Determination of electromagnetic Bloch modes in a medium with frequency-dependent coefficients
This work provides a computational method for electromagnetic Bloch modes in dispersive media, which is relevant for photonic crystal and metamaterial design, but the results are preliminary and incremental.
The authors developed a functional framework and numerical algorithm to compute Bloch modes for Maxwell's equations with frequency-dependent permittivity, reformulating the problem as a linear eigenvalue problem of a compact operator. Preliminary numerical examples demonstrate the scheme for both frequency-independent and frequency-dependent permittivity.
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.