Preface
Acknowledgements
Author biography
1 Topology and physics: a historical overview
1.1 Introduction: searching for holes in fields of light
1.2 Topology and physics
1.2.1 Dirac monopoles
1.2.2 Aharonov-Bohm effect
1.2.3 Topology in optics
References
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
References
3 Characterizing spaces
3.1 Loops, holes, and winding numbers
3.2 Homotopy classes
References
4 Fiber bundles, curvature, and holonomy
4.1 Manifolds
4.2 Vectors and forms
4.3 Curvature
4.3.1 One dimension: curves
4.3.2 Two dimensions and beyond
4.4 Connections and covariant derivatives
4.5 Fiber bundles
4.6 Connection and curvature in electromagnetism and optics
References
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
References
6 Vortices and corkscrews: singular optics
6.1 Optical singularities
6.2 Optical angular momentum
6.3 Vortices and dislocations
6.4
6.5 Polarization singularities
6.6 Optical M?bius strips
References
7 Optical solitons
7.1 Solitary waves
7.2 Solitons in optics
References
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
References
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
References
Appendices
编辑手记
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