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.