Electromagnetic modes in cavities made of negative-index metamaterials

TL;DR

This paper investigates electromagnetic modes in negative-index metamaterial cavities, emphasizing the importance of including frequency dispersion to obtain physically meaningful positive quality factors, supported by numerical and analytical analysis.

Contribution

It introduces a method to incorporate frequency dispersion into mode analysis, ensuring positive quality factors and consistent physical interpretation for negative-index metamaterial cavities.

Findings

Dispersion inclusion yields positive quality factors

Transition from nondispersive to dispersive case demonstrated

Analytical and numerical methods confirm results

Abstract

We discuss electromagnetic modes in cavities formed by metamaterials with negative refraction and demonstrate that the straightforward approach to substitute negative values of the electric permittivity and the magnetic permeability leads to quasi-bound states with a negative quality factor. To ensure positive quality factors and a consistent physical interpretation of the quasi-bound states it is essential to include the frequency dispersion of the permittivity and the permeability, as required by positive field energy and causality. The basic mode equation and the boundary conditions including linear frequency dispersion are derived. As an example we consider a disk-like cavity with deformed cross sectional shape. The transition from the unphysical nondispersive case with negative quality factors to the dispersive case with positive quality factors is demonstrated numerically and in an analytical perturbative treatment.