Bulk-Boundary Correspondence in 2D Photonics: Analysis and Simulation

TL;DR

This paper investigates the bulk-boundary correspondence principle in two-dimensional topological photonics, providing analysis and simulations that support its validity and exploring its connection to electromagnetic energy positivity.

Contribution

It offers the first detailed analysis and numerical validation of the bulk-boundary correspondence in 2D photonic systems, extending understanding beyond 1D cases.

Findings

Numerical examples support the bulk-boundary correspondence in 2D photonics.

The BBCP is linked to the positivity of electromagnetic energy density.

The analysis highlights differences between 1D and 2D boundary conditions.

Abstract

The centerpiece of topological photonics is the bulk-boundary correspondence principle (BBCP), which relates discrete invariants of the Bloch bands to the possible presence of interface modes between two periodic heterostructures. In addition to the fundamental significance of BBCP, interface modes per se are of interest in a variety of applications. In Maxwell's electrodynamics, the BBCP has been rigorously proved for 1D problems, but the 2D case is qualitatively different, as the boundary conditions involve nontrivial Dirichlet-to-Neumann maps rather than scalar impedances as in 1D. The theoretical analysis and numerical examples in the paper are consistent with the BBCP. Moreover, the BBCP is closely connected with the positivity of electromagnetic energy density, as has also been shown to be true in 1D cases.