Physical optics 9783030252786, 9783030252793
247 92 6MB
English Pages 946 Year 2019
Foreword......Page 7
Preface to the Italian edition......Page 8
Index......Page 10
Abbreviations and used symbols......Page 21
About the Author......Page 24
Introduction to Optics......Page 25
Part I Electromagnetism......Page 27
The dawning......Page 28
The laws of electromagnetism......Page 32
The discovery of electromagnetic waves......Page 40
Suggested reading......Page 44
1.1.1 Charges and fields......Page 46
1.1.2 The scalar and vector potentials......Page 49
1.1.3 Relativistic formulation of fields and Lorentz transformations......Page 51
1.2.1 Development of equations......Page 56
1.2.2 Electromagnetic properties of media......Page 59
1.2.3 Boundary conditions at interfaces between transparent media......Page 61
1.3 Complex field representation......Page 63
1.3.1 Generalization of susceptibility for dispersive media......Page 68
1.3.2 Temporal average of the product of variables......Page 71
1.4.1 Wave equations......Page 72
1.4.2 Homogeneous plane waves......Page 74
1.4.3 Inhomogeneous plane waves......Page 77
1.4.4 Spherical waves......Page 78
1.5.1 Derivation and general concepts......Page 79
1.5.2 Flow of energy in simple media......Page 81
1.6.2 Linear polarization......Page 86
1.6.3 Circular polarization......Page 88
1.6.4 Elliptical polarization......Page 91
1.6.5 Angular momentum of radiation......Page 93
1.6.6 Natural light......Page 95
1.6.7 Coherency matrix and Stokes’ parameters......Page 96
1.7 Reflection and refraction on plane interface......Page 99
1.7.1 Laws of reflection and refraction for homogeneous dielectric media......Page 100
1.7.2 Fresnel’s formulas......Page 101
1.7.3 Reflectivity and transmissivity......Page 105
1.7.4 Brewster’s angle......Page 106
1.7.5 Total reflection......Page 109
1.7.6 Evanescent wave......Page 113
1.7.7 Application of total internal reflection......Page 114
1.8 Dispersion theory......Page 115
1.8.1 Dispersion and extinction in dilute media......Page 116
1.8.2 Dispersion and extinction in dense media......Page 122
1.8.3 Relationship between the real and imaginary parts of the permittivity......Page 125
1.8.4 Dispersion in conducting media......Page 128
1.8.5 Phase, group and signal velocities......Page 131
1.9 Optics of metals and absorbent materials......Page 137
1.9.1 Reflection and refraction by absorbent materials......Page 141
Bibliographical references......Page 146
Part II Geometrical Optics......Page 148
The dawning......Page 149
The Arab period......Page 152
The Middle Ages......Page 155
The Renaissance......Page 156
The New Science......Page 158
The law of refraction and the speed of light......Page 165
The debate over the nature of light......Page 168
Suggested readings......Page 179
Introduction......Page 181
2.1 Derivation of Geometrical Optics for λ → 0......Page 182
2.2.1 The light rays and the radiant energy propagation......Page 186
2.2.2 Propagation of polarization......Page 188
2.3. Tracing law of rays in inhomogeneous media......Page 189
2.3.2 Curvature and torsion of the rays......Page 191
2.3.3 The optical path......Page 196
2.3.4 Collective properties of rays......Page 197
2.3.5 The laws of refraction and reflection in Geometrical Optics......Page 199
2.3.6 The Malus-Dupin theorem......Page 201
2.3.7 Fermat’s principle......Page 202
2.3.8 Wavefronts and caustics in a homogeneous medium......Page 205
2.4.1 Introduction......Page 212
2.4.2 General theorems......Page 213
2.4.3 Aplanatic surfaces of a refractive sphere......Page 215
2.4.4 Aspherical surfaces......Page 216
2.5.1 The homography......Page 219
2.5.2 Conventions on signs......Page 221
2.5.3 Non telescopic homography......Page 222
2.5.4 The telescopic case......Page 227
2.5.5 Combination of two homographies......Page 228
2.5.6 Final remarks......Page 231
2.6.1 Domain of validity......Page 232
2.6.2 Refraction through a spherical surface......Page 235
2.6.3 Reflection from a spherical mirror......Page 237
2.6.4 Relationship between the two focal lengths......Page 238
2.6.5 The lateral, angular and longitudinal magnification, and the Smith-Helmholtz-Lagrange optical invariant......Page 239
2.6.6 The lens......Page 242
2.6.7 Variety of simple lenses......Page 246
2.6.8 Optical center of a lens......Page 253
2.6.9 Combination of two thin lenses......Page 254
2.7.1 2x2 matrices......Page 258
2.7.2 Generalized tracing of rays by means of 4x4 matrices in the absence of axial symmetry......Page 263
2.7.3 Algorithm for the calculation of the matrix......Page 265
2.7.4 Curvature of a quadric surface......Page 277
2.7.5 Transformation of the wavefront......Page 279
2.7.6 Symmetry relations and optical path......Page 282
2.8.1 Aperture diaphragm and the entrance and exit pupils......Page 286
2.8.2 Relative aperture, or f-number, and numerical aperture......Page 287
2.8.4 Field diaphragm and entrance and exit windows......Page 289
2.8.5 Vignetting......Page 290
2.9 Aberrations......Page 291
2.9.1 The aberration functions for an axial optical system......Page 293
2.9.2 The cosine theorem, Abbe’s sine condition and Herschel’s condition......Page 299
2.9.3 Spherical aberration......Page 302
2.9.4 Coma......Page 306
2.9.5 Astigmatism and curvature of field......Page 308
2.9.6 Distortion......Page 311
2.9.7 Aberration of a thin lens......Page 312
2.9.8 Chromatic aberrations......Page 314
2.10.1 Plane mirrors......Page 319
2.10.2 Reflecting prisms......Page 321
2.10.3 Dispersive prisms......Page 324
Bibliographical references......Page 329
Part III Physical Optics......Page 332
Newton’s Optics......Page 333
The progress of the 18th century......Page 340
The emission theory and the speed of light......Page 342
Young and the principle of interference......Page 344
Fresnel......Page 353
The aether and stellar aberration......Page 354
Diffraction and Interference......Page 356
The “Mémoire couronné”......Page 363
The studies on polarization......Page 366
The transverse nature of waves......Page 367
Reflection......Page 371
Propagation in anisotropic media......Page 373
Epilogue......Page 378
Suggested reading......Page 380
Introduction......Page 382
3.1.1 The principle of linear superposition......Page 383
3.1.2 Interference between monochromatic plane waves......Page 384
3.1.3 Interference produced by two point sources......Page 386
3.2.1 Classification of interference methods......Page 390
3.2.2 Interference by division of the wavefront......Page 391
3.2.3 Tautochrone properties of Optical Systems......Page 394
3.2.4 Importance of the size of the light source......Page 395
3.2.5 Interference by amplitude division......Page 401
3.2.6 Localization of interference fringes......Page 412
3.2.7 Two-wave interferometers......Page 416
3.3.1 Fabry-Perot interferometers......Page 432
3.3.2 Transmission function (Airy function) of a Fabry-Perot with plane and parallel mirrors......Page 434
3.3.3 Applications of Fabry-Perot interferometers......Page 442
3.4.1 Reflection and transmission......Page 454
3.4.2 Propagation in periodic structures......Page 461
3.4.3 Reciprocity and time reversal: the Stokes relations......Page 463
3.4.4 Applications......Page 466
3.4.5 Phase dispersion and amplitude filtering on a wave not monochromatic......Page 473
3.4.6 Chirped mirrors......Page 475
Bibliographical references......Page 476
Introduction......Page 479
4.1.1 General premises......Page 481
4.1.2 The Kirchhoff formulation of the diffraction......Page 483
4.1.3 The Rayleigh-Sommerfeld formulation......Page 486
4.1.4 Diffraction by plane screens: comparison between the theories of Kirchhoff and Rayleigh-Sommerfeld......Page 487
4.1.5 The Huygens-Young-Fresnel principle......Page 490
4.1.6 Babinet’s principle......Page 491
4.1.7 Diffraction from a black screen: Kottler’s theory......Page 492
4.1.8 Outline on the calculation methods of the diffraction integrals......Page 494
4.1.9 Diffraction with quasi-monochromatic radiation......Page 496
4.2.2 Initial approximations......Page 499
4.2.3 Fresnel’s approximation......Page 501
4.2.4 Self-consistency of Fresnel’s diffraction......Page 504
4.2.5 Fraunhofer’s approximation......Page 506
4.2.6 Debye’s approximation......Page 507
4.2.7 Diffraction through an optical system described by an ABCD matrix......Page 509
4.3 Examples of Fraunhofer’s diffraction......Page 511
4.3.1 Rectangular aperture......Page 512
4.3.2 Circular aperture......Page 514
4.3.3 Single slit......Page 517
4.3.4 Double slit......Page 518
4.4.1 Fresnel’s zones......Page 519
4.4.2 Circular aperture......Page 522
4.4.3 Poisson’s paradox......Page 525
4.4.5 Rectangular aperture......Page 528
Bibliographical references......Page 532
Part IV Fourier’s Optics......Page 535
The mathematicians......Page 536
New glasses and optical instruments......Page 537
Research on the speed of light and on the aether......Page 540
The photography......Page 542
The studies on the color and the physiology of the eye......Page 543
Suggested readings......Page 545
5.1.1 Some special, frequently used functions......Page 547
5.1.2 Fourier’s transform......Page 550
5.1.4 Fourier’s transform in polar coordinates......Page 555
5.1.4 Uncertainty relation......Page 558
5.2.1 Fourier’s series......Page 560
5.2.2 Sampling theorem in Cartesian coordinates......Page 562
5.2.3 Sampling theorem in polar coordinates......Page 565
5.2.4 The Discrete Fourier’s Transform......Page 568
5.2.5 The Fast Fourier Transform......Page 574
5.3 Applications of the Fourier’s transform to the diffraction......Page 575
5.3.1 Application of the FFT to the Fresnel diffraction......Page 576
5.3.2 Angular spectrum of the field on an opening......Page 580
5.3.3 Reconstruction of the diffracted field......Page 581
5.3.4 Application of the FFT to a spatially delimited field with limited bandwidth......Page 583
5.3.5 Extending the range of application of the angular spectrum method......Page 585
5.3.6 Talbot’s effect......Page 591
5.4 Analysis of optical systems by means of the theory of linear systems......Page 593
5.4.1 Degrees of freedom of optical signals......Page 597
5.4.2 Behavior of a lens in the paraxial approximation......Page 598
5.4.3 Image formation......Page 600
5.4.4 As a lens does the Fourier’s transform......Page 602
5.4.5 Behavior in three dimensions......Page 603
5.4.6 Image formation with a generic optical system......Page 604
5.4.7 Images with incoherent illumination......Page 609
5.4.8 Resolution......Page 612
5.4.9 The Optical Transfer Function......Page 614
5.4.10 Apodization......Page 620
5.5 Coherence......Page 621
5.5.1 Random processes......Page 623
5.5.2 The power spectrum of random processes......Page 624
5.5.3 Theory of partial coherence......Page 626
5.5.4 Hanbury Brown and Twiss’ interferometer......Page 636
5.5.5 A classic experiment......Page 637
5.5.6 Propagation of coherence in an optical system......Page 638
5.5.7 Partial coherence and microscopy......Page 642
5.6 Spatial filtering......Page 645
5.6.1 Binary filters......Page 648
5.6.2 Schlieren filter......Page 650
5.6.3 Intensity and phase filters......Page 652
5.6.4 Phase contrast microscopes......Page 654
5.6.5 VanderLugt’s filter......Page 655
5.7 Diffraction gratings......Page 657
5.7.1 Reflection and refraction law of the gratings......Page 659
5.7.2 Diffraction efficiency......Page 663
5.7.3 Resolving power......Page 670
5.7.4 Types of grating......Page 671
5.7.5 Production......Page 672
5.7.6 Tools of analysis and spectral tuning......Page 673
5.7.7 Ronchi’s ruling......Page 677
Bibliographical references......Page 679
Part V Propagation......Page 682
Relativity......Page 683
Black body radiation......Page 685
The photon......Page 693
Suggested reading......Page 698
Introduction......Page 699
6.1 The paraxial wave equation......Page 700
6.2 Propagation of the fundamental Gaussian mode......Page 701
6.3.1 Modes in Cartesian coordinates......Page 706
6.3.2 Modes in cylindrical coordinates......Page 709
6.3.3 Polarization of the modes......Page 710
6.4.2 Measure of the diameter 2w of a TEM00 mode......Page 712
6.5.1 The ABCD law......Page 714
6.5.2 Effects of a thin lens......Page 716
6.5.3 Collimation of Gaussian beams......Page 719
6.5.4 Effects of a dioptre......Page 721
6.5.5 Determination of the waist position by means of the ABCD law......Page 722
6.5.6 Amplitude and phase of a Gaussian beam transmitted by an optical system with axial symmetry......Page 723
6.6.1 Astigmatic beams......Page 726
6.6.2 ABCD law for the propagation in a non-axial system......Page 731
6.7 Bessel’s waves......Page 737
6.8.1 Zero-order Bessel-Gauss beams......Page 740
6.8.2 Generalized Bessel-Gauss beams......Page 743
6.8.3 Propagation of a Bessel-Gauss beam through an axial optical system......Page 745
6.9 Resonant cavities......Page 747
6.9.1 Resonant modes......Page 749
6.9.2 Frequency of modes......Page 754
6.9.3 Multipass cavity......Page 757
6.9.4 Confocal cavity......Page 760
Bibliographical references......Page 762
Introduction......Page 764
7.1 Crystallography......Page 765
7.1.2 Three-dimensional lattices......Page 766
7.1.3 Operations of punctual symmetry in three dimensions......Page 769
7.1.4 Crystal systems......Page 770
7.1.5 Crystal classes......Page 771
7.1.6 Space groups......Page 772
7.2 The dielectric tensor......Page 775
7.3 Crystal classes and principal axes......Page 779
7.4.1 Wave equation and eigenvectors......Page 781
7.4.2 Fresnel’s equations......Page 785
7.4.3 The surface of the wave vectors......Page 787
7.4.4 Eigenvectors......Page 789
7.4.5 Optical axes......Page 792
7.4.6 The surface of phase velocity......Page 795
7.5.1 Group and energy velocity......Page 797
7.5.2 Inversion theorem......Page 800
7.5.3 Eigenvectors and eigenvalues......Page 801
7.5.4 The surface of group velocity......Page 802
7.6 Relations between the surfaces of phase velocity, group velocity and wave vectors......Page 804
7.7 Refraction at the interface with an anisotropic medium......Page 806
7.7.1 Graphical constructions......Page 808
7.7.2 Analytical method......Page 811
7.7.3 Refraction with uniaxial crystals......Page 814
7.7.4 Conical refraction......Page 817
7.8 Interference with birefringent plates......Page 823
7.8.1 Interference with a uniaxial crystal......Page 827
7.8.2 Interference with a biaxial crystal......Page 830
7.9 Bianisotropy......Page 831
7.9.1 Optical activity......Page 832
7.9.2 Constitutive equations......Page 834
7.9.3 Maxwell’s equations......Page 840
7.9.4 Symmetries and reciprocity......Page 842
7.9.5 Fresnel-Fizeau effect......Page 845
7.9.6 Faraday’s effect......Page 846
7.9.7 Phase velocity and rotatory power......Page 847
7.9.8 Optically active crystals......Page 856
7.10 Form birefringence......Page 862
7.11 Devices of manipulation and analysis of the polarization......Page 864
7.11.1 Calculation of the transformation of pure polarization states by means of Jones vectors and matrices......Page 865
7.11.2 Calculation of the propagation of partially polarized radiation through the Stokes parameters and Mueller matrices......Page 868
7.11.3 Polarizers......Page 871
7.11.4 Wave plate......Page 881
7.11.5 Depolarizers......Page 895
7.11.6 Combination of birefringent plates rotated between them......Page 898
7.11.7 Spectral filters by birefringence......Page 900
7.11.8 Optical isolators......Page 909
Bibliographical references......Page 911
Appendix A Conventions on electromagnetism......Page 915
B.2 Integral theorems......Page 918
B.3 Bessel’s functions......Page 919
B.4 Fresnel’s integrals......Page 920
B.5 Error function......Page 921
Appendix C The founding fathers of Optics......Page 922
Index of authors......Page 926
Analytical index......Page 934
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UNITEXT for Physics
Giovanni Giusfredi
Physical Optics Concepts, Optical Elements, and Techniques
UNITEXT for Physics Series Editors Michele Cini, University of Rome Tor Vergata, Roma, Italy Attilio Ferrari, University of Turin, Turin, Italy Stefano Forte, University of Milan, Milan, Italy Guido Montagna, University of Pavia, Pavia, Italy Oreste Nicrosini, University of Pavia, Pavia, Italy Luca Peliti, University of Napoli, Naples, Italy Alberto Rotondi, Pavia, Italy Paolo Biscari, Politecnico di Milano, Milan, Italy Nicola Manini, University of Milan, Milan, Italy Morten Hjorth-Jensen, University of Oslo, Oslo, Norway
UNITEXT for Physics series, formerly UNITEXT Collana di Fisica e Astronomia, publishes textbooks and monographs in Physics and Astronomy, mainly in English language, characterized of a didactic style and comprehensiveness. The books published in UNITEXT for Physics series are addressed to graduate and advanced graduate students, but also to scientists and researchers as important resources for their education, knowledge and teaching.
More information about this series at http://www.springer.com/series/13351
Giovanni Giusfredi
Physical Optics Concepts, Optical Elements, and Techniques
123
Giovanni Giusfredi European Laboratory for Non-Linear Spectroscopy (LENS) Istituto Nazionale di Ottica—Consiglio Nazionale delle Ricerche (INO-CNR) Sesto Fiorentino, Italy
ISSN 2198-7882 ISSN 2198-7890 (electronic) UNITEXT for Physics ISBN 978-3-030-25278-6 ISBN 978-3-030-25279-3 (eBook) https://doi.org/10.1007/978-3-030-25279-3 © Springer Nature Switzerland AG 2019 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
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Chapter 2 Geometrical Optics All what we see, it is seen in a rectilinear direction. Pseudo-Eukleidēs, Catoptrics, 2nd postulate
Introduction Geometrical Optics is one of the oldest of the physical sciences, but still remains the most effective approach for explaining a good part of the most common optical phenomena. It is particularly useful for tracing the propagation of light in inhomogeneous media and for describing or designing optical instruments. The emphasis of this discipline is to find the path of light rays, imagined as geometric lines along which energy flows. It is based on a few simple observations: a) light propagates in a straight line in homogeneous media and, in particular, it is possible to produce thin beams of light, similar to geometrical rays within the physically unattainable limit of an infinite subtlety; b) the laws of reflection and refraction; c) different light beams propagate without disturbing each other; d) “natural” sources are generally uncorrelated between them, for which their light beams overlap without showing interference. On the other hand, the electromagnetic field associated with visible light is characterized by very small wavelengths, on the order of 106 107 m. Therefore, the phenomena that violate the first and the last of the above observations can be observed only with accurate experiments. Indeed, the effects of diffraction or interference are almost hidden using natural sources, for which the visibility of the fringes is reduced. The diffraction phenomena appear when there are rapid changes in the amplitude of the field, such as that produced by a sharp obstacle, particularly when some dimension of the optical system, such as the diameter of an aperture, is comparable to the wavelength; or in the neighborhood of a focal point; or over long distances compared to the transverse dimension of a wave, particularly when there is a delimitation imposed upon it. Lastly, point (c) follows from the linearity of the media at the ordinary beams’ intensity. In this chapter, we will explore the consequences of such observations taken as empirical data. However, we will derive the laws of Geometrical Optics by Maxwell’s equations within the limit at which the wavelength tends to zero. We will also see that, within such a limit, the intensity can be deduced from the transverse dimension of a thin pencil of rays and that the polarization state can be associated with each ray. Therefore, in Geometrical Optics, the rays are associated with the Electronic supplementary material The online version of this chapter (https://doi.org/10.1007/ 978-3-030-25279-3_2) contains supplementary material, which is available to authorized users.
© Springer Nature Switzerland AG 2019 G. Giusfredi, Physical Optics, UNITEXT for Physics, https://doi.org/10.1007/978-3-030-25279-3_2
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