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Tying light in knots : applying topology to optics

Author: David S Simon; Morgan & Claypool Publishers,; Institute of Physics (Great Britain),
Publisher: San Rafael [California] (40 Oak Drive, San Rafael, CA, 94903, USA) : Morgan & Claypool Publishers, Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) : IOP Publishing, [2018] [2018]
Series: IOP concise physics.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
"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,  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Simon, David S.
Tying light in knots.
San Raphael, CA : Morgan & Claypool Publishers, [2018]
(OCoLC)1066189273
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: David S Simon; Morgan & Claypool Publishers,; Institute of Physics (Great Britain),
ISBN: 9781643272344 1643272349 9781643272320 1643272322
OCLC Number: 1080122293
Notes: "Version: 20181101"--Title page verso.
Description: 1 online resource : illustrations (some color).
Contents: Topology and physics : a historical overview: Introduction. Searching for holes in fields of light --
Topology and physics --
Electromagnetism and optics: Electromagnetic fields --
Electromagnetic potentials and gauge invariance --
Linear and nonlinear optical materials --
Polarization and the Poincaré sphere --
Characterizing spaces: Loops, holes, and winding numbers --
Homotopy classes --
Fiber bundles, curvature, and holonomy: Manifolds --
Vectors and forms --
Curvature --
Connections and covariant derivatives --
Fiber bundles --
Connection and curvature in electromagnetism and optics --
Topological invariants: Euler characteristic --
Winding number --
Index --
Chern numbers --
Linking number and other invariants --
Vortices and corkscrews : singular optics: Optical singularities --
Optical angular momentum --
Vortices and dislocations --
Knotted and braided vortex lines --
Polarization singularities --
Optical Möbius strips --
Optical solitons: Solitary waves --
Solitons in optics --
Geometric and topological phases: The Pancharatnam phase --
Berry phase in quantum mechanics --
Geometric phase in optical fibers --
Holonomy interpretation --
Topological states of matter and light: The quantum hall effect --
Topological phases and localized boundary states --
Topological photonics.
Series Title: IOP concise physics.
Other Titles: Applying topology to optics.
Responsibility: David S. Simon.

Abstract:

"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"--Print version, page 4 of cover.

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