Linked e-resources
Details
Table of Contents
Intro
Author biography
Paramasivam Senthilkumaran
Chapter Introduction
1.1 Singularity
1.2 Singularities in science and engineering
1.3 Acoustic vortex
1.4 Singularities in optics
1.5 Amplitude, phase and polarization
1.6 Brief historical account of optical phase singularities
References
Chapter Topological features
2.1 Introduction
2.2 Wavefront shape
2.3 Amplitude and phase distribution of an optical vortex beam
2.4 Topological charge
2.5 Phase contours and zero crossings
2.6 Phase gradients of an optical vortex beam
2.6.1 Phase gradient near zeros
2.7 Critical points
2.8 Zero crossings and bifurcation lines
2.9 Charge, order and index
2.10 Sign rules
2.11 Disintegrations or explosions
2.12 Charge conservation
2.13 Index conservation
2.14 Limitation on vortex density
2.15 Threads of darkness
2.16 Berry's paradox
2.17 Manifolds and trajectories
2.17.1 Trajectories
2.18 Links and knots
2.19 Different types of phase defects
2.19.1 Point, edge and mixed phase defects
2.19.2 Isotropic and anisotropic vortices
2.19.3 Perfect vortex
2.19.4 Fractional vortex
2.19.5 Riemann-Silberstein vortex
2.19.6 Composite vortices
References
Chapter Generation and detection methods
3.1 Introduction
3.2 Generation
3.2.1 Spiral phase plates
3.2.2 Fork gratings
3.2.3 Spiral zone plates
3.2.4 Tilts
3.2.5 Interference methods
3.2.6 Speckles
3.2.7 Spatial light modulators
3.2.8 Dammann vortex gratings
3.2.9 Mode conversion methods
3.2.10 Intra-cavity methods
3.2.11 Adaptive helical mirrors
3.2.12 Vortex generation in optical fibers
3.2.13 Q-wave plates for vortex generation
3.2.14 Meta-surface optics
3.3 Detection
3.3.1 Interference methods
3.3.2 Diffraction methods.
3.3.3 Detection using lens aberrations
3.3.4 Detection of vortices in computational optics
References
Chapter Propagation characteristics
4.1 Introduction
4.2 Wave equations and solutions
4.3 Slowly varying envelope approximation: paraxial Helmholtz equation
4.4 Gouy phase
4.5 Divergence of singular beams
4.6 Near-core vortex structure and propagation
4.7 Propagation dynamics of optical phase singularities
4.8 Propagation of vortices in non-linear media
References
Chapter Internal energy flows
5.1 Energy flow
5.2 Internal energy flows
5.3 Visualizing internal energy flow
5.3.1 Bekshaev-Bliokh-Soskin method
5.3.2 Helmholtz-Hodge decomposition method
5.4 Focusing of singular beams: effect of aberrations
5.5 Experimental detection
5.6 Energy circulations in diffraction patterns
References
Chapter Vortices in computational optics
6.1 Introduction
6.2 Diffuse illumination in holography
6.3 Synthesized diffusers
6.4 Phase synthesis in computer-generated holograms
6.5 Stagnation problem in iterative Fourier transform algorithms
6.6 Solution to the speckle problem
6.7 Phase unwrapping in the presence of vortices
6.7.1 Residue theorem
6.8 Non-Bryngdahl transforms using branch points
6.9 Diffraction of singular beams
6.10 Phase retrieval
References
Chapter Angular momentum of light
7.1 Introduction
7.2 Linear momentum
7.3 Angular momentum
7.4 Orbital and spin angular momentum of light
7.4.1 Angular momentum due to circular polarization
7.4.2 Angular momentum due to azimuthal phase dependence in the beam
7.4.3 Angular momentum due to spatially varying circular polarization
7.5 Intrinsic and extrinsic angular momentum
References
Chapter Applications
8.1 Metrology
8.2 Collimation testing
8.3 Spiral interferometry.
8.4 Spatial filtering
8.4.1 Hilbert transform
8.4.2 Isotropic edge enhancement
8.4.3 Anisotropic edge enhancement
8.4.4 Spiral phase-contrast imaging
8.4.5 Optical vortex coronograph
8.4.6 Observation of a weak star in a bright background
8.5 Focal plane intensity manipulation
8.5.1 Polarization engineering
8.6 Stimulated emission depletion microscopy
8.7 Optical trapping and tweezers
8.8 Optically driven micro-motors
8.9 Communications
8.10 Phase-retrieval methods
References
Chapter Polarization singularities
9.1 Polarization of light
9.2 Stokes parameters and Poincaré sphere representation
9.2.1 Homogeneous polarization
9.2.2 Inhomogeneous polarization
9.2.3 Encoding phase into polarization
9.3 Stokes fields
9.4 Ellipse field singularities
9.5 Vector field singularities
9.6 Stokes phase
9.7 Topological features of polarization singularities
9.7.1 Sign rule
9.8 Angular momentum in polarization singularities
9.9 Generation
9.9.1 Polarization speckles
9.9.2 Interference methods
9.9.3 Intra-cavity methods
9.9.4 Spatial light modulators
9.9.5 Spatially varying wave plates
9.9.6 Q-wave plates
9.9.7 Phase elements versus Pancharatnam-Berry phase elements
9.9.8 Wave plates using meta-surface optics
9.9.9 J-plates and d-plates
9.9.10 Photoelasticity
9.10 Detection
9.10.1 Three Stokes fields
9.10.2 Interferometric method
9.10.3 Polarizer
9.10.4 Diffraction and polarization transformation: hybrid method for detection
9.11 Inversion and conversion methods
9.11.1 Inversion methods
9.11.2 Conversion methods
9.12 Polarization singularity distributions
9.13 Optical Möbius strips
9.14 Applications
9.14.1 Edge enhancement
9.14.2 C-points for optical activity measurement
9.14.3 Robust beams.
9.14.4 Smallest focal spot
References
Chapter Stokes fields and singularities
10.1 Introduction
10.2 Polarization optics
10.3 Stokes parameters
10.4 Stokes fields
10.5 Discussion on Stokes formalism
10.5.1 Parameters in terms of Pauli spin matrices
10.5.2 Pauli spin matrices
10.5.3 Coherency matrix using Stokes parameters and Stokes fields
10.5.4 Density matrix and Stokes parameters
10.6 Stokes singularities
10.7 Stokes space
10.8 Topological constructs
10.8.1 Poincaré sphere
10.8.2 Sphere of first-order modes
10.8.3 Higher-order Poincaré sphere
10.8.4 Hybrid-order Poincaré sphere
10.8.5 Construction of spheres
10.9 Degeneracy
10.10 Generation of Stokes singularities
10.10.1 Coaxial superposition of phase singularities
10.10.2 Non-coaxial superposition of phase singularities
10.10.3 Stokes singularities from plane waves
10.11 Detection of Stokes singularities
10.11.1 Stokes polarimetry for a higher-order Poincaré sphere
10.12 Polarization transformations
10.12.1 Action of retarders on Stokes singularities
10.12.2 Action of a q-plate on Stokes (ϕ12) singularities
10.12.3 Action of a spiral phase plate on polarization singularity
10.12.4 Action of a fork grating on polarization singularity
10.12.5 Fork grating under V-point illumination
10.12.6 Fork grating under C-point illumination
References.
Author biography
Paramasivam Senthilkumaran
Chapter Introduction
1.1 Singularity
1.2 Singularities in science and engineering
1.3 Acoustic vortex
1.4 Singularities in optics
1.5 Amplitude, phase and polarization
1.6 Brief historical account of optical phase singularities
References
Chapter Topological features
2.1 Introduction
2.2 Wavefront shape
2.3 Amplitude and phase distribution of an optical vortex beam
2.4 Topological charge
2.5 Phase contours and zero crossings
2.6 Phase gradients of an optical vortex beam
2.6.1 Phase gradient near zeros
2.7 Critical points
2.8 Zero crossings and bifurcation lines
2.9 Charge, order and index
2.10 Sign rules
2.11 Disintegrations or explosions
2.12 Charge conservation
2.13 Index conservation
2.14 Limitation on vortex density
2.15 Threads of darkness
2.16 Berry's paradox
2.17 Manifolds and trajectories
2.17.1 Trajectories
2.18 Links and knots
2.19 Different types of phase defects
2.19.1 Point, edge and mixed phase defects
2.19.2 Isotropic and anisotropic vortices
2.19.3 Perfect vortex
2.19.4 Fractional vortex
2.19.5 Riemann-Silberstein vortex
2.19.6 Composite vortices
References
Chapter Generation and detection methods
3.1 Introduction
3.2 Generation
3.2.1 Spiral phase plates
3.2.2 Fork gratings
3.2.3 Spiral zone plates
3.2.4 Tilts
3.2.5 Interference methods
3.2.6 Speckles
3.2.7 Spatial light modulators
3.2.8 Dammann vortex gratings
3.2.9 Mode conversion methods
3.2.10 Intra-cavity methods
3.2.11 Adaptive helical mirrors
3.2.12 Vortex generation in optical fibers
3.2.13 Q-wave plates for vortex generation
3.2.14 Meta-surface optics
3.3 Detection
3.3.1 Interference methods
3.3.2 Diffraction methods.
3.3.3 Detection using lens aberrations
3.3.4 Detection of vortices in computational optics
References
Chapter Propagation characteristics
4.1 Introduction
4.2 Wave equations and solutions
4.3 Slowly varying envelope approximation: paraxial Helmholtz equation
4.4 Gouy phase
4.5 Divergence of singular beams
4.6 Near-core vortex structure and propagation
4.7 Propagation dynamics of optical phase singularities
4.8 Propagation of vortices in non-linear media
References
Chapter Internal energy flows
5.1 Energy flow
5.2 Internal energy flows
5.3 Visualizing internal energy flow
5.3.1 Bekshaev-Bliokh-Soskin method
5.3.2 Helmholtz-Hodge decomposition method
5.4 Focusing of singular beams: effect of aberrations
5.5 Experimental detection
5.6 Energy circulations in diffraction patterns
References
Chapter Vortices in computational optics
6.1 Introduction
6.2 Diffuse illumination in holography
6.3 Synthesized diffusers
6.4 Phase synthesis in computer-generated holograms
6.5 Stagnation problem in iterative Fourier transform algorithms
6.6 Solution to the speckle problem
6.7 Phase unwrapping in the presence of vortices
6.7.1 Residue theorem
6.8 Non-Bryngdahl transforms using branch points
6.9 Diffraction of singular beams
6.10 Phase retrieval
References
Chapter Angular momentum of light
7.1 Introduction
7.2 Linear momentum
7.3 Angular momentum
7.4 Orbital and spin angular momentum of light
7.4.1 Angular momentum due to circular polarization
7.4.2 Angular momentum due to azimuthal phase dependence in the beam
7.4.3 Angular momentum due to spatially varying circular polarization
7.5 Intrinsic and extrinsic angular momentum
References
Chapter Applications
8.1 Metrology
8.2 Collimation testing
8.3 Spiral interferometry.
8.4 Spatial filtering
8.4.1 Hilbert transform
8.4.2 Isotropic edge enhancement
8.4.3 Anisotropic edge enhancement
8.4.4 Spiral phase-contrast imaging
8.4.5 Optical vortex coronograph
8.4.6 Observation of a weak star in a bright background
8.5 Focal plane intensity manipulation
8.5.1 Polarization engineering
8.6 Stimulated emission depletion microscopy
8.7 Optical trapping and tweezers
8.8 Optically driven micro-motors
8.9 Communications
8.10 Phase-retrieval methods
References
Chapter Polarization singularities
9.1 Polarization of light
9.2 Stokes parameters and Poincaré sphere representation
9.2.1 Homogeneous polarization
9.2.2 Inhomogeneous polarization
9.2.3 Encoding phase into polarization
9.3 Stokes fields
9.4 Ellipse field singularities
9.5 Vector field singularities
9.6 Stokes phase
9.7 Topological features of polarization singularities
9.7.1 Sign rule
9.8 Angular momentum in polarization singularities
9.9 Generation
9.9.1 Polarization speckles
9.9.2 Interference methods
9.9.3 Intra-cavity methods
9.9.4 Spatial light modulators
9.9.5 Spatially varying wave plates
9.9.6 Q-wave plates
9.9.7 Phase elements versus Pancharatnam-Berry phase elements
9.9.8 Wave plates using meta-surface optics
9.9.9 J-plates and d-plates
9.9.10 Photoelasticity
9.10 Detection
9.10.1 Three Stokes fields
9.10.2 Interferometric method
9.10.3 Polarizer
9.10.4 Diffraction and polarization transformation: hybrid method for detection
9.11 Inversion and conversion methods
9.11.1 Inversion methods
9.11.2 Conversion methods
9.12 Polarization singularity distributions
9.13 Optical Möbius strips
9.14 Applications
9.14.1 Edge enhancement
9.14.2 C-points for optical activity measurement
9.14.3 Robust beams.
9.14.4 Smallest focal spot
References
Chapter Stokes fields and singularities
10.1 Introduction
10.2 Polarization optics
10.3 Stokes parameters
10.4 Stokes fields
10.5 Discussion on Stokes formalism
10.5.1 Parameters in terms of Pauli spin matrices
10.5.2 Pauli spin matrices
10.5.3 Coherency matrix using Stokes parameters and Stokes fields
10.5.4 Density matrix and Stokes parameters
10.6 Stokes singularities
10.7 Stokes space
10.8 Topological constructs
10.8.1 Poincaré sphere
10.8.2 Sphere of first-order modes
10.8.3 Higher-order Poincaré sphere
10.8.4 Hybrid-order Poincaré sphere
10.8.5 Construction of spheres
10.9 Degeneracy
10.10 Generation of Stokes singularities
10.10.1 Coaxial superposition of phase singularities
10.10.2 Non-coaxial superposition of phase singularities
10.10.3 Stokes singularities from plane waves
10.11 Detection of Stokes singularities
10.11.1 Stokes polarimetry for a higher-order Poincaré sphere
10.12 Polarization transformations
10.12.1 Action of retarders on Stokes singularities
10.12.2 Action of a q-plate on Stokes (ϕ12) singularities
10.12.3 Action of a spiral phase plate on polarization singularity
10.12.4 Action of a fork grating on polarization singularity
10.12.5 Fork grating under V-point illumination
10.12.6 Fork grating under C-point illumination
References.