A Novel Computational Method for Band Structures of Dispersive Photonic Crystals

TL;DR

This paper introduces a new computational method for calculating the band structures of dispersive photonic crystals, capable of handling complex material properties and providing benchmark examples.

Contribution

It presents a novel eigenvalue-based approach combined with finite element discretization and spectral indicator method for dispersive photonic crystals.

Findings

Effective computation of band structures demonstrated in numerical examples.

Handles frequency-dependent, lossy, and lossless materials.

Provides benchmark cases for TM mode photonic crystals.

Abstract

We propose a new method to compute band structures of dispersive photonic crystals. It can treat arbitrarily frequency-dependent, lossy or lossless materials. The band structure problem is first formulated as the eigenvalue problem of an operator function. Finite elements are then used for discretization. Finally, the spectral indicator method is employed to compute the eigenvalues. Numerical examples in both the TE and TM cases are presented to show the effectiveness. There exist very few examples in literature for the TM case and three examples in this paper can serve as benchmarks.