The geodesic form of light-ray trace in the inhomogeneous media

TL;DR

This paper demonstrates that light-ray tracing in inhomogeneous media can be described as geodesics in a 4-dimensional curved space, extending previous models to include time as a potential term.

Contribution

It extends the geodesic formulation of optical cloaking to four-dimensional Riemannian space, incorporating time as a potential in the canonical equations.

Findings

Light-ray paths are equivalent to geodesics in 4D curved space.

Time appears as a potential term in the extended geodesic equations.

Provides a physical interpretation of the extended geodesic model.

Abstract

The canonical equations of the optical cloaking proposed by Shurig, Pendry and Smith has been proved to be equivalent to the geodesic in a 3-dimensional curved space. Carrying out the argument we extend to the 4-dimensional Riemannian space where the extra time item appears as the potential term in the canonical equations. The physical meaning of the results is interpreted.