Wave propagation in metamaterials mimicking the topology of a cosmic string

TL;DR

This paper investigates how light propagates through a metamaterial designed to mimic the spacetime of a cosmic string, revealing a gravitational analogue of the Aharonov-Bohm effect through interference and diffraction phenomena.

Contribution

It provides the first full-wave numerical simulation and analytical interpretation of wave behavior in a metamaterial mimicking a cosmic string's topology.

Findings

Wave propagation exhibits interference patterns similar to gravitational effects.

Diffraction effects are explained by four-wave interference involving geometrical and diffracted waves.

Numerical simulations agree well with asymptotic diffraction theory.

Abstract

We study the interference and diffraction of light when it propagates through a metamaterial medium mimicking the spacetime of a cosmic string, -- a topological defect with curvature singularity. The phenomenon may look like a gravitational analogue of the Aharonov-Bohm effect, since the light propagates in a region where the Riemann tensor vanishes being nonetheless affected by the non-zero curvature confined to the string core. We carry out the full-wave numerical simulation of the metamaterial medium and give the analytical interpretation of the results by use of the asymptotic theory of diffraction, which turns out to be in excellent agreement. In particular we show that the main features of wave propagation in a medium with conical singularity can be explained by four-wave interference involving two geometrical-optics and two diffracted waves.