Abatement of Computational Issues Associated with Dark Modes in Optical Metamaterials

TL;DR

This paper presents a transfer matrix numerical scheme to effectively address computational challenges caused by dark modes in optical metamaterials, improving the stability of mode amplitude calculations.

Contribution

It introduces a novel transfer matrix method specifically designed to handle dark modes in optical metamaterials, overcoming numerical conditioning issues.

Findings

The scheme successfully resolves poorly conditioned systems in a metal-dielectric metamaterial.

Demonstrates improved numerical stability over traditional methods.

Applicable to parallel plate metamaterial structures.

Abstract

Optical fields in metamaterial nanostructures can be separated into bright modes, whose dispersion is typically described by effective medium parameters, and dark fluctuating fields. Such combination of propagating and evanescent modes poses a serious numerical complication due to poorly conditioned systems of equations for the amplitudes of the modes. We propose a numerical scheme based on a transfer matrix approach, which resolves this issue for a parallel plate metal-dielectric metamaterial, and demonstrate its effectiveness.