Generalized Transformation Optics of Linear Materials

TL;DR

This paper advances a fully covariant 4D framework for transformation optics applicable to all linear dielectric materials, enabling complex transformations including motion and non-vacuum media, with demonstrated applications and a generalized inverse problem.

Contribution

It introduces a systematic, covariant approach to transformation optics that extends previous methods to all transformations and linear materials, including moving media and arbitrary space-times.

Findings

Developed a covariant 4D transformation optics framework.

Applied the framework to a uniformly moving dielectric medium.

Generalized Gordon's optical metric through the inverse problem.

Abstract

We continue the development of a manifestly 4-dimensional, completely covariant, approach to transformation optics in linear dielectric materials begun in a previous paper. This approach, which generalizes the Plebanski based approach, is systematically applicable for all transformations and all general linear materials. Importantly, it enables useful applications such as arbitrary relative motion, transformations from arbitrary non-vacuum initial dielectric media, and arbitrary space-times. This approach is demonstrated for a resulting material that moves with uniform linear velocity. The inverse problem of this covariant approach is shown to generalize Gordon's "optical metric".