Transformation Optics and the Geometry of Light

TL;DR

This paper explores the fundamental connection between transformation optics, metamaterials, and the geometry of light, highlighting how geometric principles from general relativity influence optical phenomena and device design.

Contribution

It provides a comprehensive analysis of how geometrical ideas from general relativity underpin modern transformation optics and metamaterials, opening new avenues for optical device innovation.

Findings

Link between optics and general relativity clarified

Applications in invisibility and perfect lenses demonstrated

Foundational insights for future metamaterial design provided

Abstract

Metamaterials are beginning to transform optics and microwave technology thanks to their versatile properties that, in many cases, can be tailored according to practical needs and desires. Although metamaterials are surely not the answer to all engineering problems, they have inspired a series of significant technological developments and also some imaginative research, because they invite researchers and inventors to dream. Imagine there were no practical limits on the electromagnetic properties of materials. What is possible? And what is not? If there are no practical limits, what are the fundamental limits? Such questions inspire taking a fresh look at the foundations of optics and at connections between optics and other areas of physics. In this article we discuss such a connection, the relationship between optics and general relativity, or, expressed more precisely, between geometrical ideas normally applied in general relativity and the propagation of light, or electromagnetic waves in general, in materials. We also discuss how this connection is applied: in invisibility devices, perfect lenses, the optical Aharonov-Bohm effect of vortices and in analogues of the event horizon.