Advances in Optical Physics: Volume 4 Advances in Nanophotonics 9783110307009, 9783110304312

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Qihuang Gong, Zhi Li, Limin Tong, Yipei Wang, Yufei Wang, Wanhua Zheng Advances in Nanophotonics

Advances in Optical Physics

Editor-in-Chief Jie Zhang

Volume 4

Qihuang Gong, Zhi Li, Limin Tong, Yipei Wang, Yufei Wang, Wanhua Zheng

Advances in Nanophotonics Edited by Limin Tong

DE GRUYTER

Physics and Astronomy Classification Scheme 2010 07.79.Fc, 63.22.Gh, 68.37.Uv, 81.16.−c, 85.60.Bt Editor Prof. Limin Tong Zhejiang University Yuhangtang Road 866 310058, Xihu District Hangzhou China

ISBN 978-3-11-030431-2 e-ISBN (PDF) 978-3-11-030700-9 e-ISBN (EPUB) 978-3-11-038288-4 Set-ISBN 978-3-11-030701-6 Library of Congress Cataloging-in-Publication Data A CIP catalog record for this book has been applied for at the Library of Congress. Bibliographic information published by the Deutsche Nationalbibliothek The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available on the Internet at http://dnb.dnb.de. © 2018 Shanghai Jiao Tong University Press and Walter de Gruyter GmbH, Berlin/Boston Typesetting: Compuscript Ltd., Shannon Printing and binding: CPI books GmbH, Leck Cover image: Ellende/iStock/Thinkstock ∞ Printed on acid-free paper Printed in Germany www.degruyter.com

The series: Advances in Optical Physics Professor Jie Zhang, Editor-in-chief, works on laserplasma physics and has made significant contributions to development of soft X-ray lasers, generation and propagation of hot electrons in laser-plasmas in connection with inertial confinement fusion (ICF), and reproduction of some extreme astrophysical processes with laser-­plasmas. By clever design to enhance pumping efficiency, he and his collaborators first demonstrated saturation of soft-X-ray laser output at wavelengths close to the water window. He discovered through theory and experiments that highly directional, controllable, fast electron beams can be generated from intense laser-plasmas. Understanding of how fast electrons are generated and propagated in laser-plasmas and how the resulting electron beams emit from a target surface and carry away laser excitation energy is critical for understanding of the fast-ignition process in ICF. Zhang is one of the pioneers on simulating astrophysical processes by laser-plasmas in labs. He and his collaborators used high-energy laser pulses to successfully create conditions resembling the vicinity of the black hole and model the loop-top X-ray source and reconnection overflow in solar flares. Because of his academic achievements and professional services, Professor Zhang received Honorary Doctors of Science from City University of Hong Kong (2009), Queen’s University of Belfast (2010), University of Montreal (2011) and University of Rochester (2013). He was elected member of CAS in 2003, member of German Academy of Sciences Leopoldina in 2007, fellow of the Third World Academy of Sciences (TWAS) in 2008, foreign member of Royal Academy of Engineering (FREng) of the UK in 2011 and foreign Associate of US National Academy of Sciences (NAS) in 2012. He is the Vice-President of the Chinese Academy of Sciences (CAS) and also a strong advocate and practitioner of higher education in China.

https://doi.org/10.1515/9783110307009-202

Preface After a three years’ effort by many top-tier scientists, the book series Advances in Optical Physics (English version) is completed. Optical physics is one of the most active fields in modern physics. Ever since lasers were invented, optics has permeated into many research fields. Profound changes have taken place in optical physics, which have expanded tremendously from the traditional optics and spectroscopy to many new branches and interdisciplinary fields overlapping with various classical disciplines. They have further given rise to many new cutting-edge technologies: –– For example, nonlinear optics itself is an interdisciplinary field, which has been developing since the advent of lasers and it is significantly influenced by various technological advances, including laser technology, spectroscopic technology, material fabrication and structural analysis. –– With the rapid development of ultra-short intense lasers in the past 20 years, high field laser physics has rapidly developed into a new frontier in optical physics. It contains not only rich nonlinear physics under extreme conditions, but also has the potential of many advanced applications. –– Nanophotonics, which combines photonics and contemporary nanotechnology, studies the mechanisms of light interactions with matter at the nanoscale. It enjoys important applications such as in information transmission and processing, solar energy, and biomedical sciences. –– Condensed matter optics is another new interdisciplinary field, which is formed due to the intersection of condensed matter physics and optics. Here, on the one hand, lasers are used as probes to study the structures and dynamics of condensed matter. On the other hand, discoveries from condensed matter optics research can be applied to produce new light sources, detectors, and a variety of other useful devices. In the last 20 years, with the increasing investment in research and development in China, the scientific achievements by Chinese scientists also become increasingly important. These are reflected by the greatly increased number of research papers published by Chinese scientists in prestigious scientific journals. However, there are relatively few books for a broad audience – such as graduate students and scholars – devoted to this progress at the frontiers of optical physics. In order to change this situation, three years ago, Shanghai Jiao Tong University Press discussed with me and initiated the idea to invite top-tier scientists to write the series of “Advances in Optical Physics”. Our initial plan was to write a series of introductory books on recent progresses in optical physics for graduate students

https://doi.org/10.1515/9783110307009-203

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 Preface

and scholars. It was later expanded into its current form. The first batch of the series includes eight volumes: –– Advances in High Field Laser Physics –– Advances in Precision Laser Spectroscopy –– Advances in Nonlinear Optics –– Advances in Nanophotonics –– Advances in Quantum Optics –– Advances in Ultrafast Optics –– Advances in Condensed Matter Optics –– Advances in Molecular Biophotonics Each volume covers a number of topics in the respective field. As the editor-in-chief of the series, I sincerely hope that this series is a forum for Chinese scientists to introduce their research advances and achievements. Meanwhile, I wish these books are useful for students and scholars who are interested in optical physics in general, one of these particular fields, or a research area related to them. To ensure these books could reflect the rapid advances of optical physics research in China, we have invited many leading researchers from different fields of optical physics to join the editorial board. It is my great pleasure that many top tier researchers at forefronts of optical physics accepted my invitation and made their contributions in the last three years. Almost at the same time, De Gruyter learned about our initiative and expressed their interest in introducing these books written by Chinese scientists to the rest of world. After discussion, De Gruyter and Shanghai Jiao Tong University Press reached the agreement in co-publishing the English version of the series. At this moment, on behalf of all authors of these books, I would like to express our appreciation to these two publishing houses for their professional services and supports to sciences and scientists. Especially, I would like to thank Mr. Jianmin Han and his team for their great contribution to the publication of this book series. At the end of this preface, I must admit that optical physics itself is a rapidly expanding forefront of science. Due to the nature of the subject area, this series can never cover all aspects of optical physics. However, what we can do – together with all authors of these books – is to try to pick up the most beautiful “waves” from the vast science ocean to form this series. By publishing this series, it is my cherished hope to attract minds of younger generation into the great hall of optical physics research. Professor Jie Zhang Editor-in-chief

Contents Preface

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Zhi Li and Qihuang Gong 1 Scanning near-field optical microscopy 1 1.1 Fundamentals of SNOM 2 1.1.1 Principles 2 1.1.2 Types and operating modes 7 1.1.3 Near-field optical probe 14 1.1.4 Probe–sample distance control 21 1.2 Applications of SNOM 26 1.2.1 Near-field superresolution imaging 26 1.2.2 Near-field spectroscopy 35 1.2.3 Active applications of SNOM 42 1.3 Ultrahigh time-resolved fs-SNOM 46 47 1.3.1 Femtosecond time-resolved spectroscopy 1.3.2 Combination of femtosecond spectroscopy and near-field optics 1.3.3 Applications of femtosecond near-field microscopy 54 1.3.3.1 Semiconductor nanostructures 54 1.3.3.2 Metal nanostructures 58 1.3.3.3 Femtosecond laser pulse tracking in photonic devices 65 1.4 Summary and outlook 68 Bibliography 69 Yipei Wang and Limin Tong 2 Nanofibers/nanowires and their applications in photonic components and devices 76 76 2.1 Introduction 2.1.1 Glass nanofibers 77 2.1.2 Semiconductor nanowires 80 2.1.3 Polymer nanowires 83 2.1.4 Nonlinear optical crystal nanowires 85 2.1.5 Metal nanowires 87 2.2 Optical waveguiding properties 93 2.2.1 Dielectric nanofibers/nanowires 93 2.2.1.1 Mathematical model 94 2.2.1.2 Propagation constants and single-mode condition 95 2.2.1.3 Modal fields 95 2.2.1.4 Power distributions and effective diameters 98 2.2.1.5 Waveguide dispersion 101

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2.2.2 Metal nanowires 101 2.2.2.1 Propagation constants 102 2.2.2.2 Modal profiles 103 2.2.2.3 Energy confinement 104 2.2.2.4 Propagation loss 105 2.3 Nanofiber/nanowire-based photonic components and devices 106 2.3.1 Nanofiber/nanowire router/coupler 107 Nanofiber/nanowire filter 2.3.2 108 2.3.3 Nanofiber/nanowire Mach–Zehnder interferometer 2.3.4 Nanofiber/nanowire grating 110 2.3.5 Nanofiber/nanowire resonator 114 2.3.6 Nanofiber/nanowire laser 116 2.3.7 Nanofiber/nanowire sensor 119 2.3.8 Nanofiber/nanowire photodetector 121 2.4 Summary 127 Bibliography 128

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Yufei Wang and Wanhua Zheng 3 Micro/nano-optoelectronic devices based on photonic crystal Properties and applications of PC 3.1 135 Passive photonic devices based on PC 3.2 140 Integrated devices based on PC waveguides 3.2.1 140 Magneto-optical PC devices 3.2.2 141 PC self-collimation sensor 3.2.3 143 Active optoelectronic devices based on PC 3.3 146 Optically pumped PC surface-emitting laser 3.3.1 146 PC-deformed H1 cavity laser 3.3.1.1 148 PC H3 cavity laser 3.3.1.2 149 3.3.1.3 PC triangular cavity laser 150 3.3.2 Optically pumped PC edge-emitting laser 151 3.3.3 Electric injection PC VCSELs 153 3.3.3.1 Point-defect PC-VCSEL 154 3.3.3.2 Ring-defect PC-VCSEL 155 3.3.3.3 Petal-shaped holey VCSEL 160 3.3.4 Electric injection lateral cavity PC surface-emitting laser (LC-PCSEL) 163 3.3.5 PC lasers with high beam quality 167 3.3.6 Silicon-based hybrid integrated laser 171

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3.3.7 PC semiconductor optical amplifier 3.4 Summary and outlook 173 Bibliography 174 Index

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1 Scanning near-field optical microscopy In nanophotonics, studies mainly focus on micrometer- or nanometer-scale optical phenomena. The characteristic sizes of the sample structures and related optical fields are often less than half the wavelength. However, given the optical diffraction limit, traditional far-field optical detecting methods are unable to achieve an optical resolution better than half the wavelength. Therefore, measuring the optical information with high spatial resolutions beyond the diffraction limit is a significant issue. This topic is important for the effective optical characterization of nanophotonic devices. The emergence of near-field optical detecting techniques solves this problem. By scanning a nanometric optical probe at only a few nanometers from the sample surface, ultrahigh optical resolutions less than a few tens of nanometers may be obtained, thus providing an important characterization method for nanophotonic research. This approach is called scanning near-field optical microscopy (SNOM) or near-field scanning optical microscopy. SNOM was first developed in the 1980s and 1990s and belongs to the family of scanning probe microscopy (SPM). SNOM has various unique advantages compared with other spatially high-resolution microscopy methods, such as scanning electron microscopy (SEM), scanning tunneling microscopy (STM), and atomic force microscopy (AFM), because of its optical detecting method. For example, SNOM does not require a vacuum environment and can directly work in the atmosphere or in a liquid environment. SNOM usually engages visible or near-infrared lights as detected signals; thus, the sample does not incur any damage effects. More importantly, the optical spectroscopic detections by SNOM can provide information on the chemical compositions and structures of the samples. These detections are significant for the in-depth understanding of sample property. Given these advantages, SNOM has been widely applied to diverse research areas such as low-dimensional nanomaterials, nanophotonic devices, surface plasmons (SPs), thin films, and biological samples. In this chapter, we introduce some basics on SNOM and several important applications. In Chapter 1.1, the fundamentals of SNOM are provided. We first explain the basic working principle of SNOM and then introduce the different types and operation modes of SNOM. Thereafter, two key elements in SNOM are discussed, namely, the near-field optical probe and the probe–sample distance control mechanism. In Chapter 1.2, we present several typical SNOM applications, including near-field

Zhi Li and Qihuang Gong: State Key Laboratory for Mesoscopic Physics and Department of Physics, Peking University, Beijing 100871, China https://doi.org/10.1515/9783110307009-001

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super-resolution imaging, near-field spectroscopy, and active SNOM applications. In Chapter 1.3, we focus on the ultrahigh time-resolved femtosecond SNOM (fs-SNOM), which is an important research topic. In Chapter 1.4, a summary and outlook is ­provided.

1.1 Fundamentals of SNOM 1.1.1 Principles The spatial resolution of a conventional optical microscope is restricted by the optical diffraction limit [1, 2]. According to the diffraction effect of the objective lens with a finite aperture, a point light source at the object plane will be imaged to a ­Fraunhofer diffraction pattern at the image plane (Figure 1.1a). The zero-order diffraction spot possesses nearly 84% of the total light energy, which is known as the Airy disk, and has a half-angular breadth of 1.22 λ/D, where λ and D denote the wavelength and the diameter of the objective lens, respectively. If two or more point light sources are close to one another, their Airy disks will overlap. Thus, a pair of point sources can be resolved only if the central peaks of their diffraction patterns are not closer than the radius of the Airy disks (Figure 1.1b). This is known as the Rayleigh criterion. For two point light sources with equal intensities, the corresponding total light-intensity distribution is displayed by the solid line in Figure 1.1b. The light intensity at the central depression is approximately 74.5% of the maximum light intensity, which can distinguish the two point sources. According to the ­Rayleigh criterion, the spatial resolution of a conventional optical microscope can be expressed as 0.61 λ0/nsinθ [3, 4], where λ0 is the vacuum wavelength of the incident light, n is the refractive index of the media in the object space (between the sample and the objective lens), and θ is the half-angle of the maximum cone of light that can enter the objective lens. Here, nsinθ is also called the numerical aperture (NA) of the objective lens. According to the previous equation, to improve the spatial resolution of a microscope, one may use light sources with short wavelengths or increase the NA of the objective. Efforts using short-wavelength light sources include applications of UV and X-ray sources in photolithography and the production of large-scale integrated circuits. The high spatial resolutions of electron microscopes are also based on short working wavelengths. For example, electrons with 10 keV of energy have a de Broglie wavelength of only 0.037 nm. However, these methods lose the advantages of optical detections in the visible wavelength range. By contrast, the NA of the objective lens can be increased by increasing the refractive index of the media in the object space. However, the improvements are quite limited because the highest NA of oil immersion objectives is generally less than 1.5. Therefore, the spatial resolution of a conventional optical microscope can only reach about half of the working wavelength.

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Fig. 1.1: Illustration of the optical diffraction limit. (a) Light distribution at the image plane of the objective lens from a point light source. (b) Light-intensity distribution corresponding to the Rayleigh criterion.

Is it possible to achieve superresolution imaging beyond the diffraction limit with visible light? The earliest proposal was presented by Synge in 1928 [5]. He proposed to place an opaque plate with a nanometric aperture upon the sample, with the plate and sample spacing maintained at only a few nanometers (Figure 1.2). Light illuminates the sample through the nanometric aperture, and the transmitted or reflected light from the sample is collected and detected by a conventional microscope. Given that the divergence of the illumination light field is small after propagating through the short spacing between the aperture and the sample, the irradiated area on the sample surface is approximately equal to the nanometric aperture. Thus, the collected light signals by the far-field microscope are only contributed from the nanometric irradiated area on the sample. Therefore, detailed optical information of the sample with a spatial scale smaller than the diffraction limit can be effectively resolved. The according optical resolution mainly depends on the size of the aperture and the spacing between the aperture and the sample and is nearly independent of the incident wavelength. For a small spacing and thin sample, the resolution is approximately equal to the diameter of the aperture. By relatively scanning the aperture to the sample point by point, the superresolution optical image of the entire sample can be obtained. Although the above idea of near-field optical detection was presented quite early, the experimental demonstration was rather difficult, particularly the stable control of the small distance between the aperture and the sample. In 1972, a high optical resolution beyond the diffraction limit (λ/60) was achieved for the first time by Ash and Nicholls [6] at a wavelength of 3 cm, which is in the microwave band. This achievement of imaging beyond the diffraction limit largely benefits from the released requirement on distance control between the aperture and the sample, as the distance is located in the millimeter lever in the microwave region. Stable distance control on the nanometer scale was only possible until the early 1980s, with the development of STM [7] and AFM [8] techniques. In 1984, Pohl et al. [9] and Lewis et al. [10] independently realized SNOM and successfully obtained optical imaging beyond the diffraction limit at visible wavelengths. Later, in 1991, Betzig et al. [11]

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Fig. 1.2: Schematic of the scanned aperture microscopy showing the potential of achieving high resolution by restricting the sample to the near field.

produced near-field probes with high optical throughputs by depositing metal films on the sides of pulled optical fibers; this approach greatly improves the signal-tonoise ratio of SNOM. Betzig et al. [12] also proposed to control the probe–sample distance by shear force, which greatly facilitated the stable control of the probe–sample distance on the nanometer level. Since then, SNOM has been widely used in various research fields. Some companies also launched commercial near-field optical microscopes, such as TopoMetrix in the United States, Nanonics in Israel, Jasco in Japan, and NT-MDT in Russia. So far, many research groups have conducted studies with SNOM. In China, the group of Xing Zhu in Peking University started to study nearfield optics early and successfully constructed the first low-temperature SNOM, and the group of Qihuang Gong established an ultrahigh time-resolved fs-SNOM system. Furthermore, groups from the Institute of Physics, University of Science and Technology of China, Tsinghua University, and Dalian University of Technology also conducted research in near-field optics early. In recent years, more groups have joined this field through the use of commercial SNOM. To further understand the concept of optical near field and the principle of nearfield superresolution imaging, we introduce the angular spectrum representation in Fourier optics [13, 14]. The function of a microscope is to magnify and reconstruct the nonuniform distribution of the light field on sample surfaces. During the imaging process, the external irradiation lights interact with the sample. The transmitted, reflected, scattered, or reemitted lights (such as the fluorescence) from the sample are then collected by the lens for imaging. Such an electromagnetic interaction process cannot be described well by simple geometrical optics. One method is to expand the electromagnetic field at the sample surface into a series of plane waves and evanescent waves with different amplitudes and propagation directions. The propagation process of the total light field can be described by the superposition of the propagations of different wave compositions. This method is called angular spectrum representation.

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For instance, assuming an optical field U (x, y, 0) distributed at the z = 0 plane (x, y, z are the Cartesian coordinates), a new optical field distribution U (x, y, z) exists at a distance of z from the initial z = 0 plane after the diffraction and propagation of the optical field along the z direction. According to the Huygens–Fresnel principle, U (x, y, z) can be completely determined by U (x, y, 0). To identify the relationship between the two, we first perform two-dimensional (2D) Fourier transform on U (x, y, 0) to obtain the related angular spectrum A0 (kx, ky, 0):

A0 (k x , k y , 0) =

+∞

1 � � U(x, y, 0) exp[−i(k x x + k y y)]dxdy,(1.1) 2𝜋 −∞

where kx and ky are the corresponding components of wave vector k in the x and y directions, respectively; kx and ky have the same dimension as the spatial frequency (which is defined as the reciprocal of the spatial period). A high spatial frequency in the Fourier space corresponds to a small period in the real space, which represents small sample structures. The inverse Fourier transform is then expressed as follows: +∞



1 � � A0 (k x , k y , 0) exp[i(k x x + k y y)]dk x dk y .(1.2) U(x, y, 0) = 2𝜋 −∞

This means U (x, y, 0) can be decomposed into a series of plane waves propagating along different directions with different amplitudes. The specific propagation direction of a plane wave is indicated by the wave vector k, which is determined by components kx and ky and module k. The corresponding amplitude of the plane wave is A0 (kx, ky, 0). Similarly, the light-field distribution U (x, y, z) can be expressed as follows:

U(x, y, z) =

+∞

1 � � A(k x , k y , z) exp[i(k x x + k y y)]dk x dk y .(1.3) 2𝜋 −∞

The light-field propagation process can be described by the relationship between amplitudes A0 (kx, ky, 0) and A (kx, ky, z). The light field should satisfy the Helmholtz equation:

∇2 U + k2 U = 0(1.4)

where the module of the wave vector k is determined by k = nk0, with n as the refractive index of the media and k0 as the vacuum wave vector. Inserting the Fourier representation of the light field into the Helmholtz equation yields the following expression:

A(k x , k y , z) = A0 (k x , k y , 0) exp�−iz�k2 − k2x − k2y � (1.5)

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Equation (1.5) shows that the angular spectrum A (kx, ky, z) of field distribution U (x, y, z) can be directly deduced from the angular spectrum A0 (kx, ky, 0) of field distribution U (x, y, 0). Mathematically, the only difference between the two angular spectra is an exponential factor. However, two completely different situations exist in physics. If ​k​x 2 ​  + ​k ​ 2y​ ​ < k2, the exponential term in Equation (1.5) becomes an oscillating function of z, which represents a phase shift factor. This means the corresponding light field can propagate along the z direction with the amplitude unchanged with z. In this case, the light field corresponds to a plane wave, which is a propagating field. For the total light field at z = 0, the low spatial frequency ( k2, the exponential term corresponds to an exponentially decaying function of z. The propagation equation of the angular spectrum can be rewritten as follows:

A(k x , k y , z) = A0 (k x , k y , 0) exp(−𝜇z),(1.6)

where 𝜇 = �k2x + k2y − k2 is a real positive number. In this case, the amplitude of the light field attenuates exponentially with an increase in the propagation distance in the z direction. This type of light field is called the evanescent field or evanescent wave because the amplitude of such a light field decays rapidly with increasing distance from the z = 0 plane. The evanescent field, which is also called a nonradiative field, only exists near the surface of the sample and cannot spread far. This light field has high spatial frequencies (>k) and carries optical information from small sample structures. The light field that contains information on the fine structure of the sample cannot propagate and is limited to a region near the sample surface, and such a region is called the near-field zone. The attenuation length d = 1/𝜇 indicates the dimension of the near-field zone. A higher-order diffracted wave (with larger spatial frequency) has a shorter attenuation length d. The value of d is typically less than half the wavelength. By contrast, the region outside the near-field zone is generally defined as the far-field region. In an actual diffraction process, the propagating and evanescent fields generally coexist, with the relative weights depending on the sample structure. The evanescent waves dominate when a sample mainly consists of structures smaller than the wavelength. The imaging process of a microscope can be analyzed by using the angular spectrum method. For a conventional far-field optical microscope, the objective lens operates in the far-field region with a distance from the sample much larger than the wavelength. Given the finite aperture of the objective lens, only propagating waves that satisfy ​kx​ 2 ​  + ​k 2​ y​ ​ < k2sinθ 2 can be collected by the objective, with θ being the halfangle of the maximum cone of light that can enter the objective. That is, only field components with spatial frequencies kx, ky< ksinθ of the total light field U (x, y, 0) are collected by the objective lens. Therefore, the detected lateral spatial period is larger than λ/sinθ. This spatial period corresponds to the diffraction limit proposed by Abbe [3]. Field components with spatial frequencies larger than k must be detected

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effectively to break the diffraction limit, that is, the detection of the nonradiative evanescent field in the near-field zone. In SNOM, this process is realized by using a nanometric optical probe to detect the evanescent field, at a short distance from the sample surface much smaller than the wavelength. The spatial frequency components collected by the near-field probe depend primarily on the probe aperture and probe–sample distance. A larger probe aperture allows the detection of a smaller spatial frequency, resulting in worse SNOM resolution. A larger probe–sample distance suggests that the evanescent fields with higher spatial frequencies exhibit more attenuation; this phenomenon also results in a worse SNOM resolution. The nearfield probe generally has an aperture size of a few tens of nanometers and detects the light field at a short distance from the sample surface below 10 nm, thus providing an SNOM spatial resolution that is approximately equal to the probe aperture.

1.1.2 Types and operating modes The various SNOM systems can be divided into two main categories, namely, the aperture-type SNOM (a-SNOM) and the apertureless SNOM or scattering-type SNOM (s-SNOM). The concept of a-SNOM, which was developed earlier and is relatively more mature than s-SNOM, is very close to that proposed by Synge [5] in 1928. This type of SNOM generally uses a near-field probe with a nanometric open aperture at the end of the probe. In an a-SNOM experiment, either the excitation light or the probe light should pass through the nanometric open aperture (Figure 1.3a). Different operating modes are available for an a-SNOM. According to the role of the near-field probe, this process can be mainly divided into the illumination mode (I-mode), the collection mode (C-mode), and the illumination–collection mode (IC-mode) [15–17].

Fig. 1.3: Different types of scanning near-field optical microscopes: (a) aperture SNOM, (b) apertureless SNOM, and (c) PSTM. Reprinted with permission from Painter et al. [17]. Copyright 2000, AIP Publishing LLC.

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In the I-mode, the excitation light is coupled into the near-field probe and illuminates the sample through the probe aperture (Figure 1.4a). The objective lens in the far field is used to collect the reflected, transmitted, or fluorescence signals of the sample. In this process, the probe aperture is used to generate a highly localized nanometric light source, which can be used to realize the high-resolution optical imaging of the sample. According to angular spectrum theory, the light fields emitted by this highly localized source contain a large amount of evanescent fields with large kx and ky. After interacting with (such as through diffractions) small structures with high spatial frequencies in the sample, parts of the evanescent fields can be efficiently converted to propagation fields with small kx and ky. These fields are then collected and detected by the far-field lens, which carries the optical information of the sample structures with high spatial frequencies. Given that only the small sample area under the nanometric aperture is illuminated in the experiment, the I-mode has few stray lights, which helps achieve near-field optical imaging with high spatial resolution and high signal-to-noise ratio. For most of the a-SNOM experiments, the I-mode is generally engaged if possible. For example, in single-molecule fluorescence experiments, the small excitation volume of the I-mode can provide high excitation intensity with a relatively weak incident light. This characteristic ensures the signal intensity of single-molecule fluorescence. Moreover, the small excitation volume also leads to high spatial resolution, minimal noise signal, and the reduction of photobleaching effects of neighboring fluorescent molecules. Thus, SNOM is an important tool in single-molecule detections [18,  19]. However, some luminescent materials, such as several semiconductors, present relatively different cases. Although the excitation volume of the I-mode is small, the luminescent volume may be larger because of the diffusions of the excited carriers inside the luminescent material before carrier recombination and reemission. Moreover, various waveguides may also form in the semiconductor materials. These factors may complicate the interpretation of the scanned near-field image in I-mode SNOM.

Fig. 1.4: Different operating modes of the aperture SNOM: (a) I-mode, (b) C-mode, and (c) IC-modes.

Contrary to the I-mode, in the C-mode SNOM, the excitation light illuminates the sample through the far-field lens (Figure 1.4b) or couples into the sample in a certain

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manner; this process determines the optical field distribution of the sample. There­ after, the light field is collected for detection by the nanometric aperture of the probe in the near field of the sample. Thereby, a high-resolution image of the field distribution can be obtained through scanning. In this process, the probe aperture can be viewed as a nanometric optical detector. Considering angular spectrum theory, the nanometric aperture in the C-mode SNOM acts as a grating with high spatial frequency, which can effectively convert evanescent fields with large kx and ky on the sample surface to the propagation fields with small kx and ky through diffraction effects. Such propagation fields can be detected by the far-field detector, thus providing a measurement to the intensity of the original evanescent fields. The C-mode SNOM is commonly used in the study of the light-emitting properties of semiconductor devices, particularly the electroluminescent properties. The spatial resolution of the C-mode SNOM is mainly determined by the size of the probe aperture, and the image contrast is generally assumed to directly correspond to the detected light-field distribution. One main drawback of the C-mode SNOM is the possible disturbance of the near-field probe to the detected optical field because the existence of the probe may change the field distribution of the sample. This case is a general phenomenon, specifically for the commonly used metal-coated near-field probe. A probe with metal coating may not only strongly couple to the detected metal nanostructures but also cause evident quenching on the detected fluorescence molecules. Another drawback is that the collection efficiency of the nanometric aperture to the detected light field is low; thus, the signal-to-noise ratio is also low in the C-mode SNOM. Moreover, the C-mode SNOM has a large excitation area with more stray lights and more noise signals, if far-field excitation is engaged. The large excitation area may easily lead to damage to the neighboring sample molecules. All these drawbacks limit the application of the C-mode SNOM. A special class of near-field optical microscopes is known as the photon scanning tunneling microscope (PSTM) or scanning tunneling optical microscope [20, 21]. In the PSTM, the sample is generally illuminated by an evanescent field generated through the total internal reflection (TIR), and the near-field light signal of the sample is collected by the probe (Figure 1.3c). Considering that the evanescent field generated by TIR decays exponentially with an increase in the probe–sample distance, the basic concept of PSTM is similar to the STM. The detected physical quantity in PSTM is the optical intensity of the evanescent field instead of the tunneling current in STM. Therefore, this type of near-field microscope is called the PSTM. The PSTM is mainly used for the detection of the evanescent optical field, including SPs and evanescent fields in various waveguides and microcavities. The measured imaging contrast is typically interpreted as the intensity distribution of the detected evanescent field. PSTM experiments usually use uncoated fiber probes. This type of probe has relatively high signal collection efficiency and less disturbance to the detected field because of the purely dielectric probe. However, in addition to the probe tip, light signals may also enter the uncoated fiber probe from the probe side, thus resulting in

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a complex detected signal. Therefore, the PSTM is more suitable for detecting a purely evanescent field (i.e., with other scattered light components negligible) than a field consisting of both evanescent and propagating components. Typical spatial resolutions of PSTM are approximately 100 nm. To some extent, the PSTM can be viewed as a specific form of the C-mode SNOM because both excite the samples by far-field lights and collect the signal light by near-field probes. The only difference is that the detected field in the PSTM is primarily the evanescent field. Considering that such evanescent field decays rapidly away from the sample surface, it can be assumed that only the probe tip nearest to the sample surface interacts strongly with the evanescent field. In this case, the PSTM probe tip without a metal coating works similarly to the metal-coated fiber probe in the conventional C-mode SNOM. Both parts convert the evanescent field of the sample into propagation modes in the optical fiber for further detections through diffraction or scattering. The last commonly used operating mode in the a-SNOM is the IC-mode (Figure 1.4c). In the experiment, the incident light illuminates the sample through the probe aperture, and the signal light is collected through the same probe aperture. The excitation and signal lights can be separated by a beam splitter in the outer optical system or by a fiber coupler. The IC-mode can offer small excitation volume and high spatial resolution. However, given the low optical throughput of the near-field probe (typically 10−3 to 10−6), the signal light intensity is low after passing through the nanometric aperture twice. This is the main drawback of the IC-mode. To improve the signal intensity, the IC-mode generally uses probes with high optical throughputs, such as uncoated fiber probes or metal-coated fiber probes with large cone angles. The IC-mode SNOM can avoid the far-field optical elements near the sample for delivering the excitation light or collecting the signal light. Thus, this type of SNOM is suitable for experiments under extreme conditions, such as in low temperature or ultrahigh vacuum cases, wherein installing ancillary optical elements near the sample are inconvenient [22]. Compared with the traditional a-SNOM, the s-SNOM can provide higher spatial resolutions and has been considerably developed in recent years [23]. The resolution of the traditional a-SNOM is determined by the optical aperture of the near-field probe. Given that the highly localized light field in the probe always has a certain extension in the metal coating, the resolution of the a-SNOM can only reach twice the skin depth of the light field in the metal coating. In the visible wavelength, even for a good conductor, the corresponding skin depth is still approximately 6–10 nm. This characteristic indicates that even if the geometric aperture of the metal-coated nearfield probe is zero, the actual optical aperture is still approximately 10–20 nm because of the expansion of the light field in the metal coating. This factor limits the resolution of the a-SNOM [1]. Moreover, considering the cutoff effects of the waveguide mode in the metal-coated aperture probe (i.e., when the diameter of the metal-coated fiber probe is below a certain value, the propagation waveguide mode will not exist in the probe, and only evanescent modes exist), the optical throughput of an aperture probe decreases rapidly with increasing wavelength or decreasing probe aperture. Therefore,

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to maintain a certain optical throughput to ensure the effective detection of the signal light, the probe aperture cannot be too small in practice, normally not smaller than λ/10. For example, in the visible wavelength range, the probe aperture and corresponding spatial resolution of the a-SNOM is generally approximately 50–100 nm. By contrast, the nanometric optical aperture is unnecessary in the s-SNOM experiment. Under the irradiation of the far-field excitation light, a highly localized light field is produced near the end of the probe tip in the s-SNOM (Figure 1.3b). This localized light source interacts with the nanometric sample area just below, and the scattered light is collected by the far-field lens for detection. A high spatial resolution can be achieved because the scattered light signal carries the optical information of the local sample area interacting with the highly localized light field. Here, both the delivery of the incident excitation light and the collection of the scattered signal light are performed by far-field optical elements without the need to pass through a nanometric aperture; thus, this type of SNOM is called the apertureless SNOM or scattering-type SNOM. The optical resolution of such SNOM system mainly depends on the size of the localized light field generated by the near-field probe, which usually has no relation with the working wavelength and is approximately equal to the diameter of the probe tip. Thus, a higher resolution can be achieved compared with the a-SNOM. The typical spatial resolution of the s-SNOM reaches 10–20 nm, with the best resolution of approximately 1 nm [24, 25]. The simplest and most commonly used configuration in the s-SNOM experiment is to detect the backscattered light signal, given that one lens can accomplish both the delivery of the incident excitation light and the collection of the signal light. The s-SNOM experiment strongly depends on the light polarization, with only the incident polarization along the probe axis (z direction) providing significant image contrasts [26, 27]. This phenomenon is because the apertureless near-field probe can be considered an optical antenna, which can only be effectively excited to the resonance by the incident light polarized parallel to the probe axis. This point can also be well understood by considering the continuity of Maxwell’s equations at the boundary. According to Maxwell’s equations, the normal component of the electric displacement vector is continuous at an interface. Therefore, if the excitation field polarization is normal to the surface of the near-field probe tip and the probe material has a high dielectric constant, a high electric field intensity can be obtained in the low-refractive-index air gap in the vicinity of the probe tip. On the contrary, if the excitation polarization is parallel to the surface of the tip end, the electric field intensity is comparative in the probe, the sample, and the intermediate air gap because of the continuity of the tangential component of the electric field at an interface. Consequently, a highly localized light field cannot be produced. From the above analysis, it can also be inferred that a larger dielectric constant of the material used by the probe leads to a better locality and enhancement of the light field near the probe tip. That is why the probe for s-SNOM is usually made of materials with high dielectric constants, including high-refractive-index dielectrics (such as silicon and

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silicon nitride) and metal materials with large negative dielectric constants. Metals with good conductivities generally provide better effects because of the stronger resonance effect of the metallic optical antennas. If the laser light is incident from the side of the probe, the p-polarization should be engaged to enable the main component of the electric field along the axis of the probe, i.e., the z direction. However, if the laser light is normally incident from the substrate side, a radially polarized light is preferred because the main component of the focused electric field is along the z direction at the focal center. The scattered light signals from the nanometric probe are weak in the s-SNOM experiments; such scattered light signals are generally detected by interferometric detections. The weak scattered light signal is mixed with a strong reference light for interference. The interference signal is then detected, thus offering information on the amplitude and phase of the signal light. The absolute signal intensity detected in the s-SNOM experiment, i.e., the intensity of the total scattered light signal into the detector, depends primarily on the shape and size of the near-field probe. The more important quantity that provides the near-field image contrast, i.e., the relative change of the scattered light signals at different sample positions, is mainly determined by the near-field probe–sample interactions that can usually be described by a relatively simple point-dipole model [23, 28, 29]. The near-field image contrast primarily comes not from the shaft of the probe but from the probe tip, which can be approximately represented by a sphere inscribed in the apex of the probe. Considering only the electromagnetic effect, the sphere can be further simplified to a polarization dipole located at the sphere center. Thereafter, the polarization effect of the sample induced by this dipole is approximately represented by a mirror dipole. Thus, the near-field probe–sample interaction can be described by the interaction between the dipole at the probe tip and mirror dipole of the sample. A detailed quantitative formula is given by Equation 1 in Ref. [29]. This formula can qualitatively explain the main imaging mechanism of the s-SNOM. For instance, the near-field signal contrast is primarily induced by the dielectric constant change in the sample given a specific apertureless probe and a fixed probe–sample distance. The variation in the near-field signal can also be deduced with respect to the probe–sample distance. The results indicate that the near-field scattering amplitude and phase show obvious changes only when the probe–sample distance is small (roughly less than the diameter of the probe tip). This phenomenon implies that the true near-field interactions in the a-SNOM occur in a small spatial scale; thus, an ultrahigh spatial resolution may be achieved. Moreover, the nonlinear dependence of the near-field scattering signals on the probe–sample distance is an important signature of the emergence of near-field interactions. The nonlinear dependence of near-field scattering signals on the probe–sample distance can be used to effectively eliminate the background signal scattered by the apertureless probe [23, 30]. In an s-SNOM experiment, the laser spot irradiating the sample generally has a micrometer-scale dimension. However, the true near-field interaction only occurs in the vicinity of the nanometric probe tip. Thus, the near-field

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signal contributes only a small portion to the total detected signals. The main contributions of the detected signals are the scattered lights from the probe shaft, which are background-scattered signals that are independent of near-field interactions. Therefore, the effective suppression of this strong background scattering signal is important to obtain the correct near-field optical image. Given that the near-field probe can scan the sample in the tapping mode with the probe–sample distance oscillating at a certain frequency Ω, the corresponding near-field scattering signals will oscillate at the same frequency because the near-field signals change significantly with the probe–sample distance. The signals at the oscillating frequency Ω can be directly extracted by electronic methods (such as by using a lock-in amplifier) to effectively detect the near-field signals and suppress the background signals. However, entire probe oscillates as a whole, so the scattered light signals from the probe shaft also oscillate at the frequency Ω to a certain extent. Thus, such background signals cannot be suppressed well at the detection frequency of Ω. A better choice is to detect the scattered light signals at the high harmonic frequency of the probe oscillation, such as 2Ω or 3Ω. Given that the background-scattered signals from the probe shaft do not drastically change with the probe oscillation, the dependence of such signals to the probe–sample distance can be considered approximately linear. Hence, such signals will be effectively eliminated with the high harmonic frequency detections. By contrast, pure near-field signals vary significantly with the probe oscillation and show nonlinear dependence on the probe–sample distance. Thus, this signal component can still be effectively detected at a high harmonic frequency. Using the different dependencies of the signals on the probe–sample distance, the strong backgroundscattered signals can be highly suppressed and the weak pure near-field interaction component can be effectively extracted by detecting the high harmonic frequency of the probe oscillation. SNOM has various operating modes that should be selected properly according to specific experimental conditions and requirements. Nevertheless, these different types of SNOM have many common elements, such as the near-field optical probe, probe–sample distance feedback system controlling the z motion of the probe, 2D scan system driving the sample or the probe to scan in the x–y plane, and signal acquisition and image processing systems. Certain light sources and the auxiliary outer optical path are also needed. The x–y scan and image processing systems in SNOM are similar to those in the STM and AFM techniques. All these SPM techniques are based on computer controlled and highly precise (control accuracy of