Transformation Optics for the Modelling of Waves in a Universe with Nontrivial Topology

TL;DR

This paper explores how transformation optics can create metamaterial models that simulate wave behavior in universes with complex topologies, potentially enabling cosmological simulations in laboratory settings.

Contribution

It introduces a method to model waves in nontrivial topologies using transformation optics, linking metamaterials to cosmological universe simulations.

Findings

Metamaterial devices can replicate wave measurements in complex topological spaces.

The models simulate waves in a universe with a nontrivial topology using transformation optics.

Potential for physical implementation of cosmological models with metamaterials.

Abstract

We consider how transformation optics and invisibility cloaking can be used to construct models in subsets $\mathbb{R}^3$ with a varying metric, where the time-harmonic waves for a given angular wavenumber $k$, are equivalent to the waves in some closed orientable manifold. The obtained models could in principle be physically implemented using a device built from metamaterials. In particular the measurements in the metamaterial device given by the Helmholtz source-to-solution operator are equivalent to Helmholtz source-to-solution measurements in a universe given by $(\mathbb{R}_+\times M, -dt^2 +g)$, where $(M,g)$ is a closed, orientable, $C^\infty$-smooth, 3-dimensional Riemannian manifold. Thus the obtained construction could be used to simulate cosmological models using metamaterial devices.