Electromagnetic Waves in Variable Media

TL;DR

This paper presents exact methods for solving Maxwell's equations in media with spatially varying electromagnetic properties, enabling advanced optical device design including cloaks and waveguides.

Contribution

It introduces new exact solution techniques for Maxwell's equations in variable media and applies them to design innovative optical devices like cloaks and waveguides.

Findings

Exact solutions for one-coordinate dependent media

Solutions for two-coordinate dependent media

Design principles for optical cloaks and waveguides

Abstract

Two methods are explained to exactly solve Maxwell's equations where permittivity, permeability and conductivity may vary in space. In the constitutive relations, retardation is regarded. If the material properties depend but on one coordinate, general solutions are derived. If the properties depend on two coordinates, geometrically restricted solutions are obtained. Applications to graded reflectors, especially to dielectric mirrors, to filters, polarizers and to waveguides, plain and cylindrical, are indicated. New foundations for the design of optical instruments, which are centered around an axis, and for the design of invisibility cloaks, plain and spherical, are proposed. The variability of material properties makes possible effects which cannot happen in constant media, e.g. stopping the flux of electromagnetic energy without loss. As a consequence, spherical devices can be constructed which bind electromagnetic waves.