Metamaterial claddings for homotopic control of waveguide modes

Abstract

Engineers know that the path followed by an electromagnetic wave is determined according to Fermat's principle by the bulk constitutive properties of the medium in which the wave propagates. Physicists are equally familiar with the fact that the ray path of a wave in a vacuum is influenced by the metric of space. According to Einstein's General Theory of Relativity, massive objects cause spacetime curvature, and the metric or distance measure becomes different from the flat Euclidean metric ds2 = dx2 + dy2 + dz2. In a curved space, waves follow geodesics, leading to such effects as gravitational lensing and a shift in the apparent position of a near-occulted star. It follows from the above two facts that wave propagation paths can be influenced through (1) local electrical interactions governed by the constitutive relationships in Maxwell's equations and (2) distant gravitational interactions through the metric of space. The duality between constitutive relationships and spatial metric interactions has been recently exploited by the electromagnetics community in practical applications. Rays that travel along non-straight paths can in principle be realized either by the gravitational field of some mass distribution or by a medium with a chosen set of constitutive parameters. Even though the gravitational fields would need to be too strong to produce the desired effects in the length scales of interest, properly designed metamaterials can indeed approximate the necessary constitutive parameters. This has been exploited in recent years to develop methods for electromagnetic cloaking [1,2], masking [3,4], field rotation [5], and reflectionless waveguide bends [6].