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E-raamat: Topological Charge of Optical Vortices [Taylor & Francis e-raamat]

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  • Formaat: 302 pages, 9 Tables, black and white; 30 Line drawings, black and white; 166 Halftones, black and white; 196 Illustrations, black and white
  • Ilmumisaeg: 30-Dec-2022
  • Kirjastus: CRC Press
  • ISBN-13: 9781003326304
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  • Taylor & Francis e-raamat
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Topological Charge of Optical VorticesSuurem pilt
  • Formaat: 302 pages, 9 Tables, black and white; 30 Line drawings, black and white; 166 Halftones, black and white; 196 Illustrations, black and white
  • Ilmumisaeg: 30-Dec-2022
  • Kirjastus: CRC Press
  • ISBN-13: 9781003326304
Teised raamatud teemal:
Taylor & Francis e-raamatudRohkem infot Taylor & Francis e-raamatute kohta
Raamatu kodulehekülg: https://www.taylorfrancis.com/books/9781003326304
This book is devoted to the consideration of unusual laser beams vortex or singular beams. It contains many numerical examples, which clearly show how the phase of optical vortices changes during propagation in free space, and that the topological charge is preserved.

Topological Charge of Optical Vortices shows that the topological charge of an optical vortex is equal to the number of screw dislocations or the number of phase singularities in the beam cross-section. A single approach is used for the entire book: based on M. Berrys formula. It is shown that phase singularities during beam propagation can be displaced to infinity at a speed greater than the speed of light. The uniqueness of the book is that the calculation of the topological charge for scalar light fields is extended to vector fields and is used to calculate the PoincareHopf singularity index for vector fields with inhomogeneous linear polarization with V-points and for the singularity index of vector fields with inhomogeneous elliptical polarization with C-points and C- lines.

The book is written for opticians, and graduate students interested in an interesting section of optics singular optics. It will also be of interest to scientists and researchers who are interested in modern optics. In order to understand the content of the book, it is enough to know paraxial optics (Fourier optics) and be able to calculate integrals.
Preface xi
Acknowledgments xiii
Authors xv
Introduction xvii
Chapter 1 Topological Charge of Superposition: Conservation of Topological Charge
1(40)
1.1 Topological Charge and Asymptotic Phase Invariants of Vortex Laser Beams
1(8)
1.1.1 Orbital Angular Momentum and Topological Charge
2(1)
1.1.2 Propagation of a Light Field in Free Space and Conservation of Its Orbital Angular Momentum
2(1)
1.1.3 Conservation of the Topological Charge
3(2)
1.1.4 Asymptotic Phase Invariants of Vortex Laser Beams
5(1)
1.1.5 Numerical Simulation
6(3)
1.2 Topological Charge of a Linear Combination of Optical Vortices: Topological Competition
9(16)
1.2.1 TC of an OV after Passing an Amplitude Mask
10(3)
1.2.2 TC of an Off-Axis Optical Vortex
13(2)
1.2.3 TC of an Optical Vortex with Multi-Center Optical Singularities
15(1)
1.2.4 TC of an On-Axis Combination of Optical Vortices
16(1)
1.2.5 TC of the Sum of Two Optical Vortices
16(3)
1.2.6 Topological Charge in an Arbitrary Plane
19(2)
1.2.7 Topological Charge for an Optical Vortex with an Initial Fractional Charge
21(2)
1.2.8 Topological Charge of an Elliptic Optical Vortex Embedded in a Gaussian Beam
23(2)
1.3 Topological Charge of Asymmetric Optical Vortices
25(16)
1.3.1 TC of an Asymmetric LG Beam
26(3)
1.3.2 TC of an Asymmetric BG Beam
29(2)
1.3.3 TC of an Asymmetric Kummer Beam
31(1)
1.3.4 TC of an OV Composed of Two HG Modes
32(2)
1.3.5 TC of a Vortex HG Beam
34(1)
1.3.6 Numerical Simulation
35(6)
Chapter 2 Evolution of an Optical Vortex with an Initial Fractional Topological Charge
41(46)
2.1 Change in TC During Propagation in Free Space and Stability to Phase Noise
41(15)
2.1.1 Theoretical Background
42(4)
2.1.2 Numerical Simulation
46(5)
2.1.3 Experiment
51(2)
2.1.4 Stability of the Topological Charge to Phase Noise
53(3)
2.2 Nonparaxial Modeling of the Evolution of an Optical Vortex with an Initial Fractional TC
56(11)
2.2.1 Topological Charge of an Initial Fractional-Charge Vortex in the Near Field
57(3)
2.2.2 Topological Charge of an Original Fractional-Charge Vortex in the Fresnel Zone
60(2)
2.2.3 Topological Charge of an Initial Fractional-Charge Vortex in the Far Field
62(5)
2.3 Orbital Angular Momentum and Topological Charge of a Multi-Vortex Gaussian Beam
67(11)
2.3.1 Complex Amplitude of a Multi-Vortex Gaussian Beam
67(1)
2.3.2 Orbital Angular Momentum and the Topological Charge of the Multi-Vortex Gaussian Beam
68(3)
2.3.3 Asymptotic Phase Invariants of the Multi-Vortex Gaussian Beam
71(1)
2.3.4 Multi-Singularity Spiral Phase Plate
71(1)
2.3.5 Stability of Shape, Orbital Angular Momentum, Topological charge, and Asymptotic Phase Invariants of the Multi-Vortex Gaussian Beam to Random Phase Distortions
72(3)
2.3.6 Numerical Simulation of Asymptotic Phase Invariants
75(3)
2.4 Influence of Optical "Dipoles" on the Topological Charge of a Field with a Fractional Initial Charge
78(9)
2.4.1 Formulation of the Problem
79(2)
2.4.2 Topological Charge of the Beam in the Far Field, Initial TC 3 & lt; & mu; & lt; 4
81(1)
2.4.3 Topological Charge of the Beam in the Far Field when TC Is 2 & lt; & mu; & lt; 3
82(5)
Chapter 3 Topological Charge Superposition of only Two Laguerre-Gaussian or Bessel--Gaussian Beams with Different Parameters
87(58)
3.1 Optical Phase Singularities "Going To" Infinity with a Higher-Than-Light Speed
87(13)
3.1.1 Theoretical Background
88(2)
3.1.2 Movement of Phase Singularities in the Propagating Beam
90(2)
3.1.3 Numerical Modeling
92(8)
3.2 Conservation of the Half-Integer Topological Charge on Propagation of a Superposition of Two Bessel-Gaussian Beams
100(12)
3.2.1 Topological Charge of a Coaxial Superposition of Bessel-Gaussian Beams
101(5)
3.2.2 Numerical Simulation
106(6)
3.3 Topological Charge of Two Parallel Laguerre--Gaussian Beams
112(19)
3.3.1 Structurally Stable Superposition of Off-Axis LG Beams
113(3)
3.3.2 Superposition of Two On-Axis LG Beams
116(1)
3.3.3 Superposition of Two Off-Axis LG Beams
117(2)
3.3.4 Numerical Modeling and Experiment
119(1)
Numerical modeling of structurally stable superposition of off-axis LG beams
119(1)
Numerical modeling of a superposition of two off-axis LG beams
120(6)
Determining the topological charge by interferograms
126(2)
Comparison of analytical, simulated, and --- experimentally recorded results
128(3)
3.4 Topological Charge of Polychromatic Optical Vortices
131(14)
3.4.1 Topological Charge of a Two-Color Superposition of Optical Vortices
132(2)
3.4.2 Topological Charge of a White Optical Vortex
134(2)
3.4.3 Numerical Simulation
136(1)
Numerical simulation of two-color vortices
136(3)
Numerical simulation of a three-color vortex
139(3)
Numerical simulation of three-color vortex with different permutations of light rings colors
142(3)
Chapter 4 Optical Vortex Beams with an Infinite Topological Charge
145(46)
4.1 Propagation-Invariant Laser Beams with an Array of Phase Singularities
145(22)
4.1.1 Form-Invariant Gaussian Beams
146(1)
4.1.2 Gaussian Beam with a Vortex-Argument Cosine Function
147(1)
Theory
147(6)
Numerical simulation
153(3)
4.1.3 Gaussian Beam with a Vortex-Argument Bessel Function
156(1)
Theory
156(2)
Numerical simulation
158(1)
4.1.4 Gaussian Beam with the Cosine Function of the Squared Vortex-Argument
159(1)
Theory
159(2)
Numerical simulation
161(2)
4.1.5 Higher-Order Cosine Vortex Optical Beam
163(1)
Theory
163(2)
Numerical simulation
165(2)
4.2 Orbital Angular Momentum of Generalized Cosine Gaussian Beams with an Infinite Number of Screw Dislocations
167(8)
4.2.1 Complex Amplitude, Space Propagation, and Intensity Distribution of the Generalized Cosine Gaussian Beams with an Infinite Number of Screw Dislocations
168(2)
4.2.2 OAM Spectrum, Energy, and Normalized-to-Power OAM of the Generalized Cosine Gaussian Beams
170(2)
4.2.3 Numerical Simulation
172(3)
4.3 Astigmatic Transform of a Gaussian Beam with an Infinite Number of Edge Dislocations
175(2)
4.4 Optical Vortex Beams with a Symmetric and Almost Symmetric OAM-Spectrum
177(14)
4.4.1 Orbital Angular Momentum of a Beam with a Symmetric OAM-Spectrum
178(2)
4.4.2 Sample Beams with the Symmetric OAM-Spectrum
180(1)
4.4.3 Family of Form-Invariant Beams with an Almost Symmetric OAM-Spectrum
181(3)
4.4.4 Numerical Simulation
184(1)
Simulation of beams with a symmetric OAM-spectrum
184(3)
Numerical simulation of form-invariant beams with an almost symmetric OAM-spectrum
187(4)
Chapter 5 Transformation of an Edge Dislocation of a Wavefront into an Optical Vortex
191(34)
5.1 Converting an Array of Edge Dislocations into a Multi-Vortex beam
191(15)
5.1.1 Complex Amplitude at the Double Focal Length
192(4)
5.1.2 Orbital Angular Momentum
196(3)
5.1.3 Two Asymmetric Parallel Zero-Intensity Lines
199(1)
5.1.4 An Astigmatic Cosine--Gauss Beam
200(1)
5.1.5 Numerical Modelling
201(1)
Modeling the evolution of the optical vortices
201(1)
Modeling the evolution of OAM
202(3)
Modeling a beam with two non-axisymmetric parallel zero-intensity lines
205(1)
Modeling an astigmatic Cosine-Gauss beam
205(1)
5.2 Converting an nth-Order Edge Dislocation to a Set of Optical Vortices
206(6)
5.2.1 Complex Amplitude of Edge Dislocation at Double Focal Length
207(2)
5.2.2 Structurally Stable Vortex Beams
209(1)
5.2.3 Orbital Angular Momentum
210(1)
5.2.4 Numerical Simulation
211(1)
5.3 Astigmatic Transformation of a Fractional Order Edge Dislocation
212(13)
5.3.1 Complex Amplitude of a Field with a Fractional Order Edge Dislocation
213(1)
5.3.2 Complex Amplitude of the Field at Twice the Focal Length
214(1)
5.3.3 Kummer's and Tricomi Function Zeros
215(4)
5.3.4 Results of the Numerical Simulation
219(3)
5.3.5 Discussion of Results
222(3)
Chapter 6 Fourier-Invariant and Structurally Stable Optical Vortex Beams
225(28)
6.1 Fractional-Order-Bessel Fourier-Invariant Optical Vortices
225(9)
6.1.1 Fractional-Order Bessel Fourier-Modes
226(2)
6.1.2 Energy of the Fractional-Order Bessel Fourier-Modes
228(1)
6.1.3 Numerical Simulation
229(1)
Beam width
229(3)
Beam divergence
232(1)
Beam propagation in free space
233(1)
6.2 New Type of Elegant Laser Beams: Sinusoidal Gaussian Optical Vortex
234(5)
6.2.1 Hypergeometric Beams with a Parabolic Wavefront
235(1)
6.2.2 Special Case: An Elegant Sinusoidal Gaussian Vortex
236(3)
6.2.3 Numerical Simulation
239(1)
6.3 Propagation-Invariant Off-Axis Elliptic Gaussian Beams with the Orbital Angular Momentum
239(14)
6.3.1 Propagation-Invariant Off-Axis Gaussian Beams
242(2)
6.3.2 Propagation-Invariant Elliptic Gaussian Beams
244(6)
6.3.3 Beam Power and the Orbital Angular Momentum
250(3)
Chapter 7 Topological Charge of Polarization Singularities
253(28)
7.1 Tightly Focusing Vector Beams Containing V-Point Polarization Singularities
253(15)
7.1.1 Vector Field Polarization Index in the Source Plane
254(1)
7.1.2 Number of Local Intensity Maxima at the Focus of a Vector Field
255(3)
7.1.3 Polarization Singularity Index for a Generalized Vector Field
258(1)
Calculating polarization singularity Index of a generalized vector field
259(3)
7.1.4 Numerical Modeling
262(6)
7.2 Sharp Focusing of a Hybrid Vector Beams Containing C-Point Polarization Singularity
268(13)
7.2.1 Source Hybrid Vector Field with Polarization Singularity Points
269(2)
7.2.2 Vector Field with Polarization ngularity Points in the Plane of the Tight Focus
271(3)
7.2.3 Numerical Modeling
274(7)
Conclusion 281(2)
References 283(18)
Index 301
Victor V. Kotlyar is Head of the Laboratory at Image Processing Systems Institute of the Russian Academy of Science, a branch of the Federal Scientific Research Center "Crystallography and Photonics", and Professor of Computer Science at Samara National Research University, Russia. He earned his MS, PhD, and DrSc degrees in Physics and Mathematics from Samara State University (1979), Saratov State University (1988), and Moscow Central Design Institute of Unique Instrumentation, the Russian Academy of Sciences (1992). He is a SPIE- and OSA-member. He is coauthor of 400 scientific papers, 7 books, and 7 inventions. His current interests are diffractive optics, gradient optics, nanophotonics, and optical vortices.

Alexey A. Kovalev graduated in 2002 from Samara National Research University, Russia, majoring in Applied Mathematics. He earned his PhD in Physics and Maths in 2012. He is senior researcher of Laser Measurements at the Image Processing Systems Institute of the Russian Academy of Science, a branch of the Federal Scientific Research Center "Crystallography and Photonics". He is a co-author of more than 270 scientific papers. His research interests are mathematical diffraction theory, photonic crystal devices, and optical vortices.

Anton G. Nalimov graduated from Samara State Aerospace University, Russia, in February 2003. He entered postgraduate study in 2003 with a focus on the specialty 05.13.18 "Mathematical Modeling and Program Complexes". He finished it in 2006 with the specialty 01.04.05 "Optics". Nalimov works in the Technical Cybernetics department at Samara National Research University as an associate professor, and also works as a scientist in the Image Processing Systems Institute of the Russian Academy of Science, a branch of the Federal Scientific Research Center "Crystallography and Photonics" in Samara. He is a PhD candidate in Physics and Mathematics, co-author of 200 papers and 3 inventions.
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