Preprint 25-2016

Bandgap Calculations for Photonic Crystals

Author(s) : Marine Froidevaux , Cornelia Gamst

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 25-2016

MSC 2000

78A25 Electromagnetic theory, general

35P30 Nonlinear eigenvalue problems, nonlinear spectral theory for PDO

Abstract :
We study the propagation of light in a three-dimensional periodic photonic crystal, of which the electric permittivity is a complex nonlinear function of both space and frequency. We introduce the correct functional space needed to ensure that the operator corresponding to the weak formulation has a discrete spectrum, i.e., at most countably many isolated eigenvalues of finite multiplicity. Moreover, for two-dimensional photonic crystals, we present an a posteriori error estimator that can be used for the development of adaptive finite element methods.

Keywords : Maxwell equations, photonic crystals, eigenvalue problem, adaptive finite element method, a posteriori error estimator