On the Spectral Properties of Dispersive Photonic Crystals

This thesis is concerned with a parameter-nonlinear spectral problem which describes light propagation in certain two-dimensional, dispersive photonic crystals. A realization of the equation leads to the analysis of an operator pencil with a periodic coefficient depending on the spectral variable. It is shown that the corresponding spectrum is related to a family of eigenvalue equations posed on the underlying periodicity cell. Spectra and eigenfunctions of these problems are analyzed in detail.