Geometry and Topological photonics

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.

24 pages

References in corpus (6)

• Topological Photonics
• Analogs of quantum Hall effect edge states in photonic crystals
• Topological photonic crystals: physics, designs and applications
• Bulk-edge correspondence for topological photonic continua
• Stationary Charge Radiation in Anisotropic Photonic Time Crystals
• Ill-defined Topological Phases in Dispersive Photonic Crystals

Cited by in corpus (2)

• Roadmap on Nonlocality in Photonic Materials and Metamaterials
• Longitudinal optical phonons in photonic time crystals containing a stationary charge