"Version: 20210205"--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 physics

2. 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 sphere

3. Characterizing spaces -- 3.1. Loops, holes, and winding numbers -- 3.2. Homotopy classes

4. 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 optics -- 4.7. The Hopf fibration and polarization

5. Topological invariants -- 5.1. Euler characteristic -- 5.2. Winding number -- 5.3. Index of zero points of vector fields -- 5.4. Chern numbers -- 5.5. Pontrjagin index -- 5.6. Hopf index -- 5.7. Linking number and other invariants -- 5.8. Atiyah-Singer index theorem

6. Vortices and corkscrews : singular optics -- 6.1. Optical singularities -- 6.2. Optical angular momentum -- 6.3. Vortices and dislocations -- 6.4. Polarization singularities -- 6.5. Optical M�obius strips

7. Knotted and braided vortex lines -- 7.1. Knotted vortex lines -- 7.2. Creating and characterizing knotted vortices -- 7.3. Variations and applications

8. Optical solitons -- 8.1. Solitary waves -- 8.2. Simple example : Sine-Gordon equation -- 8.3. Solitons in optics

9. Geometric and topological phases -- 9.1. The Pancharatnam phase -- 9.2. Berry phase in quantum mechanics -- 9.3. Geometric phase in optical fibers -- 9.4. Holonomy interpretation

10. Topological states of matter -- 10.1. The quantum Hall effect -- 10.2. One-dimensional example : the SSH model -- 10.3. Topological phases and localized boundary states -- 10.4. The role of discrete symmetries -- 10.5. Varieties of topological insulators and related systems -- 10.6. Dirac, Majorana, and Weyl points

11. Topological photonics -- 11.1. Overview : topological effects in photonic systems -- 11.2. Photonic walks -- 11.3. Photonic crystals, waveguides, and coupled resonant cavities -- 11.4. Topologically protected waveguides and topological lasers -- 11.5. Topological optical computing.

Topology in Optics: Tying light in knots (Second Edition) provides the background needed to understand a broad range of unexpected phenomenon and developments arising from topological effects in optics. Assuming only a background in physics at the advanced undergraduate level, it requires no prior familiarity with topology. Revised and expanded with two new chapters, Topological Photonics and Optical Knots and Links, this will be an invaluable reference for undergraduate and graduate students as well as researchers and engineers in optics and related areas.

Undergraduate and graduate students.

Also available in print.

Mode of access: World Wide Web.

System requirements: Adobe Acrobat Reader, EPUB reader, or Kindle reader.

After a bachelor's degree from Ohio State University, David Simon earned doctoral degrees in theoretical physics (Johns Hopkins) and engineering (Boston University), he now works primarily in quantum optics and related areas. He has been the author or coauthor of several books and dozens of research papers on topics ranging from the use of supersymmetry in quantum mechanics to applications of quantum entanglement in optical measurement and cryptography. He is currently Professor of Physics at Stonehill College (Easton, MA), program manager of the photonics certificate program there, and a visiting researcher at Boston University.

Title from PDF title page (viewed on June 11, 2021).