Guided Modes of Elliptical Metamaterial Waveguides

TL;DR

This paper investigates guided electromagnetic modes in elliptical metamaterial waveguides with negative-index cores, revealing the potential for highly localized surface waves through numerical solutions of dispersion relations involving Mathieu functions.

Contribution

It introduces a numerical method to analyze mode spectra in elliptical metamaterial waveguides with negative-index media, highlighting the existence of highly localized surface modes.

Findings

Existence of highly localized surface waves in elliptical metamaterial waveguides.

Numerical calculation of mode spectra using Mathieu functions.

Potential applications in surface wave transmission and waveguide design.

Abstract

The propagation of guided electromagnetic waves in open elliptical metamaterial waveguide structures is investigated. The waveguide contains a negative-index media core, where the permittivity, $\epsilon$ and permeability $\mu$ are negative over a given bandwidth. The allowed mode spectrum for these structures is numerically calculated by solving a dispersion relation that is expressed in terms of Mathieu functions. By probing certain regions of parameter space, we find the possibility exists to have extremely localized waves that transmit along the surface of the waveguide.