Calculation and analysis of complex band structure in dispersive and dissipative two-dimensional photonic crystals

TL;DR

This paper presents a finite element method extension for calculating complex band structures in dispersive, absorptive 2D photonic crystals, enabling detailed analysis of resonances and revealing new spectral features.

Contribution

The paper introduces a versatile finite element approach that simplifies complex pole analysis and accurately computes complex band structures in dispersive, dissipative photonic systems.

Findings

Excellent agreement with analytical and literature results

Revealed unexpected features in complex band structures

Applicable to various geometries and materials

Abstract

Numerical calculation of modes in dispersive and absorptive systems is performed using the finite element method. The dispersion is tackled in the frame of an extension of Maxwell's equations where auxiliary fields are added to the electromagnetic field. This method is applied to multi-domain cavities and photonic crystals including Drude and Drude-Lorentz metals. Numerical results are compared to analytical solutions for simple cavities and to previous results of the literature for photonic crystals, showing excellent agreement. The advantages of the developed method lie on the versatility of the finite element method regarding geometries, and in sparing the use of tedious complex poles research algorithm. Hence the complex spectrum of resonances of non-hermitian operators and dissipative systems, like two-dimensional photonic crystal made of absorbing Drude metal, can be investigated in detail. The method is used to reveal unexpected features of their complex band structures.