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E-raamat: Singular Optics

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(University of North Carolina, Charlotte, USA)
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"This engagingly written text provides a useful pedagogical introduction to an extensive class of geometrical phenomena in the optics of polarization and phase, including simple explanations of much of the underlying mathematics." Michael Berry, University of Bristol, UK

"The author covers a vast number of topics in great detail, with a unifying mathematical treatment. It will be a useful reference for both beginners and experts." Enrique Galvez, Charles A. Dana Professor of Physics and Astronomy, Colgate University

"a firm and comprehensive grounding both for those looking to acquaint themselves with the field and those of us that need reminding of the things we thought we knew, but hitherto did not understand: an essential point of reference." Miles Padgett, Kelvin Chair of Natural Philosophy and Vice Principal (Research), University of Glasgow

This book focuses on the various forms of wavefield singularities, including optical vortices and polarization singularities, as well as orbital angular momentum and associated applications. It highlights how an understanding of singular optics provides a completely different way to look at light. Whereas traditional optics focuses on the shape and structure of the non-zero portions of the wavefield, singular optics describes a waves properties from its null regions. The contents cover the three main areas of the field: the study of generic features of wavefields, determination of unusual properties of vortices and wavefields that contain singularities, and practical applications of vortices and other singularities.

Arvustused

"This lecture-based book is pleasant and contains careful discussions of a large number of topics dealing with the multifaceted aspects of wavefield singularities. The target audience for Gburs book includes undergraduate students of engineering and science, and optical engineers and designers." Optics & Photonics News (May 2017)

"Not just the first complete overview of Singular Optics, but also eminently readable!" Taco Visser, Professor, Vrije Universiteit Amsterdam

"This new book provides a firm and comprehensive grounding both those looking to acquaint themselves with the field and those of us that need reminding of the things we thought we knew, but hitherto did not understand: an essential point of reference." Miles Padgett, Kelvin Chair of Natural Philosophy, University of Glasgow

This engagingly written text provides a useful pedagogical introduction to an extensive class of geometrical phenomena in the optics of polarization and phase, including simple explanations of much of the underlying mathematics. Michael Berry, University of Bristol, UK

"Professor Greg Gbur is both an expert in the field and a talented writer. this comprehensive yet accessible text gives a clear and engaging introduction to the newcomer as well as a useful reference to the expert." Miguel A. Alonso, The Institute of Optics, University of Rochester

"The author covers a vast number of topics in great detail, with a unifying mathematical treatment. It will be a useful reference for both beginners and experts. I found myself learning many new things and will definitely have it handy on my shelf!" Enrique Galvez, Charles A. Dana Professor of Physics and Astronomy, Colgate University

"this book is a delight. Just as Nyes text is a singular contribution to the field (pun intended!), I hope that Gburs text becomes an indispensable reference for optical vortices and together, these books form an essential foundation for the study of optical singularities." Contemporary Physics (Nov 2017), review by Andrew Resnick "This lecture-based book is pleasant and contains careful discussions of a large number of topics dealing with the multifaceted aspects of wavefield singularities. The target audience for Gburs book includes undergraduate students of engineering and science, and optical engineers and designers." Optics & Photonics News (May 2017)

"Not just the first complete overview of Singular Optics, but also eminently readable!" Taco Visser, Professor, Vrije Universiteit Amsterdam

"This new book provides a firm and comprehensive grounding both those looking to acquaint themselves with the field and those of us that need reminding of the things we thought we knew, but hitherto did not understand: an essential point of reference." Miles Padgett, Kelvin Chair of Natural Philosophy, University of Glasgow

This engagingly written text provides a useful pedagogical introduction to an extensive class of geometrical phenomena in the optics of polarization and phase, including simple explanations of much of the underlying mathematics. Michael Berry, University of Bristol, UK

"Professor Greg Gbur is both an expert in the field and a talented writer. this comprehensive yet accessible text gives a clear and engaging introduction to the newcomer as well as a useful reference to the expert." Miguel A. Alonso, The Institute of Optics, University of Rochester

"The author covers a vast number of topics in great detail, with a unifying mathematical treatment. It will be a useful reference for both beginners and experts. I found myself learning many new things and will definitely have it handy on my shelf!" Enrique Galvez, Charles A. Dana Professor of Physics and Astronomy, Colgate University

"this book is a delight. Just as Nyes text is a singular contribution to the field (pun intended!), I hope that Gburs text becomes an indispensable reference for optical vortices and together, these books form an essential foundation for the study of optical singularities." Contemporary Physics (Nov 2017), review by Andrew Resnick

Series Preface xiii
Preface xv
Chapter 1 Introduction: Vortices in Nature
1(8)
Chapter 2 Anatomy of a Vortex Beam
9(24)
2.1 Maxwell's Equations And Paraxial Beams
9(5)
2.2 Laguerre--Gauss Paraxial Beams
14(8)
2.3 Properties Of Phase Singularities
22(1)
2.4 Derivation Of Higher-Order Gaussian Beams
23(9)
2.5 Exercises
32(1)
Chapter 3 Generic Properties of Phase Singularities
33(30)
3.1 Young's Interferometer And Phase Singularities
34(6)
3.2 Typical Forms Of Wave Dislocations
40(6)
3.2.1 Screw Dislocation
41(1)
3.2.2 Edge Dislocation
42(2)
3.2.3 Mixed Edge-Screw Dislocations
44(2)
3.3 Crystal Dislocations And Wavefronts
46(5)
3.4 Topological Charge And Index
51(3)
3.5 Creation And Annihilation Events
54(6)
3.6 Exercises
60(3)
Chapter 4 Generation and Detection of Optical Vortices
63(48)
4.1 Generation
63(21)
4.1.1 Spiral Phase Plate
64(4)
4.1.2 Mode Conversion
68(4)
4.1.3 Computer-Generated Holograms
72(5)
4.1.4 Direct Laser Generation
77(2)
4.1.5 Nonuniform Polarization
79(3)
4.1.6 Other Methods
82(2)
4.2 Detection
84(23)
4.2.1 Interference-Based Methods
84(3)
4.2.2 Diffraction-Based Method
87(2)
4.2.3 Shack-Hartmann Method
89(5)
4.2.4 Computer-Generated Holograms and Modans
94(7)
4.2.5 Geometrical Mode Separation
101(6)
4.3 Method Of Stationary Phase
107(2)
4.4 Exercises
109(2)
Chapter 5 Angular Momentum of Light
111(38)
5.1 Momentum And Angular Momentum In Wavefields
112(6)
5.2 Orbital And Spin Angular Momentum
118(4)
5.3 Angular Momentum Of Laguerre-Gaussian Beams
122(5)
5.4 Intrinsic And Extrinsic Angular Momentum
127(4)
5.5 Trapping Forces
131(5)
5.6 Momentum In Matter And The Abraham-Minkowski Controversy
136(10)
5.7 Exercises
146(3)
Chapter 6 Applications Of Optical Vortices
149(36)
6.1 Micromanipulation, Spanning, And Trapping
149(7)
6.2 Optical Communications
156(5)
6.3 Phase Retrieval
161(5)
6.4 Coronograph
166(5)
6.5 Signal Processing And Edge Detection
171(5)
6.6 Rotational Doppler Shifts
176(6)
6.7 Exercises
182(3)
Chapter 7 Polarization Singularities
185(74)
7.1 Basics Of Polarization In Optical Wavefields
186(8)
7.1.1 Linear Polarization
192(1)
7.1.2 Circular Polarization
193(1)
7.2 Stokes Parameters And The Poincare Sphere
194(8)
7.3 Polarization Singularities: C-Points And L-Lines
202(5)
7.4 Generic Features Of Polarization Singularities
207(5)
7.5 Topological Reactions Of Polarization Singularities
212(4)
7.6 Higher-Order Polarization Singularities
216(2)
7.7 Nonuniformly Polarized Beams
218(4)
7.8 Poincare Beams
222(3)
7.9 Poincare Vortices
225(2)
7.10 Partially Polarized Light And Singularities Of The Clear Sky
227(8)
7.11 The Pancharatnam Phase
235(9)
7.12 Second-Order Tensor Fields And Their Singularities
244(8)
7.13 The Hairy Ball Theorem
252(4)
7.14 Exercises
256(3)
Chapter 8 Singularities Of The Poynting Vector
259(34)
8.1 Power Flow In Electromagnetic Waves
260(6)
8.2 Conceptual Difficulties With The Poynting Vector
266(2)
8.3 The First Optical Vortex
268(7)
8.4 Other Early Observations Of Poynting Singularities
275(4)
8.5 Generic Properties Of Poynting Vector Singularities
279(7)
8.6 Singularities, Transmission, And Radiation
286(6)
8.7 Exercises
292(1)
Chapter 9 Coherence Singularities
293(42)
9.1 Optical Coherence
294(11)
9.2 Singularities Of Correlation Functions
305(7)
9.3 Generic Structure Of A Correlation Singularity
312(5)
9.4 Phase Singularities In Partially Coherent Fields
317(4)
9.5 Electromagnetic Correlation Singularities
321(3)
9.6 Experiments And Applications
324(2)
9.7 Twisted Gaussian Schell-Model Beams
326(5)
9.8 Oam And Rankine Vortices
331(3)
9.9 Exercises
334(1)
Chapter 10 Singularities And Vortices In Quantum Optics
335(92)
10.1 Quantization Of The Electromagnetic Field
336(7)
10.2 Quantum Cores Of Optical Vortices
343(4)
10.3 Introduction To Entanglement
347(8)
10.4 Nonlinear Optics And Angular Momentum
355(8)
10.5 Entanglement Of Angular Momentum States
363(12)
10.6 A Nonlocal Optical Vortex
375(5)
10.7 Bell's Inequalities For Angular Momentum States
380(10)
10.8 Vortices In Schrodinger's Equation
390(9)
10.9 Uncertainty Principle For Angular Momentum
399(17)
10.10 Dirac's Magnetic Monopole
416(9)
10.11 Exercises
425(2)
Chapter 11 Vortices In Random Wavefields
427(26)
11.1 Speckle Statistics At A Single Point
428(4)
11.2 Speckle Statistics At Multiple Points
432(5)
11.3 Statistics Of Vortices In Random Wavefields
437(5)
11.4 Correlations Of Vortices In Random Wavefields
442(3)
11.5 Quasicrystalline Order
445(2)
11.6 Polarization Singularities In Random Wavefields
447(1)
11.7 Multivariate Complex Circular Gaussian Random Processes
448(4)
11.8 Exercises
452(1)
Chapter 12 Unusual Singularities And Topological Tricks
453(52)
12.1 Bessel-Gauss Vortex Beams
453(12)
12.2 Riemann-Silberstein Vortices
465(8)
12.3 Fractional Charge Vortex Beams
473(6)
12.4 Knots, Braids, And Linked Vortices
479(6)
12.5 Cascades Of Singularities
485(4)
12.6 Lissajous Singularities
489(6)
12.7 Optical Mobius Strips
495(4)
12.8 Superoscillatory Fields
499(5)
12.9 Exercises
504(1)
References 505(28)
Index 533
Gregory J. Gbur received a B.A. with honors from the University of Chicago in 1993 and his M.A. and Ph.D. from the University of Rochester in 1996 and 2001. Since 2005, he has been a faculty member at the University of North Carolina at Charlotte, becoming an Associate Professor in 2010. His research is in classical theoretical optics, focusing on singular optics, coherence theory, plasmonics and invisibility/cloaking. He has written or coauthored over 80 journal papers to date, including three reviews for Progress in Optics. He has written another textbook, Mathematical Methods for Optical Physics and Engineering. He has an active interest in science communication, writing the personal science blog Skulls in the Stars since 2007, and has written popular articles for a number of magazines, including La Recherche, American Scientist, and Optics and Photonics News.
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