Complex dispersion relation calculations with the symmetric interior penalty method

Abstract

AbstractA high‐order discontinuous Galerkin method for calculations of complex dispersion relations of two‐dimensional photonic crystals is presented. The medium is characterized by a complex‐valued permittivity and we relate for this absorptive system the spectral parameter to the time frequency. We transform the non‐linear eigenvalue problem for a Lorentz material in air into a non‐Hermitian linear eigenvalue problem and uses a Krylov space method to compute approximate eigenvalues. Moreover, we study the impact of the penalty term numerically and illustrate the high convergence rate of the method. Copyright © 2010 John Wiley & Sons, Ltd.