General Relativistic Contributions in Transformation Optics

TL;DR

This paper develops a covariant four-dimensional approach to transformation optics in curved space-times, analyzing the impact of Earth's curvature on satellite-based devices and their required fabrication precision.

Contribution

It introduces a covariant, four-dimensional framework for transformation optics applicable to arbitrary space-times, extending beyond flat Minkowski space.

Findings

Curvature effects are negligible for current satellite device precision.

The approach enables accurate modeling of transformation media in curved space-times.

Estimates show curvature contributions are significant only at very high fabrication precision.

Abstract

One potentially realistic specification for devices designed with transformation optics is that they operate with high precision in curved space-time, such as Earth orbit. This raises the question of what, if any, role does space-time curvature play in determining transformation media? Transformation optics has been based on a three-vector representation of Maxwell's equations in flat Minkowski space-time. I discuss a completely covariant, manifestly four-dimensional approach that enables transformations in arbitrary space-times, and demonstrate this approach for stable circular orbits in the spherically symmetric Schwarzschild geometry. Finally, I estimate the magnitude of curvature induced contributions to satellite-borne transformation media in Earth orbit and comment on the level of precision required for metamaterial fabrication before such contributions become important.