Covariant Description of Transformation Optics in Linear and Nonlinear Media

TL;DR

This paper develops a comprehensive covariant formalism for transformation optics applicable to diverse media, including nonlinear and moving materials, enabling precise design of complex electromagnetic devices.

Contribution

It introduces a general covariant transformation law for transformation optics that encompasses nonlinear, bianisotropic, and moving media, advancing the theoretical framework.

Findings

Derived a covariant transformation law for arbitrary media.

Applied the formalism to second harmonic generation in a twisted concentrator.

Demonstrated the formalism's applicability to complex media and transformations.

Abstract

The technique of transformation optics (TO) is an elegant method for the design of electromagnetic media with tailored optical properties. In this paper, we focus on the formal structure of TO theory. By using a complete covariant formalism, we present a general transformation law that holds for arbitrary materials including bianisotropic, magneto-optical, nonlinear and moving media. Due to the principle of general covariance, the formalism is applicable to arbitrary space-time coordinate transformations and automatically accounts for magneto-electric coupling terms. The formalism is demonstrated for the calculation of the second harmonic generation in a twisted TO concentrator.