation index is controlled to be approximately 0.46 by setting the power of the microwave drive signal to be 18 dBm. The phase-modulated signals are converted to an intensity-modulated signal at a polarization beam splitter serving as the optical polarizer. A wavelength-fixed notch filter

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Fig. 4. Global suppression ratio and the corresponding as a function of .

Fig. 6. Optical spectra (a) before the FBG filter and (b) after the FBG filter. (c) Electrical spectrum of the generated microwave signal. Fig. 5. Transmission spectra of two wavelength-fixed notch filters employed in the experiment.

is employed to suppress the undesired first-order sidebands. An EDFA is used to increase the power of the optical signal to a satisfactory level before photodetection at a 100-GHz unitraveling carrier photodetector ( t XPD4120R). The optical signal is monitored by an optical spectrum analyzer (Ando AQ 6317B) with a resolution of 0.01 nm, and the generated signal is observed by an electrical spectrum analyzer (Agilent E4448A, 3 Hz–50 GHz). Since most of our measurement instruments only cover a frequency range from several megahertz to less than 50 GHz, we first investigate the performance of the frequency sextupler when it generates a microwave signal with a frequency less than 50 GHz. In this case, an FBG with its central wavelength (1548.73 nm) equal to the wavelength of the optical carrier is used as an optical notch filter, with the transmission spectrum shown in Fig. 5(a). The FBG is measured to have a bandwidth between the two minimum attenuation points of approximately 0.15 nm ( 18.75 GHz) and a bandwidth between the 20-dB attenuation points of approximately 0.09 nm ( 11.25 GHz).

According to (5), the tuning range is about 18.75 33.75 GHz. Due to the limited dynamic range of the optical spectrum analyzer, Fig. 5(b) only shows a rejection ratio at the central wavelength of about 36 dB. However, the actual rejection ratio should be much greater. In our measurement, we introduce a double-sideband signal into the filter. The carrier is 27 dB greater than the sidebands before the filter and is 34 dB lower than the sidebands after the filter, thus the rejection ratio should be over 60 dB. Fig. 6(a) shows the optical spectrum at the output of the polarization beam splitter. The frequency of the electrical drive signal is set to be 3.5 GHz. Two first-order, two third-order, and two very weak fifth-order sidebands are observed. Excellent even-order sideband suppression is confirmed. The wavelengths of the two third-order sidebands are 1548.646 and 1548.814 nm, giving a wavelength spacing of 0.168 nm (21 GHz), which is six times the frequency of the electrical drive signal. With the two first-order sidebands removed by the FBG filter, the remaining two third-order sidebands are 24.1 dB higher than that of the optical carrier and other sidebands, as shown in Fig. 6(b). By applying the two wavelengths to the photodetector, a strong electrical signal with a frequency that is six times the frequency of

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Fig. 7. Phase-noise spectra of the generated 21-GHz signal and the 3.5-GHz drive signal.

the electrical drive signal is observed, with the electrical spectrum shown in Fig. 6(c). Other harmonics in the electrical signal are also observed. As predicted in Fig. 3(b), the powers of and are greater than other undesirable harmonics. However, they are 20 dB lower than that of the frequency-sextupled component, which can be ignored for most of the applications. From the earlier analysis, a global suppression ratio of 20 dB requires at least 52-dB attenuation of the two first-order sidebands. Comparing Fig. 6(b) with Fig. 6(a), the two first-order sidebands are suppressed by 40 dB, which is much smaller than the actual value due to the limited dynamic range of the optical spectrum analyzer. To investigate the spectral quality of the generated microwave signal, the phase noise of the signal is measured. Fig. 7 shows the single-sideband (SSB) phase noise spectrum of the generated 21-GHz signal measured by an Agilent E5052B signal source analyzer incorporating an Agilent E5053A downconverter. As a comparison, the phase noise spectrum of the 3.5-GHz microwave drive signal is also shown in Fig. 7. The phase noises of the 3.5- and 21-GHz signals are 122.82 and 107.57 dBc/Hz, respectively, at a 10-kHz offset frequency. The generated 21-GHz signal presents a 15.3-dB phase-noise degradation compared with the 3.5-GHz electrical drive signal. Theoretically, the phase noise of a frequency-sextupled signal should have a phase noise degradation of about 15.56 dB. The measurement is consistent with the theoretical prediction. One of the key features of this technique is that no bias is needed for the polarization modulator, which makes the generated microwave signal have good power stability. To verify the conclusion, we allow the system to operate in a room environment for a period of 60 min with the optical and electrical spectra recorded at a 5-min interval. The results are shown in Fig. 8. As can be seen the amplitude variations of the 21-GHz component are small, which are within 0.4 dB. Since the 3.5-, 10.5-, 14-, and 17.5-GHz components are very small, they are more sensitive to the environmental variations. However, during the entire 60-min period, the 20 dB suppression ratio is always maintained. The tunability of the generated microwave signal is also experimentally studied. When the frequency of the electrical drive signal is tuned from 3 to 4.6 GHz, a frequency-sextupled signal with a frequency tunable from 18 to 27.6 GHz is generated, as shown in Fig. 9. Because the optical notch filter used in the

Fig. 8. Stability measurement of: (a) the optical spectra of the FBG filtered optical signal: (b) the electrical spectra of the generated electrical signal (RBW =1 MHz); and (c) power variations and suppression ratios at 5-min interval over a 60-min period.

experiment does not have an ideal isosceles-trapezoid-shaped transmission spectral profile as assumed in the analysis, the attenuation for the first-order sidebands at different frequencies will vary. As a result, the suppression ratio changes from 15.6 to 21.3 dB when the frequency of the microwave drive signal is tuned. Compared with the previously reported results for frequency-sextupled microwave signal generation [30], our method provides a better suppression ratio. It should be noted that only the frequency of the microwave drive signal is changed during the tuning process and other parameters are kept unaltered. If the phase-modulation index is also adjusted, as indicated in Fig. 4, the suppression ratio should be further improved. To generate a subterahertz-wave signal using the proposed frequency sextupler, the FBG-based notch filter is replaced by an optical interleaver. From the transmission spectrum of the interleaver, as illustrated in Fig. 5(b), we can see that it has a bandwidth between the two minimum attenuation points of approximately 0.53 nm ( 66 GHz) and a bandwidth between the 20-dB attenuation points of approximately 0.32 nm ( 40 GHz). According to (5), the use of this interleaver would provide a frequency-tunable range of 66–120 GHz. Fig. 10 shows a typical optical spectrum of the filtered optical subterahertz-wave signal. As can be seen, the optical carrier and the two second-order sidebands are almost eliminated by carefully adjusting the polarization controller. The two third-order sidebands are 22 dB

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Fig. 10. Optical spectrum of the optical subterahertz wave signal at 108 GHz.

Fig. 9. Spectra of (a) the FBG filtered optical signal and (b) the generated electrical signal (RBW = 1 MHz) when the frequency of the electrical drive signal is tuned from 3 to 4.6 GHz.

higher than that of the first-order sidebands, indicating an effective suppression of the first-order sidebands by the optical interleaver. The wavelengths of the two third-order sidebands are 1554.794 and 1555.664 nm, giving a wavelength spacing of 0.87 nm ( 108 GHz), which is six times the frequency of the electrical drive signal (18 GHz). It should be noted that the fourth-order sidebands are observed from Fig. 10. This is because the polarization modulator is polarization-maintainingfiber pigtailed. Mathematically, the influence of the differential group delay of the polarization-maintaining fiber on the signal generation performance can be considered by modifying (1) to yield

(15) where is the differential group delay. Equation (2) is then changed to

(16) In obtaining (16), we assume that the fixed phase shift of is compensated by a wave plate or a polarization controller that is placed between the PolM and the polarizer. As can be seen from (15) and (16), the differential group delay introduces an additional phase shift between the signals along the two principal axes, which would deteriorate the suppression of the even-order sidebands when the two signals are combined at the polarizer. The amplitude of the th even-order sideband is

Fig. 11. Electrical spectra of the generated subterahertz wave at (a) 66–90 GHz and (b) 90-114 GHz when the frequency of the electrical drive signal is tuned from 11 to 19 GHz. RBW = 100 kHz.

written as . In our demonstration, the differential group delay of the pigtailed polarization-maintaining fiber is about 0.35 ps, so it only degrades the suppression of the high-order sidebands. Practically, the polarization modulator and the polarizer would be integrated in a single monolithic chip, so the impact of the differential group delay on the system performance would be small and negligible, and thus the fourth-order sidebands should be fully eliminated. To observe the 66–120-GHz subterahertz wave signal using the 3 Hz–50 GHz electrical spectrum analyzer, two external harmonic waveguide mixers (Tektronix WM782E 60-90 GHz and WM782F 90–140 GHz) are employed. Fig. 11 shows the spectra of the generated subterahertz-wave signal at different frequencies. When the frequency of the electrical drive signal is tuned from 11 to 19 GHz, the frequency of the generated frequency-sextupled signal varies from 66 to 114 GHz. Due to the

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Fig. 12. Electrical spectra of the 114-GHz signal generated locally and remotely after transmission over a 40-km single-mode fiber. RBW = 91 Hz.

different conversion losses of the harmonic waveguide mixers, the powers of the subterahertz-wave signal in Fig. 11(a) are generally larger than that in Fig. 11(b). In the spectrum of the 66-GHz signal, a small 88-GHz component is also observed, but it is more than 19 dB lower than the 66-GHz component. Other spectra present only a single spectral line because the powers of the undesired beat signals are below the noise level. To evaluate the quality of the generated electrical signal after fiber distribution, we transmit the optical subterahertz-wave signal over a 40-km standard single-mode fiber before photodetection. Fig. 12 gives the spectra of the 114-GHz signal generated locally and remotely. As can be seen, no obvious linewidth broadening is observed after fiber distribution, which indicates that the signal quality of the remotely generated signal is maintained. This feature is desirable for ultra-broadband wireless communications, where subterahertz-wave signals should be distributed to remote access points via optical fibers. It should be noted that an optical interleaver always have two complementary output; while one port outputs the two third-order sidebands, the other port outputs two first-order sidebands, which can be used to carry independent multiband services in a radio-over-fiber system [34]. IV. CONCLUSION A novel method to implement microwave frequency sextupling using a polarization modulator and a wavelength-fixed optical notch filter was proposed and comprehensively studied. A theoretical analysis on the frequency tuning range and harmonic suppression ratio under different phase-modulation indices and filter attenuations were performed, with the analysis verified by a two-step experiment. In the first step, the frequency sextupler was operating at low-frequency regime, which allowed us to perform a comprehensive investigation of the performance of the proposed system using low-frequency measurement instruments. A narrow-bandwidth optical notch filter was employed in this step. A frequency-tunable microwave signal from 18 to 27.6 GHz was obtained by tuning the microwave drive signal from 3 to 4.6 GHz. The electrical harmonic suppression ratio was 20 dB. The phase-noise performance of the generated microwave signal was also evaluated. The phase noise of the generated signal was measured as low as 107.57 dBc/Hz at a 10-kHz offset frequency. The stability of the system was also investigated. In the second step, the narrow-bandwidth notch filter

was replaced by an optical interleaver. A high-spectral-purity subterahertz-wave signal from 66 to 114 GHz was generated when the frequency of the drive signal was tuned from 11 to 19 GHz. Compared with the previously reported optical frequency multiplication schemes based on an MZM, the proposed technique has three major advantages, which are: 1) the multiplication factor is six, which allows the generation of high-quality electrical signal with a frequency up to the subterahertz range using relatively low-frequency electrical and electrooptic devices; 2) the use of the polarization-modulator-based intensity modulator would provide a better performance in eliminating the even-order sidebands even if the frequency of the drive signal is high, so the spectral purity of the generated subterahertz wave could be significantly improved; and 3) no dc bias is needed for the polarization modulator, so the system is free from the bias drift, a serious problem when an MZM is biased at the minimum or maximum transmission point. The proposed system also features a simple and compact structure, which can be used as a terahertz source for applications in spectroscopic sensing and ultra-broadband wireless communications. REFERENCES [1] B. B. Hu and M. C. Nuss, “Imaging with terahertz waves,” Opt. Lett., vol. 20, no. 16, pp. 1716–, Aug. 15, 1995. [2] Q. Wu, T. D. Hewitt, and X. C. Zhang, “Two-dimensional electrooptic imaging of THz beams,” Appl. Phys. Lett., vol. 69, no. 8, pp. 1026–1028, Aug. 19, 1996. [3] W. L. Chan, J. Deibel, and D. M. Mittleman, “Imaging with terahertz radiation,” Rep. Prog. Phys., vol. 70, no. 8, pp. 1325–1379, Aug. 2007. [4] A. Hirata, T. Kosugi, H. Takahashi, R. Yamaguchi, F. Nakajima, T. Furuta, H. Ito, H. Sugahara, Y. Sato, and T. Nagatsuma, “120-GHz-band millimeter-wave photonic wireless link for 10-Gb/s data transmission,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 5, pp. 1937–1944, May 2006. [5] J. Wells, “Faster than fiber: The future of multi-Gb/s wireless,” IEEE Microw. Mag., vol. 10, no. 3, pp. 104–112, May 2009. [6] J. R. Demers, R. T. Logan, and E. R. Brown, “An optically integrated coherent frequency-domain THz spectrometer with signal-to- noise ratio up to 80 dB,” in Microw. Photon. Technol. Dig., Victoria, BC, Canada, Oct. 2007, pp. 92–95. [7] T. Nagatsuma, “Generating millimeter and terahertz waves,” IEEE Microw. Mag., vol. 10, no. 4, pp. 64–74, Jun. 2009. [8] X. F. Chen, J. P. Yao, and Z. Deng, “Ultranarrow dual-transmissionband fiber Bragg grating filter and its application in a dual-wavelength single-longitudinal-mode fiber ring laser,” Opt. Lett., vol. 30, no. 16, pp. 2068–2070, Aug. 15, 2005. [9] S. L. Pan and J. P. Yao, “A wavelength-switchable single-longitudinalmode dual-wavelength erbium-doped fiber laser for tunable microwave generation,” Opt. Exp., vol. 17, no. 7, pp. 5414–5419, Apr. 2009. [10] S. L. Pan and J. P. Yao, “Frequency-switchable microwave generation based on a dual-wavelength single-longitudinal-mode fiber laser incorporating a high-finesse ring filter,” Opt. Exp., vol. 17, no. 14, pp. 12167–12173, Jul. 2009. [11] L. Xia, P. Shum, and T. H. Cheng, “Photonic generation of microwave signals using a dual-transmission-band FBG filter with controllable wavelength spacing,” Appl. Phys. B, Lasers Opt., vol. 86, no. 1, pp. 61–64, Jan. 2007. [12] M. Tani, P. Gu, M. Hyodo, K. Sakai, and T. Hidaka, “Generation of coherent terahertz radiation by photomixing of dual-mode lasers,” Opt. Quantum Electron., vol. 32, no. 4–5, pp. 503–520, May 2000. [13] S. Hoffmann and M. R. Hofmann, “Generation of Terahertz radiation with two color semiconductor lasers,” Laser Photon. Rev., vol. 1, no. 1, pp. 44–56, Feb. 2007. [14] Z. C. F. Fan and M. Dagenais, “Optical generation of a megahertzlinewidth microwave signal using semiconductor lasers and a discriminator-aided phase-locked loop,” IEEE Trans. Microw. Theory Tech., vol. 45, no. 8, pp. 1296–1300, Aug. 1997.

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[15] L. N. Langley, M. D. Elkin, C. Edge, M. J. Wale, U. Gliese, X. Huang, and A. J. Seeds, “Packaged semiconductor laser optical phase-locked loop (OPLL) for photonic generation, processing and transmission of microwave signals,” IEEE Trans. Microw. Theory Tech., vol. 47, no. 7, pp. 1257–1264, Jul. 1999. [16] M. Hyodo and M. Watanabe, “Optical generation of millimeter-wave signals up to 330 GHz by means of cascadingly phase locking three semiconductor lasers,” IEEE Photon. Technol. Lett., vol. 15, no. 3, pp. 458–460, Mar. 2003. [17] A. Wiberg, P. Perez-Millan, M. V. Andres, and P. O. Hedekvist, “Microwave-photonic frequency multiplication utilizing optical four-wave mixing and fiber Bragg gratings,” J. Lightw. Technol., vol. 24, no. 1, pp. 329–334, Jan. 2006. [18] Q. Wang, H. Rideout, F. Zeng, and J. P. Yao, “Millimeter-wave frequency tripling based on four-wave mixing in a semiconductor optical amplifier,” IEEE Photon. Technol. Lett., vol. 18, no. 24, pp. 2460–2462, Dec. 2006. [19] T. L. Wang, H. W. Chen, M. H. Chen, J. Zhang, and S. H. Xie, “Highspectral-purity millimeter-wave signal optical generation,” J. Lightw. Technol., vol. 27, no. 12, pp. 2044–2051, Jun. 15, 2009. [20] S. Fukushima, C. F. C. Silva, Y. Muramoto, and A. J. Seeds, “Optoelectronic millimeter-wave synthesis using an optical frequency comb generator, optically injection locked lasers, and a unitraveling-carrier photodiode,” J. Lightw. Technol., vol. 21, no. 12, pp. 3043–3051, Dec. 2003. [21] M. Musha, A. Ueda, M. Horikoshi, K. Nakagawa, M. Ishiguro, K. Ueda, and H. Ito, “A highly stable mm-wave synthesizer realized by mixing two lasers locked to an optical frequency comb generator,” Opt. Commun., vol. 240, no. 1–3, pp. 201–208, Oct. 1, 2004. [22] H. J. Song, N. Shimizu, T. Furuta, K. Suizu, H. Ito, and T. Nagatsuma, “Broadband-frequency-tunable sub-terahertz wave generation using an optical comb, AWGs, optical switches, and a uni-traveling carrier photodiode for spectroscopic applications,” J. Lightw. Technol., vol. 26, no. 15, pp. 2521–2530, Aug. 2008. [23] G. Qi, J. P. Yao, J. Seregelyi, S. Paquet, and C. Bélisle, “Generation and distribution of a wideband continuously tunable millimeter-wave signal with an optical external modulation technique,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 10, pp. 3090–3097, Oct. 2005. [24] J. Zhang, H. W. Chen, M. H. Chen, T. L. Wang, and S. H. Xie, “A photonic microwave frequency quadrupler using two cascaded intensity modulators with repetitious optical carrier suppression,” IEEE Photon. Technol. Lett., vol. 19, no. 14, pp. 1057–1059, Jul. 2007. [25] C. T. Lin, P. T. Shih, J. Chen, W. Q. Xue, P. C. Peng, and S. Chi, “Optical millimeter-wave signal generation using frequency quadrupling technique and no optical filtering,” IEEE Photon. Technol. Lett., vol. 20, no. 12, pp. 1027–1029, Jun. 2008. [26] G. Qi, J. P. Yao, J. Seregelyi, S. Paquet, and C. Bélisle, “Optical generation and distribution of continuously tunable millimeter-wave signals using an optical phase modulator,” J. Lightw. Technol., vol. 23, no. 9, pp. 2687–2695, Sep. 2005. [27] P. Shen, N. J. Gomes, P. A. Davies, W. P. Shillue, P. G. Huggard, and B. N. Ellison, “High-purity millimetre-wave photonic local oscillator generation and delivery,” in Proc. Int. Top. Meeting Microw. Photon., Sep. 10–12, 2003, pp. 189–192. [28] S. L. Pan, C. L. Wang, and J. P. Yao, “Generation of a stable and frequency-tunable microwave signal using a polarization modulator and a wavelength-fixed notch filter,” in Proc. OFC, 2009, paper JWA51. [29] J. Zhang, H. W. Chen, M. H. Chen, T. L. Wang, and S. Z. Xie, “Photonic generation of a millimeter-wave signal based on sextuple-frequency multiplication,” Opt. Lett., vol. 32, no. 9, pp. 1020–1022, May 1, 2007. [30] X. G. Chen, Z. L. Wang, and D. Chen, “Effects of direct current biasdrifting on radio on fiber link,” Int. J. Infrared Millim. Waves, vol. 29, pp. 424–431, Apr. 2008.

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[31] J. D. Bull, N. A. Jaeger, H. Kato, M. Fairburn, A. Reid, and P. Ghanipour, “40-GHz electro-optic polarization modulator for fiber optic communications systems,” in Proc. Photon. North 2004: Opt. Compon. Devices, Ottawa, ON, Canada, 2004, pp. 133–143. [32] C. C. Renaud, M. Robertson, D. Rogers, R. Firth, P. J. Cannard, R. Moore, and A. J. Seeds, “A high responsivity, broadband waveguide uni-travelling carrier photodiode,” in Millimeter-Wave and Terahertz Photon. Conf., Strasbourg, France, 2006, pp. 61940C–8. [33] J. D. Bull, H. Kato, A. R. Reid, M. Fairburn, B. P. Tsou, D. R. Seniuk, P. H. Lu, and N. A. Jaeger, “Ultrahigh-speed polarization modulator,” in Proc. Conf. Lasers Electro-Opt./Quantum Electron. Laser Sci. Photon. Applic. Syst. Technol., 2005, paper JTuC54. [34] Z. Jia, J. Yu, A. Chowdhury, G. Ellinas, and G. Chang, “Simultaneous generation of independent wired and wireless services using a single modulator in millimeter-wave-band radio-over-fiber systems,” IEEE Photon. Technol. Lett., vol. 19, no. 20, pp. 1691–1693, Oct. 2007. Shilong Pan (S’06–M’09) received the B.S. and Ph.D. degrees in electronics engineering from Tsinghua University, Beijing, China, in 2004 and 2008, respectively. In August 2008, he joined the Microwave Photonics Research Laboratory, School of information Technology and Engineering, University of Ottawa, Ottawa, ON, Canada, as a Postdoctoral Research Fellow. His current research interests include ultra-wideband over fiber, ultrafast optical signal processing, fiber lasers, and terahertz wave generation. Dr. Pan is a member of the Optical Society of America and the IEEE Photonics Society.

Jianping Yao (M’99–SM’01) received the Ph.D. degree in electrical engineering from the Université de Toulon, Toulon, France, in 1997. He joined the School of Information Technology and Engineering, University of Ottawa, Ottawa, ON, Canada, in 2001, where he is currently a Professor, Director of the Microwave Photonics Research Laboratory, and Director of the Ottawa—Carleton Institute for Electrical and Computer Engineering. From 1999 to 2001, he held a faculty position with the School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore. He holds a Yongqian Endowed Visiting Chair Professorship with Zhejiang University, China. He spent three months as an Invited Professor with the Institut National Polytechnique de Grenoble, Grenoble, France, in 2005. He has authored or coauthored over 270 papers including 150 papers in peer-reviewed journals and over120 papers in conference proceeding. His research has focused on microwave photonics, which includes all-optical microwave signal processing, photonic generation of microwave, millimeter-wave, and terahertz, radio over fiber, ultra-wideband over fiber, fiber Bragg gratings for microwave photonics applications, and optically controlled phased array antenna. He is an Associate Editor of the International Journal of Microwave and Optical Technology. His research interests also include fiber lasers, fiber-optic sensors and bio-photonics. Dr. Yao is a Registered Professional Engineer in the Province of Ontario. He is a Fellow of the Optical Society of America (OSA) and a Senior Member of the IEEE Photonics Society and the IEEE Microwave Theory and Techniques Society. He is on the Editorial Board of the IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES. He was the recipient of the 2005 International Creative Research Award of the University of Ottawa and the 2007 George S. Glinski Award for Excellence in Research. He was named University Research Chair in Microwave Photonics in 2007. He was the recipient of a Natural Sciences and Engineering Research Council of Canada (NSERC) Discovery Accelerator Supplements Award in 2008.

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Photonic-Crystal-Based Polarization Converter for Terahertz Integrated Circuit Khadijeh Bayat, Student Member, IEEE, Golamreza Z. Rafi, George S. A. Shaker, Student Member, IEEE, Nazy Ranjkesh, Sujeet K. Chaudhuri, Senior Member, IEEE, and Saffiedin Safavi-Naeini, Member, IEEE

Abstract—In this paper, the fabrication and characterization of newly developed photonic crystal (PC) polarization-controlling devices on a silicon-on-insulator wafer for integrated terahertz applications are presented. The polarization converter is composed of periodic asymmetric loaded PC slab waveguide. Square- and circular-hole PC slab waveguides were studied using a 3-D finite-difference time-domain method. For a square-hole PC-based polarization rotator, polarization rotation efficiency higher than 90% was achieved within the normalized frequency band of . In circular-hole PC polarization converter, the polarization conversion efficiency dropped to 70% for the aforementioned frequency band. Low polarization conversion efficiency of the circular-hole PC-based device is attributed to scattering loss at the top loaded layers. Thus, the square-hole PC structure is a better candidate for integrated terahertz polarization-controlling devices. Planar terahertz integrated circuit technology was developed to implement the proposed device. Characterization setup was designed using rigorous numerical methods to use the newly introduced Agilent Millimeter-wave PNA-X network analyzer (up to 500 GHz) as a source. Scattering parameter characterizations provide a good measure of polarization extinction ratio. For the de200 GHz, it was vices designed for the central frequency of observed that, within the frequency band of 198–208 GHz 0.26-0.272 , the ratio of 21 to 11 was higher than 15 dB. The bandwidth is in good agreement with our preliminary design presented before.

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Index Terms—Birefringence, integrated terahertz, photonic crystal (PC), polarization converter, polarization rotator, silicon-on-insulator (SOI), waveguide.

I. INTRODUCTION ITH RECENT advances in terahertz generation and detection, terahertz technology is becoming very attractive for imaging, communications, and chemical and biological detection [1], [2]. Terahertz signal generation, guidance, manipulation, and detection all can be realized in an integrated

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Manuscript received October 10, 2009; revised March 05, 2010; accepted March 22, 2010. Date of publication June 21, 2010; date of current version July 14, 2010. This work was supported in part by the Natural Science and Engineering Research Council of Canada (NSERC), Ontario Centres of Excellence (OCE), and Research In Motion (RIM). K. Bayat is with the Electrical and Computer Engineering Department, South Dakota State University, Brookings, SD 57006 USA (e-mail: [email protected]). G. Z. Rafi, G. S. A. Shaker, N. Ranjkesh S. K. Chaudhuri, and S. SafaviNaeini are with the Electrical and Computer Engineering Department, University of Waterloo, Waterloo, ON, Canada N2L 3G1 (e-mail: [email protected]; [email protected]; nazyranjkesh; [email protected]; safavi@maxwell. uwaterloo.ca). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2010.2050371

ultrasmall-size solid-state platform by employing the photonic crystal (PC) structures [3]. It was shown that highly resistive silicon ( 3 k cm) provides a lossless media for terahertz wave propagation [4]. In this study, we have employed highly resistive silicon ( 5-10 k cm) to implement PC-based membrane structures for terahertz applications. There are some research groups that have utilized PC technology for terahertz application [5], [6]. For example, a metallic PC in a parallel waveguide was implemented and tested for a terahertz frequency band [6]. SU8 was employed to create several rows of PC rods, by sputtering silver, and the metallic PC rods were implemented and tested. The bandgap measurement was reported utilizing tera600 GHz. Jukam et al. reported the hertz pulse centered at implementation of a PC structure on highly resistive thin silicon layer and bandgap measurement of the PC structure [5]. One of the main obstacles of implementing PC structures on thin silicon layer is handling and integration of PC structures. In this paper, we introduce a novel PC membrane technology for terahertz frequencies on silicon-on-insulator (SOI) wafer. In fact, the optical approaches for integrated circuits are extended to applications at the terahertz frequency regime. This technology has a potential for large-scale integration. Waveguides, resonators, couplers, and other components of an integrated terahertz circuit can be implemented on a single chip using this technique. In this technology, the integrated circuit is implemented on a highly resistive silicon device layer of the SOI wafer. Handle silicon underneath the optical components is removed to maintain low loss terahertz propagation. Having developed terahertz PC-based integrated circuit technology; one of the main obstacles in the implementation of an integrated terahertz-optical circuit is the polarization dependence of wave propagation [7]. Our goal is to overcome this obstacle by implementing PC-based polarization controlling devices. One of the crucial elements of polarization controlling devices is the polarization rotator. The polarization rotator is utilized to manipulate and rotate the polarization of a propagating wave. We have proposed, designed, and implemented an ultra-compact passive PC-based polarization rotator for terahertz frequency applications [8]–[11]. The “optical” design approaches are utilized to design the structure. Passive polarization rotator structures are mostly composed of geometrically asymmetric structures [12]–[14]. The proposed polarization rotator structure consists of a periodic asymmetric loaded PC slab waveguide. Due to the compactness of the proposed structure, a rigorous numerical method, 3-D finite-difference time-domain

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BAYAT et al.: PC-BASED POLARIZATION CONVERTER FOR TERAHERTZ INTEGRATED CIRCUIT

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Fig. 1. Schematic of periodic asymmetric loaded triangular PC slab waveguide.

(3D-FDTD) method can be employed to analyze and simulate the final designed structure. In our previous publications, coupled-mode theory and normal mode analysis methods were employed to design the polarization converter for terahertz frequency band. 3D-FDTD analysis was used to verify and refine the design [8], [9]. For a square-hole PC polarization rotator, a polarization conversion efficiency higher than 90% over the propagation dis( -wavelength) was achieved within the normaltance of ized frequency band of , where is the unit cell dimension shown in Fig. 1. The design was extended to a circular-hole PC-based polarization rotator. Maximum polarization conversion efficiency of 70% within the aforementioned frequency band was achieved. The excessive loss observed for circular-hole PC-based structure is attributed to the scattering loss at the top loaded layer [11]. Therefore, square-hole PC structure is a better candidate for polarization converter structure. In this paper, a summary of the design methodology is presented in Section II. The fabrication technique is presented in Section III. The characterization setup and associated HFSS and SEMCAD simulations are presented in Section V. Finally, we conclude the paper with a summary of the key achievements. II. DESIGN OF POLARIZATION CONVERTER The schematic of the asymmetric square-hole PC slab polarization converter is shown in Fig. 1. In this structure, the unit cell, the width of the square holes, the thicknesses of PC slab and waveguide and top loaded layer are represented by , respectively. The top cladding layer is asymmetric with respect to the -axis (propagation direction) and alternates periodically throughout the propagation direction to synchronize the coupling between the two polarizations. Fig. 2 shows the flowchart of the design. The width of the square holes and the size of the unit cell of the PC are optimized for a maximum bandgap. The most important design parameter is the thickness of the PC slab waveguide. In designing the thickness of the PC slab waveguide, not only must the maximum overlap between -polarized and -polarized waves be achieved, but the - diagram for these two modes must also be parallel to each other so that the difference between the refractive indexes remains constant within the overlap frequency band. For preliminary and quick design, coupled-mode theory was developed for square-hole PC-based structures. Therefore,

Fig. 2. Flowchart of the design methodology of a PC slab waveguide-based polarization rotator.

the length and total number of the top loaded layers can be estimated using coupled-mode theory. The design can be verified and fine tuned using 3D-FDTD. 3D-FDTD simulation results suggest that coupled-mode theory provides fairly accurate results. Details of the design procedure have been reported in [8], [9], and [11]. For more complex structures such as circular-hole PC structures, coupled-mode theory requires fine meshing, which is a tedious process. Another design methodology based on normal-mode analysis (2’Design in Fig. 2) was proposed. In this method, first, the vector-propagation characteristics of the normal modes were calculated using 3D-FDTD and spatial Fourier transform (SFT) analysis [9]. Having calculated the vector-propagation characteristics of the normal modes of the structure, the half-beat length and the total number of top loaded layers can be calculated. In our design example, the width of the square holes and thickness of the top loaded layer and PC slab waveguide are ( is unit cell dimension, as depicted in Fig. 1), , and , respectively [8]. A. Circular-Hole PC Polarization Converter The design was extended to circular-hole PC polarization rotators. First, we need to obtain dimensions of the circular-hole PC equivalent to the square-hole PC. In the process of changing the shape of the air holes, it is important to keep the filling factor of the dielectric material per unit cell constant to preserve the band structure characteristics [15]. Thus, the filling factor is an important parameter that must be taken into account when the shape of the air holes is changed. The radius of the circle could and . The radius of the circular be the average of air hole is estimated as follows: (1) The plane wave expansion method (PWEM) [16] can be employed to adjust the value of . After several rounds of trial and , bandgap characteristics error, it was found that, for were the same for both circular- and square-shaped air-hole PCs [11]. For both square- and circular-hole PCs for TM-like waves, the lower and upper limits of the normalized bandgap are 0.238

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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 58, NO. 7, JULY 2010

Fig. 3. Band diagram for the asymmetric loaded square- and circular-hole PC : a, t : a and w : a, slab waveguides obtained by PWEM for t r : W.

= 0 47(1 + p2)

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and 0.327, respectively. No bandgap exists for the TE-like wave for either square- or circle-air-hole PC slab structures [9], [11]. The band diagram of the asymmetric loaded circular-hole PC , , and slab waveguide with is shown by dots in Fig. 3. For PWEM, the supercell method has been employed [16]. The supercell consists of one row of asymmetric loaded PC slab waveguide [11]. The band diagram matches the equivalent square-hole PC structure shown by solid and dashed lines in Fig. 3. The two modes depicted by dashed and solid lines are called index-guided and Bloch modes, respectively [9], [11]. The index-guided mode is considered to be a -polarized wave for which the dominant electric field component is in the -direction. On the other hand, the Bloch mode is considered to be an -polarized wave. Similar to square-hole PC-based polarization rotators, the operational normalized frequency band of the circular-hole PC polarization rotator, which is the overlap frequency band between the two modes, is expected to be from to . The structural parameters can be calculated by assigning the central frequency of the polarization rotator to the normalized frequency . For example, for the central frequencies of 600 of and 200 GHz, the unit cell sizes are 131.5 and 394.5 m, respectively. To design the polarization converter structure, normal-mode analysis is employed. To obtain the vector-propagation characteristics of the defect modes, SFT analysis was applied to the transverse components of electric field distribution along the propagation direction at any point inside the defect line. The electric field distribution was obtained by 3D-FDTD analysis of asymmetric loaded PC slab waveguide [9], [11]. The effective refractive indexes of the fast and slow modes of the asymmetric loaded circular-hole PC slab waveguide calculated by SFT analysis are 2.5425 and 2.7275, respectively. The half-beat length would be and the polarization rotation angle was 12.33 [9], [11]. , the input polarization rotates by 98.4 . To comAfter pensate for the extra phase, the length of the third loaded layer and at the must be increased. Fig. 4 graphs

Fig. 4. Power exchange versus frequency for square-/circular-hole PC-based polarization converter using full 3D-FDTD simulation.

output of the polarization converter versus frequency for both square- and circular-hole PC-based polarization rotators with , ,). the same band diagrams ( The transverse electric field is expressed as , where and are the amplitude of normalized electric fields and , reand are obtained at a distance of spectively. ( 1.315 and 3.945 mm at 600 and 200 GHz, respectively) from the input plane for circular-hole PC-based polarization rotators. Fig. 4 shows that is higher than 0.7 within the normalized frequency band of 0.26–0.268. It is important to note that is around 0.1. All of these values are based on the assumption that the output power is normalized with respect to the input power or, in other words, the values of and at the input are 1 and 0, respectively. These numbers indicate that there is and graphs a 20% loss of power. On the other hand, the for square-hole PC-based polarization rotators show that, within the frequency band of 0.26–0.267, is greater than 0.9 and is less than 0.05. Low-polarization conversion efficiency of circular-hole PC polarization rotators is mainly associated with the high propagation loss. Nevertheless, the length of the last top loaded layer could be optimized to achieve higher power conversion efficiency. However, the large propagation loss is the main issue of circular-hole PC polarization rotators; 20% of the input power has been dissipated along the propagation direction. After careful examination of 3D-FDTD simulation of square-/circular-hole PC slab waveguide and asymmetric loaded slab waveguide, it was found that the top loaded layer introduces large scattering loss in circular-hole PC structures. Thus, it seems that the square-hole PC-based polarization converter is a better choice in terms of loss characteristics. III. FABRICATION TECHNIQUE Here, the fabrication process of the Si membrane PC technology for terahertz application is presented. We have employed highly resistive silicon ( k -cm) to implement PC-based membrane structures for terahertz applications. Here, we introduce a novel PC technology for terahertz wave. This

BAYAT et al.: PC-BASED POLARIZATION CONVERTER FOR TERAHERTZ INTEGRATED CIRCUIT

technology has a potential for integration with other optoelectronic and microelectronic devices. We fabricated devices in the frequency band of 200 GHz–1 THz. The thickness of the device layer is chosen between 80–400 m based on the design. The thickness of the buried oxide layer that separates the silicon device layer from the silicon handle layer could be varied between 0.5–5 m. Handle silicon layer is a low-resistive silicon that attenuates the terahertz signal significantly and must be taken into consideration in the fabrication technology design. The fabrication process consists of both front-side and backside processing of the SOI wafer. The front-side processing involves etching of deep holes into the silicon layer. Backside processing consists of opening a window at the backside of the devices to prevent coupling of the terahertz wave to the lossy substrate modes and guarantee low loss propagation. To pattern the device layer, standard lithography is utilized as opposed to the optical PC structure that requires nanometer 100 m , deep range lithography. In order to etch deep holes reactive ion etching (DRIE) is required. Thick photoresist must be utilized for photolithography in order for it to stand the long etching process. We employed 4- m-thick photoresist (S1827) as a soft mask for the DRIE process. The etching of the holes was carried out using an optimized DRIE process to create holes with smooth vertical side walls and the desired aspect ratio. We used the Bosch process which alternates between two modes of nearly isotropic plasmaetching using for 7 s and deposition of chemically inert passivation layer for 2 s. The and flow rates are 300 and 150 using sccm, respectively. The process temperature is kept at 20 C. The and can vary slightly during the etching rate is around m etching process. Buried oxide acts as an etch stop. The second phase of the process is opening a window at the backsides of the SOI wafer to construct the membrane PC structure. Handle silicon is a thick silicon 525 m , which is removed by wet chemical etching. We used 30% KOH etching at 90 C, which gave an etching rate of almost 50 m h. The front side of the wafer must be protected from the KOH etching. The KOH etching was carried out by a custom-made wet etching tool which only exposes the backside of the wafer to hot KOH solution. A KOH mask that covers the unetched areas must withstand 10 h of KOH at 90 C. A thick amorphous silicon nitride film (a-SiN) of 1 m was deposited using the PECVD technique to function as the hard mask at the backside of the SOI wafer. The second lithographic step was performed to pattern the SiN layer for the opening windows at the backside of the SOI wafer. Again, buried silicon dioxide functions as the etching stop. The SEM image of a fabricated membrane PC slab waveguide is shown in Fig. 5(a). It shows that the window under the active area (waveguide area) has been etched nicely. Fig. 5(b) shows the SEM image of the top side showing the air holes close up. It can be seen that the walls are sharply etched. The backside etching is also very important and critical. Fig. 5(c) shows the SEM image of the backside. It can be seen that the back is etched uniformly; the oxide at the back can be easily removed by buffered HF (BHF).

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Fig. 5. SEM picture of fabricated: (a) PC membrane slab waveguide, (b) front side, and (c) backside of the PC structure.

We fabricated the polarization rotation devices for potential applications in the terahertz frequency band (200 GHz–1 THz). The fabrication of this PC-based polarization rotator is more complex in a sense that the front-side processing requires two sets of masks. The first mask is employed to create the periodic loading layers. The second mask is for patterning of the PC slab waveguide. The third mask is used to open windows at the back side of the structure. Fig. 6(a) shows the SEM image of the periodic asymmetric loaded PC slab waveguide with square holes. The SEM picture shows that the walls are very sharp. In Fig. 6(b), the SEM picture of the periodic asymmetric loaded PC slab waveguide for circular air holes pattern is presented. IV. CHARACTERIZATION SETUP Series of devices in the frequency range of 0.2–1 THz are fabricated. The devices are being prepared to be characterized using newly introduced Agilent Millimeter-wave PNA-X network analyzer (up to 500 GHz). The proposed characterization setup is simulated using finite-element-based modeling [High Frequency Software Simulator (HFSS) v.11] as well as FDTD modeling (SEMCAD X v.14). Here, we have presented full HFSS simulation results that are considered strong validations of expected measurement outcomes. In the new setup, submillimeter metallic waveguides are employed as the interface between the PNA coaxial cables and input/output (I/O) tapers of the PC-slab waveguide devices. For example, for a central frequency of 200 GHz, WR-5 is utilized 0.0255 (1.295 mm 0.647 mm). The with a size of 0.0510 total thickness of the polarization rotator assuming that 200 GHz 0.263 would corresponds to a normalized frequency of be 0.0155 (0.395 mm); thus, there is a good match between

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Fig. 7. (a) Schematic of the characterization setup consisting of a PC slab waveS (return guide, input/output tapers, and rectangular waveguides. (b) S loss-insertion loss) plots of the PC slab waveguide.

0

Fig. 6. SEM picture of: (a) square-hole PC polarization converter and (b) circular-hole PC polarization converter.

WR-5 and input taper. A single-defect line PC slab waveguide is employed as the calibration reference. The waveguide is designed to guide both TE-like and TM-like waves. We employed the same design methodology presented in our previous publication to design the waveguide [17]. Fig. 7(a) shows the diagram of the setup designed to couple electromagnetic wave in and out of the waveguide utilizing submillimeter metallic waveguides. To couple the electromagnetic wave to the defect line, a taper structure is utilized, as shown in Fig. 7(a). The geometry of the I/O tapers must be designed properly to maximize the coupling efficiency to the defect line of PC slab waveguide. In our HFSS (v.11) simulations, the input wave is the TE mode of the rectangular transition waveguide that has been polarized along the -direction. The structural parameters of the , , PC slab waveguide are as follows: 0.378 mm, 3.48, and , where , and are the unit cell, width of square holes, thickness of the PC slab waveguide, refractive index, and loss tangent of silicon, respectively. The central frequency is set to 200 GHz, corresponding to the normalized frequency of . The power transmission takes place through the PC defect line. The frequency response of the setup is plotted in Fig. 7(b). (reflection) and (transmission) are depicted by dashed and solid lines, respectively. The graphs show that the insertion

loss is less than 2 dB in the entire band from 190 to 210 GHz. The return loss is higher than 20 dB. Thus, the waveguide can be employed as a wideband low-loss transmission line. The same setup as in Fig. 7(a) has been used to characterize the polarization rotator. The input wave is TE mode with the electric field pointing in the –direction . For a 90 polarization rotator, the input polarization rotates by 90 so that, at the output plane, the -component of the electric field is dominant. The output rectangular metallic waveguide is to be rotated field. by 90 to support the Fig. 8(a) shows the schematic of the polarization rotator with two alternating top loaded layers. Previously, we have shown that, for this design, the rotation angle for each top loaded layer is 6.5 [11]; therefore, the polarization rotator with two top loaded layers rotates the input polarization by an angle of . In this design, a normalized (where and are the unit cell size frequency of and free-space wavelength, respectively) is assigned to 200 GHz; thus, it is expected to see approximately 26 polarization rotation in the frequency band of 196–204 GHz, corresponding . to a normalized frequency band of If the output taper shown in Fig. 7(a) was placed at the output, the component of the field would have been exposed to the geometry variation of the output taper imposing reversed rotation; the width of the taper in the -direction is decreasing along the propagation. To improve the polarization extinction ratio and component to the rectangular enhance the coupling of the

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Fig. 9. Field distribution at the (a) input and (b) output ports of the polarization rotator at 200 GHz.

Fig. 8. (a) Schematic of the polarization rotator with the rotation angle of 26 with input/output tapers and waveguides. (b) S and S plots of the structure.

metallic waveguide, the output taper was rotated by 90 , shown in Fig. 8(a). Having rotated the output waveguide, it supports component, and the component of the field reonly the flects back. Thus, and parameters would provide a good measure of the polarization extinction ratio. Fig. 8(b) shows and plots from the HFSS simulations. is It shows that, within the frequency band of 196–206 GHz, is less than 10 dB. The bandwidth higher than 4 dB and is in good agreement with our design presented in our previous publications [8]. The electric field distribution at the input and output ports is shown in Fig. 9. The input and output electric fields are laid out in the - and -directions, respectively. The electric field distribution clearly illustrates the electric field rotation. The structure shown in Fig. 10(a) is designed to rotate the input polarization by 90 . The 4.5 top loaded layers provide 90 rotation. The output taper has not been rotated 90 because of the fabrication limits and feasibility issues of such taper. Thus, we would expect to observe lower coupling efficiency of the component to the output rectangular waveguide. Due to the computational/program-size limits of finite element tools (HFSS), SEMCAD was employed to simulate the structure using the 3D-FDTD method. Fig. 10(b) shows the spectrum of -parameters, which is very similar to the -parameters graph presented in Fig. 8(b). In

Fig. 10. (a) Schematic of the polarization rotator with an angle of rotation of 90 . (b) S and S plots.

Fig. 10(b), within the frequency band of 199–208 GHz, and are higher and less than 5 dB and 15 dB, respectively. Since the structure was designed for 90 rotation, a higher polarization extinction ratio was expected in comparison with the polarization rotator with 26 angle of rotation.

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edge of the input rectangular waveguide, to the tip of the output 205 GHz. waveguide at is At the input, inside the rectangular metallic waveguide, gradually being coupled to the input taper along the propagation direction. At the output taper, is being coupled to the output rectangular metallic waveguide. Inside the PC-based polarizais gradually decreasing while is increasing, tion rotator, which is an indication of polarization rotation. At the edge of the output rectangular waveguide, the extinction ratio between and at 205 GHz the polarization states is 20 dB. are 20.8 and 3 dB, respectively. Thus, it seems that there is a correlation between the polarization extinction ratio and -parameter values, and -parameters can provide a good measure of the polarization extinction ratio. V. CONCLUSION Fig. 11. Imagess of: (a) E and (b) E components obtained using 3D-FDTD analysis.

Fig. 12. Electric field distribution (E along the propagation direction.

;E

An integrated membrane PC on SOI wafer for terahertz frequency application was developed. It has a potential for largescale integration. Polarization-controlling devices were studied to solve the polarization dependence issue of integrated terahertz circuits. A highly compact integrated polarization converter that could be integrated in a planar terahertz circuit was introduced and designed using several methods. The devices fabricated for 0.1–0.5-THz operation are being prepared to be characterized using the newly introduced Agilent Millimeter-wave PNA-X network analyzer (up to 500 GHz). The characterization setup was designed and analyzed using rigorous numerical methods. We showed that the -parameters can provide a good measure of polarization extinction ratio. For the devices designed for the central frequency of 200 GHz, it was observed that, within the frequency band of 198–208 GHz, the polarization extinction ratio was higher than 15 dB. The bandwidth is in good agreement with our preliminary design presented before.

) at the center of the defect line

Snap shots of and components at 205 GHz is presented in Fig. 11. Fig. 11(a) shows that the TE mode has fields in the left side, and it is well-confined inside launched the input taper and then couples into the defect line of the PC slab waveguide. On the other hand, the field component in Fig. 11(b) is weak at the left (input) side of the defect line; the color bar shows that it is one order of magnitude smaller than component. As the field mode propagates inside the defect line of PC slab waveguide-based polarization rotator, it graducomponent. At the other end ally rotates and converts to the component seems to be one of the PC slab waveguide, the order of magnitude larger than . At the output taper, will be exposed to the geometry variation of the taper resulting in reverse polarization conversion. Thus, the polarization conversion efficiency would decrease. and distribution along the propagation Fig. 12 presents direction at the middle of the defect line of the PC slab waveguide from the tip of the input taper, which is aligned to the

ACKNOWLEDGMENT The authors would like to thank the Nanofabrication Center, University of Minnesota, Twin Cities Campus, for facility access and training on DRIE equipment. REFERENCES [1] P. H. Siegel, “Terahertz technology,” IEEE Trans. Microw. Theory Tech., vol. 50, no. 3, pp. 910–928, Mar. 2002. [2] T. Baras, “On-chip detection of biomaterials: A numerical study,” J. Bio. Phys., vol. 29, pp. 187–194, 2003. [3] C. Lin, C. Chen, G. J. Schneider, P. Yao, S. Shi, A. Sharkawy, and D. W. Prather, “Wavelength scale terahertz two-dimensional photonic crystal waveguides,” Opt. Exp., vol. 12, pp. 5723–5728, 2004. [4] D. Grischkowsky, S. Keiding, and M. E. Fattinger, “Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors,” J. Opt. Soc. Amer. B, Opt. Phys., vol. 7, no. 10, pp. 2006–2015, 1990. [5] N. Jukam and M. S. Sherwin, “Two-dimensional terahertz photonic crystals fabricated by deep reactive ion etching in Si,” Appl. Phys. Lett., vol. 83, no. 1, pp. 21–23, 2003. [6] Y. Zhao and D. R. Grischkowsky, “2-D terahertz metallic photonic crystals in parallel-plate waveguides,” IEEE Trans. Microw. Theory Tech., vol. 55, no. 4, pp. 656–663, Apr. 2007. [7] J. Fini, “Microphotonic devices: The polarization gates open,” Nature Photon., vol. 1, pp. 17–18, 2006.

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[8] K. Bayat, S. K. Chaudhuri, and S. Safavi-Naeini, “Ultra-compact photonic crystal based polarization rotator,” Opt. Exp., vol. 17, pp. 7145–7158, 2009. [9] K. Bayat, S. K. Chaudhuri, and S. Safavi-Naeini, “Design and simulation of photonic crystal based polarization converter,” J. Lightw. Technol., vol. 27, no. 23, pp. 5483–5491, Dec. 2009. [10] K. Bayat, S. K. Chaudhuri, S. Safavi-Naeini, and M. F. Baroughi, “SOI based photonic crystal polarization converter for terahertz frequency applications,” in Proc. IPNRS, 2009, pp. 1–3, Paper: ITuc3. [11] K. Bayat, “Design, simulation and fabrication of photonic crystal slab waveguide based polarization processors,” Ph.D. dissertation, Elect. Comput. Eng. Dept., Univ. Waterloo, Waterloo, ON, Canada, 2009. [12] B. M. A. Rahman, S. S. A. Obayya, N. Somasiri, M. Rajarajan, K. T. V. Grattan, and H. A. El-Mikathi, “Design and characterization of compact single-section passive polarization rotator,” J. Lightw. Technol., vol. 19, no. 4, pp. 512–519, Apr. 2001. [13] Y. Shani, R. Alferness, T. Koch, U. Koren, M. Oron, B. I. Miller, and M. G. Young, “Polarization rotation in asymmetric periodic loaded rib waveguides,” Appl. Phys. Lett., vol. 59, pp. 1278–1280, 1991. [14] M. R. Watts and H. A. Haus, “Integrated mode-evolution-based polarization rotators,” Opt. Lett., vol. 30, pp. 138–140, 2005. [15] S. Khorasani, An Introduction to Optics of Photonic Crystals. Tehran, Iran: Novin, 2007. [16] S. G. Johnson, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Guided modes in photonic crystal slabs,” Phys. Rev. B, Condens. Matter, vol. 60, pp. 5751–5758, 1999. [17] K. Bayat, S. K. Chaudhuri, and S. Safavi-Naeini, “Polarization and thickness dependent guiding in photonic crystal slab waveguide,” Opt. Exp., vol. 15, pp. 8391–8400, 2007.

Khadijeh Bayat (S’07) was born in Zanjan, Iran, in 1976. She received the B.Sc. degree in electronic engineering from the Iran University of Science and Technology, Tehran, Iran, in 1997, the M.Sc. degree in electronic engineering from Tarbiat Modares University, Tehran, Iran, in 2000, and the M.Sc. and Ph.D. degrees from the University of Waterloo, Waterloo, ON, Canada, in 2004 and 2009, respectively. From 1999 to 2002, she was with Iran Telecommunication Research Center as a Design Engineer. In 2003, she joined the Electrical and Computer Engineering Department, University of Waterloo, as a Research Assistant. She held Natural Science and Engineering Research Council of Canada (NSERC) Postgraduate scholarship and Ontario Graduate Scholarship on Science and Technology (OGSST) during her Ph.D. studies. She joined South Dakota State University, Brookings, as an Assistant Professor in 2009. She is the author and coauthor of several scientific articles. Her research interests include nanophotonics, optoelectronics, and emerging terahertz-photonic integrated circuit technologies based on PBG.

Gholamreza Z. Rafi received the B.Sc. degree from the Isfahan University of Technolgy, Isfahan, Iran, 1991, and the M.Sc. and Ph.D. degrees from the Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran, in 1997 and 2000, respectively, all in electrical engineering. He was an Assistant Professor with the Electrical Engineering Department, University of Zanjan, from 2000 to 2001, and collaborated with the Iran Telecommunication Center (ITRC) as Research Scientist. He was a Postdoctoral Fellow with the Electrical and Computer Engineering Department, University of Manitoba, Winnipeg, MB, Canada, from 2001 to 2004. He has been a Senior Scientist with the Electrical and Computer Engineering Department, University of Waterloo, Waterloo, ON, Canada, from 2004 to 2008, and introduced and managed an industrial-scientific group entitled Vehicular Wireless Communication with many successful industrial projects. He also recently joined the Centre of Integrated Antenna and Radio System (CIARS), RF Microwave and Photonics, University of Waterloo, as an Assistant Director and Manager. His research activities are the integration of RF circuits with antennas and applied electromagnetics.

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George S. A. Shaker (S’99) received the B.Sc. degree (with honors) in electronics and communications engineering from the University of Cairo, Cairo, Egypt, in 2003, the M.A.Sc. degree in electrical and computer engineering from the University of Waterloo, Waterloo, ON, Canada, in 2006, and is currently working toward the Ph.D. degree at the University of Waterloo. He is currently a Natural Science and Engineering Research Council of Canada (NSERC) Canada Alexander Graham Bell Research Scholar with the Intelligent Radio/Antenna Research Group, University of Waterloo. He has authored or coauthored more than 40 journal publications, patent applications, conference papers, and technical reports. His current research interests are in the areas of antenna synthesis and design, integrated and adaptive front-ends, electromagnetic bandgaps and engineered surfaces (meta-materials), biomedical wireless systems, and advanced optimization computer-aided design techniques. He serves regularly as a reviewer for the International Journal of Microwave Science and Technology and Progress in Electromagnetics Research. Mr. Shaker is a student member of the IEEE Antennas and Propagation Society (IEEE AP-S), the IEEE Microwave Theory and Techniques Society (IEEE MTT-S), the IEEE Communications Society, the IEEE Computer Society, and the Applied Computational Electromagnetic Society. He regularly serves as a reviewer for the IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS, and the IEEE Antennas and Propagation Magazine. He has also served as session co-chairman in several international scientific conferences including the IEEE Antennas and Propagation Symposiums. He was the recipient of several prestigious awards and scholarships, including the NSERC Graduate Scholarship (CGS-D3–2007), the Ontario Graduate Scholarship (OGS-2007), the European School of Antennas Grant at IMST-GmbH (2007), the IEEE AP-S Honorable Mention Paper Award (APS 2008), the IEEE AP-S Best Paper Award (APS 2009, Third Place) , the IEEE Antennas and Propagation 2008/2009 Graduate Research Award, and the IEEE MTT-S Graduate Fellowship 2009.

Nazy Ranjkesh was born in Tehran, Iran, on January 24, 1981. She received the B.Sc. and M.Sc. degrees in communication engineering, fields, and waves from the University of Tehran, Tehran, Iran, in 2003 and 2006, respectively, and is currently working toward the Ph.D. degree in communication engineering at the University of Waterloo, Waterloo, ON, Canada. Her research interests are terahertz integrated circuit design, novel waveguide structures for realization of high- -factor passive components, electromagnetic wave theory, numerical methods in electromagnetic bandgap structures, and photonic crystals.

Q

Sujeet K. Chaudhuri (SM’85) was born in Kolkata, India, on August 25, 1949. He received the B.E. degree in electronics engineering (with honors) from the Birla Institute of Technology and Science, Pilani, India, in 1970, the M.Tech degree in electrical communication engineering from the Indian Institute of Technology, Delhi, India, in 1972, and the M.A.Sc. degree in microwave engineering and Ph.D. degree in electromagnetic theory from the University of Manitoba, Winnipeg, MB, Canada, in 1973 and 1977, respectively. In 1977 he joined the University of Waterloo , Waterloo, ON, Canada, where he is currently a Professor with the Electrical and Computer Engineering Department and was the Chair of Electrical and Computer Engineering Department from 1993 to 1998 and 2007 to 2008 and the Dean of the Engineering Faculty from 1998 to 2003. He has also held a Visiting Associate Professor’s position with the Electrical Engineering and Computer Science Department, University of Illinois at Chicago, during 1981 and 1984, a Visiting Professorship with the National University of Singapore from 1990 to 1991, and the Erskine Fellowship with the University of Canterbury, New Zealand, in 1998. In 2004, 2005, and 2009, he visited the Korea Advanced Institute of Science and Technology and POSTECH as BK-21 International Fellow. He has been involved in contract research and consulting work with several Canadian and U.S. in-

1984

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 58, NO. 7, JULY 2010

dustry and government research organizations. His current research interests are in guided-wave/electrooptic structures, planar microwave structures, dielectric resonators, optical and EM imaging, fiber/RF-based broadband networks, and the emerging technologies based on the EBG/PBG-nanostructures. Dr. Chaudhuri is a member of URSI Commission B and Sigma Xi. In 2004, in recognition of his sustained outstanding scholarship and academic leadership, he was installed as the O’Donovan Research Chair of RF/Microwaves and Photonics at the University of Waterloo.

S. Safavi-Naeini (M’79) received the B.Sc. degree from the University of Tehran, Tehran, Iran, 1974, and the M.Sc. and Ph.D. degrees from the University of Illinois at Champaign-Urbana in 1975 and 1979, respectively, all in electrical engineering. He joined the University of Waterloo, Waterloo, ON, Canada, in 1996, where he is now a Professor with the Department of Electrical and Computer Engineering and holds the RIM/NSERC Industrial Research Chair in Intelligent Radio/Antenna and Photonics. He is also the Director of a newly established Center for Intelligent Antenna and Radio System (CIARS), University of Waterloo. He has authored or coauthored more than 80 journal papers and 200 conference papers in international conferences. His research activities deal with RF/microwave technologies, smart integrated antennas and radio systems, millimeter-wave/terahertz integrated technologies, nano-electromagnetics and photonics, electromagnetics (EM) in health science and pharmaceutical engineering antenna, wireless communications and sensor systems and networks, new EM materials, bio-EMs, and computational methods. He has led several international collaborative research programs with research institutes in Germany, Finland, Japan, China, Sweden, and the U.S.

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 58, NO. 7, JULY 2010

1985

Single-Mode Terahertz Bragg Fiber Design Using a Modal Filtering Approach Yunhua Zhang, Student Member, IEEE, and Ian D. Robertson, Senior Member, IEEE

Abstract—This paper proposes a single-mode Bragg fiber design method based on a modal filtering technique and applies it to the design of a hollow-core single-mode Bragg fiber, which can achieve low loss by avoiding material loss. The proposed method exploits the Brewster phenomenon to filter out the 01 mode so that only the fundamental 11 mode exists. Consequently, this proposed method maintains a balance between single-mode propagation and low-loss propagation so that it is specially suitable for terahertz single-mode Bragg fiber design. An explicit relationship between the first bandgap width and the layer thickness is derived. As a result, for a certain design bandwidth requirement, the Bragg fiber parameters can be determined. The proposed design strategy is applied to a hollow-core single 11 -mode Bragg fiber operating in the 0.65–1.35-THz range with a calculated loss ranging from 0.2 to 1 dB/m.

TM

HE

HE

Index Terms—Bragg scattering, dielectric waveguides, electromagnetic propagation, optical fiber, submillimeter-wave waveguides, waveguides.

I. INTRODUCTION

I

N RECENT years, terahertz technology has been researched extensively. Due to the particular wavelengths, terahertz technology can find applications in chemical and biological identification, medical diagnostics, and security [1], [2]. In constructing a flexible terahertz system, it is necessary to transmit terahertz signals with low loss and distortion within the system or to remote antennas, sensors, or applicators. Therefore, a low-loss and single-mode terahertz waveguide is important for developing terahertz systems. Current terahertz waveguides are mostly scaled from their millimeter-wave or optical counterparts. Up until now, various types of terahertz waveguides have been reported, including metal tube waveguides [3], single-metal-wire guides [4], plastic fibers [5], photonic crystal fibers [6], and so on. The single-metal-wire terahertz waveguide can achieve low loss but requires a sophisticated setup, while the free-space terahertz transmission systems used in many experimental setups make a system too bulky to be used in many commercial applications. Polymer designs suffer from considerable loss due to the unacceptable material loss in the terahertz region.

Manuscript received October 01, 2009; revised February 18, 2010; accepted February 20, 2010. Date of publication June 21, 2010; date of current version July 14, 2010. This work was supported in part by the China Scholarship Council and the Agilent Foundation. The authors are with the Institute of Microwaves and Photonics, School of Electronic and Electrical Engineering, University of Leeds, Leeds LS2 9JT, U.K. (e-mail: [email protected]; [email protected]). Digital Object Identifier 10.1109/TMTT.2010.2050180

Recently, efforts have been made to transmit terahertz energy in holey fiber structures. A porous fiber has been shown to transmit terahertz signals with a propagation loss as low as 5 dB/m [7]. The porous fiber is created by arranging subwavelength air holes within the core of the fiber. In contrast to photonic crystal fibers, where energy is transmitted in solid material, in the porous fiber, 70%–80% of the power propagates in air holes so that the propagation loss can be reduced. Propagation loss can be further reduced by confining power in a hollow air core without incurring material loss. The metal-pipe waveguide is a popular hollow-core structure, but the limited conductivity and small dimensions generally preclude its application as a terahertz waveguide of substantial length. As an alternative to a metal pipe, a bandgap arrangement which is formed by periodic structures can also confine field energy in a hollow air core. The Bragg fiber consists of a hollow core and a cladding composed of layers of alternating refractive index which form a 1-D bandgap structure. In the optical region, the Bragg fiber has been demonstrated to transmit energy with single-mode propagation and low-loss properties. The design of a single-mode Bragg fiber can be classified into two types: one is a single -mode Bragg fiber; the other is a single -mode Bragg fiber. The first is designed with a hollow-core radius as large as , exploiting the significant low loss of the mode compared with other modes [8], [9]. The second is designed , with a small hollow core with a radius of around mode exists [10]. However, where only the fundamental neither of these design strategies can be applied in the terahertz region. The first type is intrinsically multimode, and an effective single mode can only be achieved when other modes have disappeared in long propagation distance applications, such as over several kilometers. Thus, this type is not suitable for obtaining single-mode propagation in the terahertz region. In the second type, the smaller core Bragg fiber supports a single mode, but mode has an unacceptably high loss, this fundamental and it would incur further loss when the cladding material is lossy. Consequently, these previously explored Bragg fiber design strategies can not be adopted for terahertz applications. In this paper, to balance the single-mode propagation and low-loss propagation in a Bragg fiber, the Brewster phenomenon mode so that only the fundais exploited to filter out the can propagate. The proposed design strategy mental mode is based on exploiting the properties of the Bragg 1-D bandgap structure. In the TM bandgap diagram, a series of bandgap closures is attributed to the Brewster phenomenon, which can be used in determining the hollow-core dimension. Furthermore, an explicit relationship between the first bandgap width and the alternating layer thickness is derived. Consequently, for a given

0018-9480/$26.00 © 2010 IEEE

1986

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 58, NO. 7, JULY 2010

single-mode bandwidth, the Bragg cladding parameters can be determined. Through calculations based on the transfer matrix method (TMM), the design is verified to have single-mode propagation. This paper is organized as follows. Section II presents a -mode Bragg fiber design, based on strategy of singlecharacterizing the Bragg bandgap diagram. The impact of the Brewster phenomenon on the TM bandgap is examined, and then the first-order bandgap edges are studied. Based on this, the structure’s parameters are derived from the bandwidth requirement. Then, a single-mode Bragg fiber design strategy is summarized. Section III presents a single-mode design in the terahertz region that applies the proposed design strategy. The single-mode propagation characteristic is verified. Finally, the advantage of using the currently proposed design method for the terahertz region design is investigated by comparing different design strategies. II. SINGLE-MODE BRAGG FIBER DESIGN The Bragg fiber is one particular form of microstructured fiber where a complex cross section is used to control the propagation parameters. Several numerical and semi-analytical methods have been used for analyzing the Bragg fiber, including the finite-element method (FEM), Galerkin’s Method, Chew’s method, and the TMM [11], [12]. These methods are capable of analyzing the propagation constant and propagation loss for given Bragg fiber parameters. However, the design of a Bragg fiber with a specific bandwidth can only be done in a laborious trial and error manner. It is essential to develop an explicit relationship between the propagation properties and the structure parameters. With the aim of designing a single-mode terahertz waveguide, we present in this section a modal filtering single-mode design strategy by investigating the Bragg bandgap properties. The Bragg fiber is composed of a core region surrounded by rings of alternate high- and low-refractive index material. A schematic diagram of a Bragg fiber is shown in Fig. 1. The refractive index of the core, higher refractive index cladding layer, and and lower refractive index cladding layer are respectively, and their dimensions are and , whilst the number of layers is . For the convenience of a generalized study, the period of the cladding structure is defined as . In the Bragg fiber, the field is confined by the constructive reflections, which are realized by the periodically arranged cladding layers. This cladding structure is essentially a 1-D bandgap structure, so only modes that are located in the forbidden region of the bandgap can propagate in the axial direction of the fiber. The Bragg cladding layers can be approximated by a planar Bragg stack when the core radius is large. Previously, the Bragg stack model and its bandgap diagram have been applied to facilitate the design of Bragg fibers. In the optical region, various designs have been carried out with the assistance of a bandgap diagram. For instance, an OmniGuide Bragg fiber with large core demonstrated that mode can survive [8]. Another example only the low-loss -mode fiber designed by setting all higher is the single-

Fig. 1. Schematic cross section of a Bragg fiber, the core has a radius of r , , and alternative cladding material have refractive filled with material of n indices of n and n and thicknesses of d and d .

modes to be in the cutoff region [10]. As stated above, neither of these two designs are suitable for a terahertz single-mode waveguide design. In Section II-A, we will further examine the properties of the Bragg bandgap for a low-loss single-mode terahertz waveguide. To improve the performance of the single-mode Bragg fiber, it is essential to investigate the propagation mechanism of Bragg fibers. Propagation modes are confined by the constructive reflections, and there is a striking difference between the TE reflections and the TM reflections. A TM wave can experience a zero reflection at a specific angle of incidence, which is the Brewster angle. Consequently, this mechanism can be exploited to filter out the TM modes. It has been shown that the TM modes will leak out when their incidence angles lie close to the Brewster angle. With a carefully chosen core radius, the mode is actually the only propagation mode [13]. Howmode is always preferred to make the waveguide ever, the more compatible with current systems. In [14], the single-mode terahertz Bragg fiber was reported for the first time. In this paper, based on the previous work, a systematic strategy of -mode fiber design is developed for the first time. single– A. Bandgap Diagram Consider a planar Bragg stack with the same parameters as the Bragg fiber cladding, with a plane wave incident on the planar stack: applying the TMM, the field in different layers can be related by a chain of matrices. With infinite alternating layers, the Bragg stack can be considered as a new composite material, and the field propagation matrix can be determined by considering the wave propagation in the composite material, which is termed as a Bloch wave [15]. A wave that is forbidden to propagate through the Bragg stack is constrained by (1)

ZHANG AND ROBERTSON: SINGLE-MODE TERAHERTZ BRAGG FIBER DESIGN USING A MODAL FILTERING APPROACH

1987

where is the Bloch-wave propagation parameter, and it can be derived from wave propagation and reflection in this multilayer structure [15]

(2) for TE modes and

(3) is the for TM modes. In the above equations, . radial propagation wavenumber and is a function For given set of structure parameters, of frequency and propagation constant, so a bandgap diagram can be generated by sweeping the normalized frequency and propagation constant. Instead of using the conventional coor, we use to dinate system depict the bandgap diagram [16], as shown in Fig. 2. The frequency normalized to the Bragg stack lattice parameter is de, and the effective propagation index is fined as . The white areas represent bandgaps where propagation can be confined within the Bragg fiber. Identification and location of the bandgap are important in determining the propagation bandwidth. It has been demonstrated that the bounding points of the bandgap can be calculated by counting the cumulative phase shift in straightly layered media [17]. Moreover, in examining the characteristics of different bandgaps, it is found that gaps with large normalized propagation constant have lower confinement loss, that is to say, only bounding points which lie close to the core material refractive index line are of interest for designing a low-loss Bragg fiber waveguide. As in Fig. 2, indicates the core material index line. It is also worth noting that a significant advantage of the bandgap diagram with coordinate is its ability to present more detail about the band behavior close to the core material refractive index line. B. Brewster Phenomenon It is found that the TM bandgaps are narrower than the TE bandgaps, and the TM bandgaps close up more often. Undoubtedly, these differences should be understood and exploited for optimum Bragg fiber design. The Bragg bandgap is formed by overlapping reflections in multilayered stacks, so it is instructive to explore a single reflection at each interface in characterizing the bandgaps. The above-mentioned differences can be attributed to TM Fresnel reflection, which can be expressed as (4) It can be inferred that, if there is no reflection in a bi-layer pair, there will be no field reflected in the Bragg stack. In TM reflection, the Brewster phenomenon is exactly such a case; the TM reflection comes to zero at a certain angle of incidence, which is termed the Brewster angle. Since the incidence angle can , the be expressed by effective propagation index effective propagation index at the Brewster incidence angle is

Fig. 2. TM bandgap diagram. The white represents the bandgaps, and n and n are the air line and the Brewster index line, respectively. Regions A, B, and C indicate the band regions which are used in different designs. Region A is used in [8], region B is used in [10], and region C is used in this paper.

termed as the Brewster index . By setting (4) to zero, the effective propagation index at the Brewster angle is found to be (5) From the viewpoint of Bloch wave propagation, the TM . Thus, it is not bandgaps close when surprising to find that a series of closing points of the TM bandgaps lie exactly on the effective propagation index at the Brewster angle. As shown in Fig. 2, the TM bandgaps close at . index line In the context of the Bragg fiber, the Brewster phenomenon indicates that there is no reflection or confined energy for the TM wave at the Brewster angle. Consequently, the single mode Bragg fiber can be designed by choosing a proper core radius, so that the TM modes will be filtered out and the TE modes are simultaneously located outside the bandgap region. Furthermore, in order to exploit the modal filtering effect, the Brewster closing point of the TM bandgap should be located , so that the effecbelow the core material refractive index tive propagation index can be larger than the Brewster propagation index. This constraint is then expressed as (6) As in Fig. 2, the propagation modes should be located below the line in a hollow-core Bragg fiber. Solving (5) and (6), a constraint for single-mode Bragg fiber design can be given as (7) In most low-loss Bragg fiber applications, an air core is employed to avoid material loss, so the material refractive index is constrained by . Due to the lack of low-loss low-refractive-index material in the terahertz region, air is the preferred choice for the lower refractive index material, although it makes fabrication difficult and requires some kind of supporting struts.

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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 58, NO. 7, JULY 2010

C. Bandwidth and Layer Thickness In the Bragg fiber, waves can propagate in the axial direction only when the propagation constant is located in the bandgap regions (the white regions in Fig. 2). Thus, the bandwidth of the Bragg fiber is determined by the band edge, which is described as [18] (8) Here, only the lower bandgap is to be examined since it has a wider range compared with other higher bandgaps. Equation (8) is a transcendent equation, and no explicit solution can be . To obtained in the whole plane of coordinate simplify the analysis of available bandwidth, the bandgap width on the core material line can be approximated as the maximum available bandwidth, which is indicated in Fig. 2. Moreover, only the TM bandgap is to be examined, since it has narrower bandgaps than that of the TE mode. As presented in Section II-B, air is chosen as the lower refractive index material, so the solution of (8) can be further simpli. If the band edges of the first TM fied by setting bandgap are and , respectively, an explicit relation between the band edges and layer thickness can be derived from (8), giving (9) (10)

. To exploit the Brewster filbandgap coordinate tering effect, the cutoff frequency can be set around the Brew. With ster closing point and the propagation mode is set to and , the core radius can be determined as (12) lies close to the This ensures that the mode curve of mode lies outside of the TE edge of TM bandgap and the bandgap at the same time. E. Single-Mode Bragg Fiber Design In the previous subsections, the property of the Bragg bandgap was investigated, with an emphasis on the relationship of bandgap width and bandgap cladding parameters such as and . An explicit function is derived to determine and from a given bandwidth requirement. Moreover, the core radius is calculated by shifting the mode to the Brewster mode, so that only the closing point so as to filter out the mode can survive in Bragg core. The design strategy can be summarized as follows. . 1) Select the material refractive index and from (9) and (10). 2) Determine the layer thickness from (12). 3) Determine the core radius from the loss require4) Determine the number of layers ment. 5) Analyze propagation properties of the designed Bragg fiber using the TMM. III. RESULTS AND DISCUSSION

and are the corresponding wavelengths of the in which bandgap edges. Equation (9) indicates that the thickness of the high-refraccan be reduced by choosing a larger refractive-index layer tive index for this layer. Also, it is worth noting that, for a given is determined only by the lower cutoff cladding material, wavelength . D. Core Design In the preceding discussions, the propagation bandgap is determined by specifying the thickness of the alternating layers. Now, the core radius is to be chosen so that propagation is located in the selected bandgap region. More specifically, in de-mode fiber, the mode should be signing a singleshifted to the TM bandgap edge which crosses the Brewster closing point. Since the propagation mode in a Bragg fiber is formed by the Bragg cladding reflection, an analogy can be drawn with a metal tube in analyzing the mode behavior in the Bragg fiber. Therefore, the propagation constant can be approximated by a metal tube model (11) where depends on the wave mode. For the TE modes, is , the th root of deviation of the th-order Bessel function is the th root of the th-order while, for the TM modes, . With the TM bandgap diagram, the first Bessel function Brewster closing point can be localized at the TM

A. Terahertz Bragg Waveguide Design Conventional polymer waveguides have limited applications in the terahertz waveband due to the unacceptable material loss in this region. Previously, a terahertz photonic crystal fiber exhibiting a loss of 430 dB/m from 0.4 to 2 THz was reported 0.5 cm .) Later on, a porous [6]. (In [6], it is quoted as fiber was reported to achieve loss as low as 5 dB/m [7] by partially transmitting energy in air holes. Thus, in the design of a terahertz Bragg fiber, an air core needs to be chosen to avoid material loss. As for the cladding structure, low-loss material is also preferred but less critical. In the terahertz region, , high-density polypolyetrafluoroethylene (PTFE) , and polystyrene are ethylene (HDPE) amongst the lowest loss materials [19]. Considering the refractive index constraint expressed in (7), in the following design, the lower refractive index cladding material is set to be air, and HDPE is chosen as the higher refractive index cladding material. To demonstrate the proposed single-mode terahertz waveguide design strategy, a terahertz waveguide with a bandwidth from 0.7 to 1.3 THz is set as a target specification, and the wavemode, with a loss no larger guide should support only the than 1 dB/m. The Bragg cladding thickness of each layer can be determined by (9) and (10). However, before applying (9) and (10) directly, and should be specified. Since and indicate the maximum available frequency range within the bandgap,

ZHANG AND ROBERTSON: SINGLE-MODE TERAHERTZ BRAGG FIBER DESIGN USING A MODAL FILTERING APPROACH

Fig. 3. TE bandgap and predicted propagation modes: d 76.8 m, and d 507.8 m.

=

=

n

Fig. 4. TM bandgap and predicted propagation modes: n d 76.8 m, and d 507.8 m.

=

=

HE

mode; d

1989

= 76.8 m, d = 507.8 m,

= 1.54, n = 1,

Fig. 5. Loss property of the 587.0 m. and r

=1.54, n = 1,

The next step is to shift the mode to the first Brewster closing point by choosing a suitable core radius. With the closing point (0.70, 0.84) identified from Fig. 4, the core radius 587.0 m. The propagation constants of the first four is modes are predicted based on (11) and overlaid on Figs. 3 and mode lies in both of TE and TM 4. As in Figs. 3 and 4, the bandgaps, the mode lies on the edge of the TM bandgap, mode lies outside of both TE and TM bandgaps, while the mode lies outside the TE bandgap. Thus, it can be the mode can propagate in this Bragg predicted that only the fiber. To verify the single-mode propagation, the propagation loss of the designed Bragg waveguide can be calculated by the TMM, since the TMM is a semi-analytical method which can provide high precision in characterizing the Bragg fiber [12]. With the TMM, the material loss can be taken into account directly by including the material loss in the refractive index. For lossy HDPE, the effective refractive index is (in the range of 0.3–2.5 THz [19]). Figs. 5 and and 6 present the propagation loss of the modes, respectively. In both figures, the solid line represents propagation loss without material loss while the dots represent propagation loss including material loss which is termed mode propagation loss. In Fig. 6, leaky loss of the decreases when the frequency increases, and this is caused by the shifting of the incidence angle away from the Brewster angle at the higher frequency. Comparing confinement loss and propagation loss in both figures, it can be seen that loss caused by lossy cladding is as low as 0.2 dB/m, and this is far lower than the material loss when the terahertz field propagates in solid material, which is 20 dB/m at 1 THz. Furthermore, comparing Figs. 5 and 6, it is found that the propagation loss mode is much smaller than that of the of the mode. Consequently, single-mode propagation can be mode achieved in a given propagation distance when the mode disappears. For instance, it takes only 1 m for the to diminish to 1% in the range of 0.65–1.35 THz, so that

this range should be larger than the demanded frequency range. In this design, the bandgap frequency range is set as 1.67 THz and 0.6 THz, respectively. Also, accordingly, the layer thickness can be calculated from (9) and (10), giving 76.8 m and 507.8 m. and have been determined, the bandgap diagram Once for this Bragg structure can be depicted as shown in Figs. 3 and 4, which depict the TE and TM bandgaps, respectively. In both figures, the white represents the forbidden bandgaps where the mode is located outwave can be confined. In Fig. 3, the mode is loside the TE bandgaps, while in Fig. 4 the cated on the TE bandgap edge. Comparing Figs. 3 and 4, the TM bandgap is much narrower than that of the TE mode. Another striking difference is that the TM bandgap closes at the . Brewster index, which is

=

1990

Fig. 6. Loss property of the TM = 587.0 m. and r

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 58, NO. 7, JULY 2010

mode; d

= 76.8 m, d = 507.8 m,

the designed Bragg waveguide works in a single mode with propagation loss ranging from 0.2 to 1 dB/m. The designed Bragg waveguide is effectively single mode mode filtered by exploiting modal difference, with the mode leaks and, eventually, any energy carried by the mode will, out. However, the energy leaking out of the of course, bring extra loss in addition to the propagation loss of mode. To avoid this loss, it would be necessary to prethe mode and other unwanted modes from arising. vent the These modes are excited mainly at discontinuities—the main ones being the fiber input transition and any bends in the fiber. Therefore, the coupling into the fiber must be engineered carefully and the radius of bends must be kept above a certain limit. mode has most of its energy in the central Fortunately, the part of the hollow core, and the energy level decreases in the ramode has maximum energy level dial direction, whilst the near the core/cladding interface and a low level of energy in the center of the core. Thus, if the coupling into the fiber is suitably mode will concentrated on the center of the core, only the be excited. For instance, feeding structures such as a focusing lens can be used to couple energy into this single-mode Bragg waveguide. In summary, mode pattern differences can be used mode. to avoid excitation of unwanted modes such as the As for bending of the fiber, the angle of incidence may be altered and other lossy modes may be excited. Consequently, the designed Bragg fiber should have a minimum bend radius specified for practical use. Furthermore, bending loss can be analyzed using the perturbation method as in [8]. and It is shown that the striking difference between the modes in propagation loss is caused by the Brewster phemode can be filtered out with a carenomenon, and the , , and . Furthermore, the cutoff frefully designed . In quency can be shifted by scaling values of , , and the following design, the same material is used, and the band1.5 THz and width specification is changed to 0.6 THz, respectively. Applying the above design strategy, the 85.4 m, structure parameters are determined as

Fig. 7. Bandwidth comparison of F1 and F2. F1: d = 587.0 m, and N =16. F2: d 507.8 m, r = 540.0 m, and N =16. 443.6 m. r

= =

76.8 m, d 85.4 m, d

= =

540.0 m, and 16. This design is termed 443.6 m. as F2, while the previous design is termed as F1. As shown in Fig. 7, F2 has a single-mode band from 0.7 to 1.2 THz, which is narrower than that of fiber F1. Therefore, it is shown that different single-mode frequency bands can be achieved by adjusting the thickness of the cladding layers. The design of F1 and F2 demonstrates the effectiveness of this proposed single-mode Bragg waveguide design strategy. Finally, it is worth remembering that air is used in the cladding layers for these example designs, so it would be impossible to fabricate them without putting bridges or struts in the air cladding layers. These bridges or struts supporting the solid layers will introduce additional modes [7], [9]. To reduce the effect of the supporting struts, the width of the struts should be kept as small as possible. Alternatively, since the low-refractive-index cladding layer is constrained by (7), which , if an air core is used, it is feasible to use is another very low-refractive-index material. There is considerable research work worldwide on ultralow dielectric constant materials, and it is expected that some type of nanocomposite material can be employed. It is anticipated, then, that the proposed terahertz Bragg fiber could be manufactured with a fairly straightforward drawing or multistage thin-film deposition process. For most applications, a flexible armor casing would be employed, and this could then be the mechanically rigid former on which to deposit the Bragg stack layers. The armoring will also restrict the bend radius and generally make the fiber rugged in use so that it could be employed in a wide range of environments. B. Comparison of Different Single-Mode Design Strategies Essentially, all modes are leaky in the Bragg fiber. Thus, nearly all single-mode design strategies exploit the loss difference among different modes to achieve single-mode propagation. However, these design strategies make use of different propagation modes and a different propagation region of the Bragg bandgap, such as regions A, B, and C in Fig. 2. Therefore,

ZHANG AND ROBERTSON: SINGLE-MODE TERAHERTZ BRAGG FIBER DESIGN USING A MODAL FILTERING APPROACH

1991

TABLE I COMPARISON OF SINGLE-MODE BRAGG FIBERS

these designed Bragg fibers have different propagation proper-mode fiber [8] which ties. OmniGuide is a low-loss singlemakes use of region A. In this design, the air-core radius is reso that the mode can exist, quired to be as large as and this large air core could bring two problems for a terahertz waveguide. First, the large core could make it too large to use in the terahertz region. Second, the mode separation [8] would become too small so that multimodes would exist. Furthermore, and in the terahertz region, other modes such as the modes would take too long a distance to diminish. In contrast to this, the design in [10] requires only a small core radius of about , which makes use of region B of the bandgap. However, this small core will cause high loss of the fundamental mode. As demonstrated, the Brewster modal filtering strategy proposed in this paper can provide a balance between reducing confinement loss and maintaining single-mode propagation, which cannot be achieved in previous Bragg fiber designs. The Brewster modal filtering strategy makes use of the Brewster mode which is closest to phenomenon to eliminate the mode. In this design, the mode the fundamental will diminish very fast so that single mode propagation is mode easily achieved, while the propagation loss of the can be kept low. A comparison of the previous two design strategies with the newly proposed one is given in Table I. It is shown that the newly proposed single-mode Bragg fiber design strategy combines the advantage of both previous designs, and it is highly suitable for designing waveguides in the terahertz region. IV. CONLUSION A novel design strategy for a terahertz single-mode Bragg fiber has been proposed. The proposed method exploits the mode so that Brewster phenomenon to filter out the only the mode can propagate. By applying this modal filtering strategy, Bragg waveguides can be designed to achieve low-loss and wideband single-mode operation in the terahertz region. In this paper, a terahertz waveguide is designed to have a bandwidth from 0.65 to 1.35 THz, with calculated propagation loss as low as 0.2 dB/m. The designed Bragg waveguide can maintain low loss by confining energy in the air core so as to avoid material loss. For the proposed design method, explicit analytical relationships between the design requirements and the physical parameters have been derived. The thickness of the cladding layers is determined by the desired working frequency range while the core radius is determined by the TM bandgap closing point at . This design strategy is the Brewster refractive index flexible enough to be used not only in designing single-mode terahertz waveguides, but also in other frequency ranges.

The proposed Bragg waveguide has been characterized with an ideal model and struts may be needed in the air cladding layers in practice. Obviously, these struts will introduce some unwanted modes, which will deteriorate the performance of the waveguide. Also, any bending of the Bragg waveguide will incur further loss and should be avoided. A number of viable solutions to these problems have been suggested and with further development it is highly likely that ruggedized Bragg fibers will find their way into practical terahertz systems for a range of applications. ACKNOWLEDGMENT The authors would like to thank R. Stancliffe, Agilent Technologies, Santa Clara, CA, for his valuable discussions. The authors would also like to thank the reviewers for their valuable comments. REFERENCES [1] P. H. Siegel, “Terahertz technology,” IEEE Trans. Microw. Theory Tech., vol. 50, no. 5, pp. 910–928, Mar. 2002. [2] D. L. Woolard, R. Brown, M. Pepper, and M. Kemp, “Terahertz frequency sensing and imaging: A time of reckoning future applications,” Proc. IEEE, vol. 93, no. 10, pp. 1722–1743, Oct. 2005. [3] R. W. McGowan, G. Gallot, and D. Grischkowsky, “Propagation of ultrawideband short pulses of terahertz radiation through submillimeterdiameter circular waveguides,” Opt. Lett., vol. 24, pp. 1431–1433, Oct. 1999. [4] K. Wang and D. M. Mittleman, “Metal wires for terahertz wave guiding,” Nature, vol. 432, pp. 376–379, Nov. 2004. [5] S. P. Jamison, R. W. McGowan, and D. Grischkowsky, “Single-mode waveguide propagation and reshaping of sub-ps terahertz pulses in sapphire fibers,” Appl. Phys. Lett., vol. 76, pp. 1987–1979, Apr. 2000. [6] H. Han, H. Park, M. Cho, and J. Kimpp, “Terahertz pulse propagation in a plastic photonic crystal fiber,” Appl. Phys. Lett., vol. 80, pp. 2634–2636, Apr. 2002. [7] A. Hassani, A. Dupuis, and M. Skorobogatiy, “Porous polymer fibers for low-loss terahertz guiding,” Opt. Exp., vol. 16, pp. 6340–6351, Apr. 2008. [8] S. G. Johnson, M. Ibanescu, M. Skorobogatiy, O. Weisberg, T. D. Engeness, M. Soljacic, S. A. Jacobs, J. D. Joannopoulos, and Y. Fink, “Low-loss asymptotically single-mode propagation in large-core omniguide fibers,” Opt. Exp., vol. 9, pp. 748–779, Dec. 2001. [9] R. Yu, B. Zhang, Y. Zhang, C. Wu, Z. Tian, and X. Bai, “Proposal for ultralow loss hollow-core plastic bragg fiber with cobweb-structured cladding for terahertz waveguiding,” IEEE Photon. Technol. Lett., vol. 19, no. 11, pp. 910–912, Jun. 2007. [10] G. Xu, W. Zhang, Y. Huang, and J. Peng, “Loss characteristics of single mode Bragg fiber,” J. Lightw. Technol., vol. 25, no. 1, pp. 359–366, Jan. 2007. [11] P. Yeh, A. Yariv, and E. Marom, “Theory of Bragg fiber,” J. Opt. Soc. Amer., vol. 68, pp. 1196–1201, 1978. [12] S. Guo, S. Albin, and R. S. Rogowski, “Comparative analysis of Bragg fibers,” Opt. Exp., vol. 12, pp. 198–207, Jan. 2004. [13] I. Bassett and A. Argyros, “Elimination of polarization degeneracy in round waveguides,” Opt. Exp., vol. 10, pp. 1342–1346, Nov. 2002. [14] Y. Zhang and I. Robertson, “Novel single mode bragg fibers for thz applications,” in Proc. 2nd U.K./Eur.-China Workshop Millimetre Waves Terahertz Technol., Oct. 2009, p. 98. [15] P. Yeh, A. Yariv, and C.-S. Hong, “Electromagnetic propagation in periodic stratified media. I. General theory,” J. Opt. Soc. Amer., vol. 67, pp. 423–438, 1977.

HE

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[16] K. Rowland, S. Afshar, and T. M. Monro, “Novel low-loss bandgaps in all-silica bragg fibers,” J. Lightw. Technol., vol. 26, no. 1, pp. 43–51, Jan. 2008. [17] K. Rowland, S. Afshar, and T. M. Monro, “Bandgaps and antiresonances in integrated-arrows and Bragg fibers: A simple model,” Opt. Exp., vol. 16, pp. 17 935–17 951, Oct. 2008. [18] T. Katagiri, Y. Matsuura, and M. Miyagi, “Photonic bandgap fiber with a silica core and multilayer dielectric cladding,” Opt. Lett., vol. 29, pp. 557–559, Mar. 2004. [19] M. Naftaly, R. Miles, and P. Greenslade, “Thz transmission in polymer materials—A data library,” in Proc. Joint 32nd Int. Conf. Infrared Millim. Waves, 2007, pp. 819–820. Yunhua Zhang (S’09) was born in Hubei, China, in 1981. He received the B.S. and M.S. degrees in electronic engineering from Wuhan University, Wuhan, China, in 2003 and 2006, respectively. He is currently working toward the Ph.D. degree at The University of Leeds, Leeds, U.K. His research interests include modeling and designing of terahertz and optics device, microstructured waveguides, microwave and high-speed circuits, computational electromagnetics, electromagnetic scattering, and remote sensing.

Ian D. Robertson (M’96–SM’05) was born in London, U.K., in 1963. He received the B.Sc. (Eng.) and Ph.D. degrees from King’s College London, London, U.K., in 1984 and 1990, respectively. From 1984 to 1986, he was with the MMIC Research Group, Plessey Research, Caswell, U.K. After that, he returned to King’s College London, London, U.K., initially as a Research Assistant and then as a Lecturer, finally becoming Reader in 1994. In 1998, he was appointed Professor of Microwave Subsystems Engineering at the University of Surrey, Surrey, U.K., where he established the Microwave Systems Research Group and was a founding member of the Advanced Technology Institute. In June 2004, he was appointed to the University of Leeds Leeds, U.K., Centenary Chair in Microwave and Millimeter-Wave Circuits. He was the Honorary Editor of Proceedings of the Institute of Electrical Engineering—Microwaves, Antennas and Propagation for many years and editor-in-chief of the rebranded IET Microwaves, Antennas and Propagation from 2005 to 2009. He has organized many colloquia, workshops, and short courses for both the Institution of Electrical Engineers (IEE) and IEEE. He edited the book MMIC Design (IEE, 1995) and coedited the book RFIC & MMIC Design and Technology, (IEE, 2001). He has authored or coauthored over 400 papers in the areas of microwave integrated circuits (MICs) and monolithic MIC design.

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 58, NO. 7, JULY 2010

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A 2-D Artificial Dielectric With 0 for the Terahertz Region

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