Singularities in Physics and Engineering: Properties, Methods, and Applications

Description

This book presents singular optics in a gradual and systematic manner and bridges the gap between a seasoned researcher and a student who aims to pursue research in this topic. The book includes illustrations, examples and references that will enable the reader to conceive their own ideas as they discover more about singular optics. PRELIMS.pdf Preface Author biography Paramasivam Senthilkumaran CH001.pdf 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 CH002.pdf 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 CH003.pdf 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 CH004.pdf 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 CH005.pdf 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 CH006.pdf 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 CH007.pdf 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 CH008.pdf 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 CH009.pdf 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