Geometry and Topological photonics
arXiv:2206.11231 · doi:10.1088/2040-8986/acdae3
Abstract
Topological photonics provides a powerful framework to describe and understand many nontrivial wave phenomena in complex electromagnetic platforms. The topological index of a physical system is an abstract global property that depends on the family of operators that describes the propagation of Bloch waves. Here, we highlight that there is a profound geometrical connection between topological physics and the topological theory of mathematical surfaces. We show that topological band theory can be understood as a generalization of the topological theory of surfaces and that the genus of a surface can be regarded as a Chern number of a suitable operator defined over the surface. We point out some nontrivial implications of topology in the context of radiation problems and discuss why for physical problems the topological index is often associated with a bulk-edge correspondence.
arXiv comment24 pages
References in corpus (17)
- Topological Photonics
- Topological Photonics
- Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry
- Robust optical delay lines via topological protection
- Analogs of quantum Hall effect edge states in photonic crystals
- A topological quantum optics interface
- Topological photonic crystals: physics, designs and applications
- Topological Photonic Phase in Chiral Hyperbolic Metamaterials
- Mapping topological order in coordinate space
- Bulk-edge correspondence for topological photonic continua
- Berry phase, Berry Connection, and Chern Number for a Continuum Bianisotropic Material from a Classical Electromagnetics Perspective
- Topological Marker Currents in Chern Insulators
- Proof of the bulk-edge correspondence through a link between topological photonics and fluctuation-electrodynamics
- Stationary Charge Radiation in Anisotropic Photonic Time Crystals
- Topological classification of Chern-type insulators with the photonic Green function
- Quantized Angular Momentum in Topological Optical Systems
- Ill-defined Topological Phases in Dispersive Photonic Crystals