Singularities in Physics and Engineering

Abstract

High level students and researchers--many of the topics covered have proven industrial applications. To name a few--spiral interferometry, robust beam engineering, optical tweezers, optical communications. All these and many more topics are covered in a chapter on Applications. "Version: 20181101"--Title page verso Title from PDF title page (viewed on December 14, 2018). Singularities are pervasive throughout nature and this book is one of the first to combine all aspects of singular optics and to give a detailed view of the subject. Singularities in Optical Physics and Engineering give a thorough introduction to singularities and their development and goes on to explain in detail important topics such as the types of singularities, their properties, detection and application and the emerging research trends that are still developing. The book concentrates mostly on phase singularities in a comprehensive development to allow a greater understanding of singularities throughout the chapters. It also discusses polarization singularities in its final chapter giving an in-depth description of this subject. With new advances being generated continuously, this book will cover a vibrant field of optics and will give an essential foundation to any students and researchers interested in singular optics. Part of IOP Series in Advances in Optics, Photonics and Optoelectronics 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 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 -- 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 -- 2.18. Links and knots -- 2.19. Different types of phase defects 3. Generation and detection methods -- 3.1. Introduction -- 3.2. Generation -- 3.3. Detection 4. 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 5. Internal energy flows -- 5.1. Energy flow -- 5.2. Internal energy flows -- 5.3. Visualizing internal energy flow -- 5.4. Focusing of singular beams--effect of aberrations -- 5.5. Experimental detection -- 5.6. Energy circulations in diffraction patterns 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 -- 6.8. Non-Bryngdahl transforms using branch points -- 6.9. Diffraction of singular beams -- 6.10. Phase retrieval 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 -- 7.5. Intrinsic and extrinsic angular momenta 8. Applications -- 8.1. Metrology -- 8.2. Collimation testing -- 8.3. Spiral interferometry -- 8.4. Spatial filtering -- 8.5. Focal plane intensity manipulation -- 8.6. STED microscopy -- 8.7. Optical trapping and tweezers -- 8.8. Optically driven micro-motors -- 8.9. Communications -- 8.10. Phase retrieval methods 9. Polarization singularities -- 9.1. Polarization of light -- 9.2. Stokes parameters and Poincare sphere representation -- 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 -- 9.8. Angular momentum in polarization singularities -- 9.9. Generation -- 9.10. Detection -- 9.11. Inversion and conversion methods -- 9.12. Polarization singularity distributions -- 9.13. Applications.