The theory of electromagnetic line waves

TL;DR

This paper develops a theoretical framework for electromagnetic line waves at the interface of three materials, deriving equations to predict their behavior and explaining phenomena like ghost line waves through surface anisotropy effects.

Contribution

It introduces a non-local integral equation for line wave properties and shows how local differential equations can approximate these, expanding understanding of anisotropic surface effects.

Findings

Derived a non-local integral equation for line waves.

Validated approximations with finite element simulations.

Explained ghost line wave oscillations via effective gauge fields.

Abstract

Whereas electromagnetic surface waves are confined to a planar interface between two media, line waves exist at the one-dimensional interface between three materials. Here we derive a non-local integral equation for computing the properties of line waves, valid for surfaces characterised in terms of a general tensorial impedance. We find a good approximation -- in many cases -- is to approximate this as a local differential equation, where line waves are one-dimensional analogues of surface plasmons bound to a spatially dispersive metal. For anisotropic surfaces we find the oscillating decay of recently discovered `ghost' line waves can be explained in terms of an effective gauge field induced by the surface anisotropy. These findings are validated using finite element simulations.