Tying light in knots :applying topology to optics /

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"Version: 20181101"--Title page verso."A Morgan & Claypool publication as part of IOP Concise Physics"--Title page verso.Includes bibliographical references.1. Topology and physics : a historical overview -- 1.1. Introduction : searching for holes in fields of light -- 1.2. Topology and physics2. Electromagnetism and optics -- 2.1. Electromagnetic fields -- 2.2. Electromagnetic potentials and gauge invariance -- 2.3. Linear and nonlinear optical materials -- 2.4. Polarization and the Poincar?e sphere3. Characterizing spaces -- 3.1. Loops, holes, and winding numbers -- 3.2. Homotopy classes4. Fiber bundles, curvature, and holonomy -- 4.1. Manifolds -- 4.2. Vectors and forms -- 4.3. Curvature -- 4.4. Connections and covariant derivatives -- 4.5. Fiber bundles -- 4.6. Connection and curvature in electromagnetism and optics5. Topological invariants -- 5.1. Euler characteristic -- 5.2. Winding number -- 5.3. Index -- 5.4. Chern numbers -- 5.5. Linking number and other invariants6. Vortices and corkscrews : singular optics -- 6.1. Optical singularities -- 6.2. Optical angular momentum -- 6.3. Vortices and dislocations -- 6.4. Knotted and braided vortex lines -- 6.5. Polarization singularities -- 6.6. Optical M?obius strips7. Optical solitons -- 7.1. Solitary waves -- 7.2. Solitons in optics8. Geometric and topological phases -- 8.1. The Pancharatnam phase -- 8.2. Berry phase in quantum mechanics -- 8.3. Geometric phase in optical fibers -- 8.4. Holonomy interpretation9. Topological states of matter and light -- 9.1. The quantum hall effect -- 9.2. Topological phases and localized boundary states -- 9.3. Topological photonics.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.Also available in print.Mode of access: World Wide Web.System requirements: Adobe Acrobat Reader, EPUB reader, or Kindle reader.David Simon received a bachelor's degree in mathematics and physics from Ohio State University, followed by doctoral degrees in theoretical physics (Johns Hopkins) and engineering (Boston University). Originally trained in mathematical physics and quantum field theory, he now works primarily in quantum optics and related areas. After more than a decade teaching at Nova Southeastern University in Fort Lauderdale, he is currently Professor of Physics in the Department of Physics and Astronomy at Stonehill College (Easton, MA) and a visiting researcher at Boston University.Title from PDF title page (viewed on December 14, 2018).

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: .,

Collation

1 online resource (various pagings) :illustrations (some color).

Language

English

ISBN/ISSN

9781643272344

Classification

535.32

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Subject(s)

SCIENCE / Physics / General.
Physics.
Topology.
Geometrical optics.

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David S. Simon.

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