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Bandgap Calculations for Photonic Crystals

Froidevaux, Marine; Gamst, Cornelia

Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin

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.