Singularities in Physics and Engineering / Paramasivam Senthilkumaran.

Format:

Book

Author/Creator:

Senthilkumaran, Paramasivam, author.

Series:

IOP series in advances in optics, photonics and optoelectronics.

IOP Series in Advances in Optics, Photonics and Optoelectronics Series

Language:

English

Subjects (All):

Engineering--Mathematical models.

Engineering.

Physical Description:

1 online resource (289 pages)

Edition:

Second edition.

Place of Publication:

Bristol, England : IOP Publishing, [2023]

Summary:

The book gives a thorough introduction to singularities and their development. It explains in detail important topics such as the types of singularities, their properties, detection and application, and emerging research trends.

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

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

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

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

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

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

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

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

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.

Notes:

Description based on publisher supplied metadata and other sources.

Description based on print version record.

Includes bibliographical references.

ISBN:

9780750349840

0750349840

OCLC:

1429724010