Band structure of photonic crystal with dispersive and lossy materials using Dirichlet-to-Neumann wave vector eigen equation method

Abstract

We present the Dirichlet-to-Neumann wave vector eigen equation (DtN-WVEE) method to calculate the band structure of photonic crystal (PhC) with dispersive and lossy materials, and then use finite-difference time-domain method to verify the validity of the results of the DtN-WVEE method. Since the material is lossy with a non-zero imaginary part of epsilon, the wave vector of PhC band structure also has a non-zero imaginary part which results in the reduction of the intensity of the mode. We further present the band structure which gives the relationship among the normalized frequency, the real part of the wave vector, and the imaginary part of the wave vector. To our knowledge, the band structure of lossy PhC has not been well studied yet, and our results can be useful in designing the devices using surface plasmon polariton effect.