# Optical Aharonov-Bohm effect due to toroidal moment inspired by general relativity

## TL;DR

This paper explores an optical analog of the Aharonov-Bohm effect caused by toroidal moments in materials, drawing parallels with gravitational effects in curved spacetime, and suggests experimental setups using multiferroic or metamaterials.

## Contribution

It introduces a novel gravitational analog of the index of refraction for magneto-electric media and predicts an optical Aharonov-Bohm effect due to toroidal moments.

## Key findings

- Light experiences a Lorentz-like force in magneto-electric media.
- An optical Aharonov-Bohm effect exists in regions with curl-free toroidal moments.
- Potential experimental realization with multiferroic or toroidal metamaterials.

## Abstract

We study the analogy between propagation of light rays in a stationary curved spacetime and in a toroidal (meta-)material. After introducing a novel gravitational analog of the index of refraction of a magneto-electric medium, it is argued that light rays not only feel a Lorentz-like force in a magneto-electric medium due to the non-vanishing curl of the toroidal moment, but also there exists an optical analog of Aharonov-Bohm effect for the rays traveling in a region with a curl-free toroidal moment. Experimental realization of this effect could utilize either a multiferroic material or a toroidal metamaterial.