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 physical system is an abstract global property that depends on the family operators describes propagation Bloch waves. Here, we highlight there profound geometrical connection between physics theory mathematical surfaces. We show band can be understood as generalization surfaces genus surface regarded Chern number suitable operator defined over surface. point out some implications topology context radiation problems discuss why for often associated with bulk-edge correspondence.