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Table of Contents
Intro
Preface
Author biography
Paramasivam Senthilkumaran
Chapter 1 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 2 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
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
Trajectories
2.18 Links and knots
2.19 Different types of phase defects
Point, edge and mixed phase defects
Isotropic and anisotropic vortex
Canonical and non-canonical vortex
Perfect vortex
Fractional vortex
Riemann-Silberstein vortex
References
Chapter 3 Generation and detection methods
3.1 Introduction
3.2 Generation
3.2.1 Spiral phase plate
3.2.2 Fork grating
3.2.3 Spiral zone plate
3.2.4 Tilts
3.2.5 Interference methods
3.2.6 Speckles
3.2.7 Spatial light modulator
3.2.8 Dammann vortex grating
3.2.9 Mode conversion methods
3.2.10 Intra-cavity methods
3.2.11 Adaptive helical mirror
3.2.12 Vortex generation in optical fibers
3.2.13 q-wave plates for vortex generation
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 4 Propagation characteristics
4.1 Introduction
4.2 Wave equations and solutions
Wave equation
Paraxial waves
4.3 Slowly varying envelope approximation-paraxial Helmholtz equation
Wave equation in cylindrical coordinates
4.4 Gouy phase
Gouy phase in Gaussian beam
Gouy phase in a Hermite-Gaussian beam
Gouy phase in a LH beam
Gouy phase in a Bessel beam
4.5 Divergence of singular beams
4.6 Near core vortex structure and propagation
4.7 Propagation dynamics of optical phase singularities
Network of vortices
Vortex at off-axis positions in LG beams
Vortices introduced in a plane wave using CGH
Off-axis vortices in a Gaussian beam
4.8 Propagation of vortices in non-linear media
References
Chapter 5 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
Half-plane diffraction
Knife-edge method
Knife-edge test on pair of vortices
Knife-edge test on fractional vortex dipoles
Near-field diffraction through a slit
5.6 Energy circulations in diffraction patterns
References
Chapter 6 Vortices in computational optics
6.1 Introduction
6.2 Diffused illumination in holography
6.3 Synthesized diffusers
6.4 Phase synthesis in computer generated holograms
6.5 Stagnation problem in IFTA
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
Non-redundant information from vortex diffraction patterns
6.10 Phase retrieval.
References
Chapter 7 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 momenta
References
Chapter 8 Applications
8.1 Metrology
8.1.1 Optical vortex lattice interferometer
8.2 Collimation testing
8.3 Spiral interferometry
8.4 Spatial filtering
Hilbert transform
Isotropic edge enhancement
Anisotropic edge enhancement
Spiral phase contrast imaging
Optical vortex coronograph
Observation of a weak star in the bright background
8.5 Focal plane intensity manipulation
Polarization engineering
8.6 STED microscopy
8.7 Optical trapping and tweezers
8.8 Optically driven micro-motors
8.9 Communications
8.10 Phase retrieval methods
References
Chapter 9 Polarization singularities
9.1 Polarization of light
9.2 Stokes parameters and Poincare 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
Sign rule
9.8 Angular momentum in polarization singularities
9.9 Generation
Interference methods
Intra-cavity methods
Spatial light modulators
Spatially varying wave plates
q-Plates
9.10 Detection
Stokes fields
Interferometric method
Polarizer
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 Applications
Edge enhancement
C-points for optical activity measurement
Robust beams
Smallest focal spot
References.
Preface
Author biography
Paramasivam Senthilkumaran
Chapter 1 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 2 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
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
Trajectories
2.18 Links and knots
2.19 Different types of phase defects
Point, edge and mixed phase defects
Isotropic and anisotropic vortex
Canonical and non-canonical vortex
Perfect vortex
Fractional vortex
Riemann-Silberstein vortex
References
Chapter 3 Generation and detection methods
3.1 Introduction
3.2 Generation
3.2.1 Spiral phase plate
3.2.2 Fork grating
3.2.3 Spiral zone plate
3.2.4 Tilts
3.2.5 Interference methods
3.2.6 Speckles
3.2.7 Spatial light modulator
3.2.8 Dammann vortex grating
3.2.9 Mode conversion methods
3.2.10 Intra-cavity methods
3.2.11 Adaptive helical mirror
3.2.12 Vortex generation in optical fibers
3.2.13 q-wave plates for vortex generation
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 4 Propagation characteristics
4.1 Introduction
4.2 Wave equations and solutions
Wave equation
Paraxial waves
4.3 Slowly varying envelope approximation-paraxial Helmholtz equation
Wave equation in cylindrical coordinates
4.4 Gouy phase
Gouy phase in Gaussian beam
Gouy phase in a Hermite-Gaussian beam
Gouy phase in a LH beam
Gouy phase in a Bessel beam
4.5 Divergence of singular beams
4.6 Near core vortex structure and propagation
4.7 Propagation dynamics of optical phase singularities
Network of vortices
Vortex at off-axis positions in LG beams
Vortices introduced in a plane wave using CGH
Off-axis vortices in a Gaussian beam
4.8 Propagation of vortices in non-linear media
References
Chapter 5 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
Half-plane diffraction
Knife-edge method
Knife-edge test on pair of vortices
Knife-edge test on fractional vortex dipoles
Near-field diffraction through a slit
5.6 Energy circulations in diffraction patterns
References
Chapter 6 Vortices in computational optics
6.1 Introduction
6.2 Diffused illumination in holography
6.3 Synthesized diffusers
6.4 Phase synthesis in computer generated holograms
6.5 Stagnation problem in IFTA
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
Non-redundant information from vortex diffraction patterns
6.10 Phase retrieval.
References
Chapter 7 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 momenta
References
Chapter 8 Applications
8.1 Metrology
8.1.1 Optical vortex lattice interferometer
8.2 Collimation testing
8.3 Spiral interferometry
8.4 Spatial filtering
Hilbert transform
Isotropic edge enhancement
Anisotropic edge enhancement
Spiral phase contrast imaging
Optical vortex coronograph
Observation of a weak star in the bright background
8.5 Focal plane intensity manipulation
Polarization engineering
8.6 STED microscopy
8.7 Optical trapping and tweezers
8.8 Optically driven micro-motors
8.9 Communications
8.10 Phase retrieval methods
References
Chapter 9 Polarization singularities
9.1 Polarization of light
9.2 Stokes parameters and Poincare 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
Sign rule
9.8 Angular momentum in polarization singularities
9.9 Generation
Interference methods
Intra-cavity methods
Spatial light modulators
Spatially varying wave plates
q-Plates
9.10 Detection
Stokes fields
Interferometric method
Polarizer
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 Applications
Edge enhancement
C-points for optical activity measurement
Robust beams
Smallest focal spot
References.