Spectral Methods for 2D Photonic Band Structures

摘要

We consider Maxwell's equations in two-dimensional periodic dielectric media cast as an eigenvalue problem. Multidomain spectral methods are applied in order to compute spectrally accurate eigenfrequencies, which provide the band structures of the photonic crystals. The domain is divided into subdomains whose interfaces include the edges of the different media so that the analytic solution of the eigenproblem is infinitely smooth in each subdomain. This promises that the multidomain spectral approximations perform the exponential rate of convergence to the analytic solution. The band structure calculations are carried out for simple domain structures, and their results are demonstrated.