Topology in optics : tying light in knots /

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 f...

Descripción completa

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Simon, David S. (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) : IOP Publishing, [2021]
Edición:Second edition.
Colección:IOP (Series). Release 21.
IOP ebooks. 2021 collection.
Temas:
Geometrical optics.
Quantum optics > Mathematics.
Topology.
Optical physics.
.TECHNOLOGY & ENGINEERING / Optics.
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
  • 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 Möbius 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.

Ejemplares similares