Complex dispersion relation calculations with the symmetric interior penalty method

Abstract

A 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.