Determination of electromagnetic Bloch modes in a medium with frequency-dependent coefficients
Numerical Analysis
2018-09-26 v1 Analysis of PDEs
Abstract
We provide a functional framework and a numerical algorithm to compute the Bloch variety for Maxwell's equations when the electric permittivity is frequency dependent. We incorporate the idea of a mixed formulation for Maxwell's equations to obtain a quadratic eigenvalue for the wave-vector in terms of the frequency. We reformulate this problem as a larger linear eigenvalue problem and prove that this results in the need to compute eigenvalues of a compact operator. Using finite elements, we provide preliminary numerical examples of the scheme for both frequency independent and frequency dependent permittivity.
Cite
@article{arxiv.1809.09239,
title = {Determination of electromagnetic Bloch modes in a medium with frequency-dependent coefficients},
author = {C. Lackner and S. Meng and P. Monk},
journal= {arXiv preprint arXiv:1809.09239},
year = {2018}
}