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On Spectral Analysis of an Operator Pencil with Applications to Wave Propagation in Periodic and Frequency Dependent Materials

By Christian Engström and Markus Richter


We study wave propagation in periodic and frequency dependent materials. The approach in this paper leads to spectral analysis of a quadratic operator pencil where the spectrum parameter relates to the quasimomentum and the frequency is a parameter. We show that the underlying operator has a discrete spectrum, where the eigenvalues are symmetrically placed with respect to the real and imaginary axis. Moreover, we derive bounds on the eigenvalues that is tight in low-frequency applications. Numerical calculations in two dimensions illustrates the method.

Year: 2008
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