Tying light in knots : applying topology to optics /

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 c...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Simon, David S. (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: San Rafael [California] (40 Oak Drive, San Rafael, CA, 94903, USA) : Morgan & Claypool Publishers, [2018]
Colección:IOP (Series). Release 5.
IOP concise physics.
Temas:
Geometrical optics.
Topology.
Physics.
SCIENCE / Physics / General.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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 Poincaré 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
  • 5. Topological invariants
  • 5.1. Euler characteristic
  • 5.2. Winding number
  • 5.3. Index
  • 5.4. Chern numbers
  • 5.5. Linking number and other invariants
  • 6. 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 Möbius strips
  • 7. Optical solitons
  • 7.1. Solitary waves
  • 7.2. Solitons in optics
  • 8. 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 interpretation
  • 9. Topological states of matter and light
  • 9.1. The quantum hall effect
  • 9.2. Topological phases and localized boundary states
  • 9.3. Topological photonics.

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