This book focuses on optical vortices, including beams carrying orbital angular momentum and vector beams. It presents an overview of, and the latest research on this novel type of optical beam, which is a hot topic in the domain of modern optics, especially in optical communication and beam manipulation.
Summarizing the fundamentals of optical vortices, it discusses their characterization and propagation, and focuses on the generation of vortices such as vortex-arrays, and the detection of vortices and their orbital angular momentum state. It also comprehensively examines the adaptive compensation systems, as well as vector beams and polarization vortices with anisotropic polarization distributions. Further it provides a detailed description of perfect vortices with beam diameters independent of the angular momentum. This book is intended for researchers, engineers and graduate students working in the field of optics and laser beam applications.
Author(s): Shiyao Fu, Chunqing Gao
Series: Advances in Optics and Optoelectronics
Publisher: Springer-TUP
Year: 2023
Language: English
Pages: 368
City: Beijing
Introduction
Contents
1 Fundamentals of Beam Propagation
1.1 Basis of Electromagnetic Theory of Light
1.1.1 Maxwell’s Equations
1.1.2 Wave Differential Equation
1.2 Wave Function
1.2.1 One-Dimensional Simple Harmonic Wave
1.2.2 Three-Dimension Simple Harmonic Plane Wave
1.3 Polarization Basis
1.3.1 Polarizations and Jones Vector
1.3.2 Wave Plates and Jones Matrix
1.4 Basis of Scalar Diffraction Theory
1.4.1 Huygens-Fresnel Principle
1.4.2 Kirchhoff Diffraction Integral
1.4.3 Angular Spectrum
1.4.4 Fresnel Diffraction
1.4.5 Fraunhofer Diffraction
References
2 Basic Characteristics of Vortex Beams
2.1 What is Vortex Beams?
2.2 The Characteristics of Vortex Beams
2.2.1 Poynting Vector
2.2.2 Orbital Angular Momentum (OAM)
2.2.3 Orthogonality
2.2.4 Mirror Image Property
2.3 Orbital Angular Momentum Spectrum
2.3.1 Helical Harmonic Expansion
2.3.2 Rotating Operator
2.4 The Common Vortex Beams
2.4.1 Laguerre–Gauss Beam
2.4.2 Bessel Beam
2.4.3 Bessel-Gauss Beam
References
3 Generation of Vortex Beams
3.1 Intra Resonator Method
3.1.1 Mode Selecting Inside the Resonator
3.1.2 Digital Lasers
3.2 Outside the Resonator
3.2.1 Mode Converter
3.2.2 Spiral Phase Plate
3.2.3 Fork-Shaped Grating
3.3 Phase-Only Vortex Gratings
3.3.1 Liquid–crystal Spatial Light Modulator
3.4 Main Parameters of Liquid–Crystal Spatial Light Modulator
3.4.1 Imitating Amplitude Grating Through Phase Grating
3.4.2 Generating Vortex Beams Through Phase-Only Vortex Grating
3.5 Polarization Scheme
3.5.1 Spatially Variable Half-Wave Plate
3.5.2 Q-plate
3.6 Integrated Vortex Emitter
3.6.1 Whispering Gallery Mode
3.6.2 Mode Selection Through Angular Gratings
3.7 Generation of Multiplexed Vortex Beams
3.7.1 Optical Field Features of Multiplexed Vortex Beams
3.7.2 Beams Combination Method
3.7.3 Interferometer Method
3.7.4 Phase Grating Method
3.7.5 Iteration Method
3.7.6 Pattern-Search Algorithm
3.8 Generation of Bessel-Gauss Beams
3.8.1 Axicon Method
3.8.2 Annular Slit Method
References
4 Vortices Lattices
4.1 Basic Vortices Lattices
4.1.1 The Composite Fork-Shaped Grating and 3 × 3 Dipole Vortices Lattices
4.1.2 3 × 3 Unipolar Vortices Lattice
4.1.3 3 × 3 Vortices Lattice with Asymmetric Topological Charge Distribution
4.2 Design and Optimization of Complex Optical Lattice
4.2.1 The Fourier Expansion of Diffraction Gratings
4.2.2 The Gerchberg–Saxton Algorithm and Grating Optimization
4.2.3 Dammann Grating
4.3 Two-Dimensional Vortices Lattice
4.3.1 Dammann Vortex Grating and Basic Rectangular Lattice
4.3.2 Special Rectangular Vortices Lattice
4.3.3 Annular Vortices Lattices
4.4 Three-Dimensional Vortices Lattices
4.4.1 Dammann Zone Plate
4.4.2 The Generation of Three-Dimensional Vortices Lattices
References
5 Diagnosing Orbital Angular Momentum for Vortex Beams
5.1 Basic Schemes for OAM Measurement
5.1.1 Measuring OAM Through Torque
5.1.2 Secondary Intensity Moment
5.1.3 Measuring OAM Using the Rotational Doppler Effect
5.1.4 Measuring OAM Using the Conjugate Relation Between OAM and the Mean Value of Rotation Operator
5.2 Interferometry
5.2.1 Interference Vortex Beams with Plane Waves
5.2.2 Interferometry for Helical Phase Measurement
5.2.3 Young’s Double-Slit Interference of Vortex Beams
5.2.4 OAM Mode Separation Through Mach-Zehnder Interferometry
5.3 Diffractometry
5.3.1 Triangular Aperture Diffraction
5.3.2 Angular Double Slit Diffraction
5.3.3 Cylindrical Lens
5.3.4 Tilted Lens
5.3.5 Gradually-Changing-Period Grating
5.3.6 Phase-Only Gradually-Changing-Period Grating
5.3.7 Annular Grating
5.3.8 Composite Fork-Shaped Grating Measurement
5.3.9 Standard Dammann Vortex Grating Measurement
5.3.10 Integrated Dammann Vortex Grating Measurement
5.4 Polarimetry
5.4.1 Spatially Variable Half-Wave Plates Measurement
5.4.2 Spatially Variable Polarizers Measurement
5.5 OAM Spectra Measurement
5.5.1 Complex Amplitude Derivation
5.5.2 Grey Scale Algorithm
5.5.3 OAM Mode Sorter
References
6 Distortion Correction for Vortex Beams
6.1 Atmospheric Turbulence Model
6.1.1 Kolmogorov Theory of Atmospheric Turbulence
6.1.2 Power Spectral Density of Refractive Index
6.1.3 Power Spectral Density of Phase
6.1.4 Establishment of an Atmospheric Turbulence Phase Screen
6.2 Atmospheric Turbulence Effects on Vortex Beams
6.2.1 Beam Propagating in Atmospheric Turbulence
6.2.2 Spiral Phase Distortion
6.2.3 OAM Spectrum Broadening
6.2.4 Turbulence Effect on Vortex Beams with Different Patterns
6.3 Adaptive Optical Distortion Correction
6.4 Shack Hartmann Compensation Method
6.4.1 Fundamentals of Shack Hartmann Wavefront Sensing
6.4.2 Distorted Vortex Beam Compensation Through the Shack Hartmann Method
6.5 GS Phase Retrieval Algorithm
6.5.1 Principles of GS Phase Retrieval Algorithm
6.5.2 Probe Calibration Available
6.5.3 Non-probe Correction
6.6 Other Vortex Beam Correction Methods
6.6.1 Stochastic Parallel Gradient Descent Algorithm
6.6.2 Digital Signal Processing Method
References
7 Vector Beams and Vectorial Vortex Beams
7.1 Overview of Vector Beams
7.1.1 Bessel Solutions of Vector Beams
7.1.2 Laguerre–Gauss Solutions of Vector Beams
7.1.3 Jones Vector Representation of Vector Beams
7.1.4 Conversion of Polarizations by Half Wave Plates
7.2 Generating Vector Beams
7.2.1 Intra-Cavity Generation
7.2.2 Sub-wavelength Gratings
7.2.3 Spatial-Varying Polarizers
7.2.4 Spatially Variable Half Wave Plates
7.2.5 Q-plates
7.3 Generating Vector Beams Through Coherent Combination
7.3.1 Principles of Coherent Combination
7.3.2 Sagnac Interference
7.3.3 Sagnac-Like Interference
7.3.4 Twyman-Green Interference
7.3.5 Wollaston Prism
7.3.6 Cascading Liquid Crystal Spatial Light Modulators
7.4 Spatial Oscillating Polarization
7.4.1 Principles of Spatial Oscillating Polarization
7.4.2 Generating Spatial Oscillating Polarization Vector Beams
7.5 Polarization Poincare Sphere
7.5.1 Stokes Vector and Fundamental Poincare Sphere
7.5.2 Higher-Order Stokes Vector and Higher-Order Poincare Sphere
7.5.3 Hybrid-Order Poincare Sphere
7.6 Vectorial Vortex Beams
7.6.1 Overview of Vectorial Vortex Beams
7.6.2 Generating Vectorial Vortex Beams
7.7 Vectorial Vortex Beams Arrays
7.7.1 Principles of Generating Vectorial Vortex Beams Arrays
7.7.2 Mode Control of Vectorial Vortex Beams Arrays
References
8 Perfect Optical Vortices
8.1 Overview of Perfect Optical Vortices
8.1.1 Theoretical Model of Perfect Optical Vortices
8.1.2 Relationships Between Perfect Optical Vortices and Bessel Gauss Beams
8.1.3 Free Space Transport Properties of Perfect Optical Vortices
8.1.4 Conversion Between Different Vortex Beams
8.2 Generating Perfect Optical Vortices
8.2.1 Axicon
8.2.2 Bessel Beam Kinoform
8.3 Mode Recognition of Perfect Optical Vortices
8.3.1 Interference Method
8.3.2 Diffraction Method
8.4 Perfect Vectorial Vortex Beam
8.4.1 Features of the Perfect Vectorial Vortex Beams
8.4.2 Principles of Generating Perfect Vectorial Vortex Beams
8.4.3 Generating Perfect Vectorial Vortex Beams
8.5 Perfect Optical Vortices Array
8.5.1 Perfect Scalar Vortices Array
8.5.2 Perfect Vectorial Vortices Beam Array
References
