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

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 topologically protected interface modes between two periodic heterostructures. In addition to the fundamental significance of BBCP, interface modes 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, because the boundary conditions involve nontrivial Dirichlet-to-Neumann maps rather than scalar impedances as in 1D. The theoretical analysis and numerical examples presented 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 the case in 1D and 1.5D.