On the Geometry and Topology of Transformation Optics

TL;DR

This paper extends transformation optics to Riemann-Cartan spaces with torsion, revealing new effects like bi-anisotropic media and orbital angular momentum generation, which could advance light control with metamaterials.

Contribution

It introduces a generalized geometrical model of transformation optics incorporating torsion and topological defects, leading to novel electromagnetic phenomena.

Findings

Equivalent media become bi-anisotropic with magnetoelectric coupling

Orbital angular momentum of light can be generated

Potential for new light manipulation techniques with metamaterials

Abstract

We generalize the geometrical model of transformation optics to Rieman-Cartan space with torsion by introducing topological defects in physical space. By relaxing the integrable condition, we show explicitly that the generalized equivalent medium are bi-anisotropic where the magnetoelectric coupling parameters emergent as the dislocation density. We also show the generation of orbital angular momentum of light. Our theory may open intriguing venues for controlling the vectorial degree of freedom of light with metamaterials.