Description

Book Synopsis
Topology 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

    Tying Light in Knots: Applying Topology to Optics

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      A Hardback by David S. Simon

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        Book details

        Publisher Morgan & Claypool Publishers
        Published 30 November 2018
        ISBN-13 9781643272351
        978-1643272351
        ISBN-10 1643272357
        Also in:
        Optical physics Particle and high-energy physics Physics

        Description

        Book Synopsis
        Topology 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

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