On geodesics of gradient-index optical metrics and the optical-mechanical analogy

TL;DR

This paper develops the geodesic equations for gradient-index optical media, explores the optical-mechanical analogy, and applies these concepts to phenomena like gravitational lensing and moving media within a pre-metric electromagnetism framework.

Contribution

It provides a detailed derivation of geodesic equations in gradient-index media and discusses their relation to optical-mechanical analogies and applications in general relativity.

Findings

Light paths in isotropic gradient-index media are geodesics of a conformally related metric.

The optical-mechanical analogy is extended to include gravitational lensing and moving media.

Applications to general relativity include effective indices of refraction for gravitational fields.

Abstract

The geodesic equations for optical media whose refractive indices have a non-vanishing gradient are developed. It is shown that when those media are optically isotropic, the light paths will be mull geodesics of a spatial metric that is conformally related to the metric of the ambient space. Various aspects of the optical-mechanical analogy are discussed as they relate to the geodesics of conformally related metrics. Some applications of the concepts of gradient-index optics to general relativity are examined, such as effective indices of refraction for gravitational lensing and Gordon's optical metrics for optical media that are in a state of relative motion with respect to an observer. The latter topic is approached from the standpoint of pre-metric electromagnetism.