Description
Book SynopsisTopology is the study of properties of geometrical objects that remain invariant as the object is bent, twisted, or otherwise continuously deformed. It has been an indispensable tool in particle physics and solid state physics for decades, but in recent years it has become increasingly relevant in classical and quantum optics as well. It makes appearances through such diverse phenomena as Pancharatnam-Berry phases, optical vortices and solitons, and optical simulations of solid-state topological phenomena. This book concisely provides the necessary mathematical background needed to understand these developments and to give a rapid survey of some of the optical applications where topological issues arise.
Table of Contents
- Preface
- Acknowledgements
- Author biography
- 1. Topology and physicsa historical overview
- 2. Electromagnetism and physics
- 3. Characterizing spaces
- 4. Fiber bundles, curvature, and holonomy
- 5. Topological invariants
- 6. Vortices and corkscrewssingular optics
- 7. Optical solitons
- 8. Geometric and topological phases
- 9. Topological states of matter and light
- Appendices
