Light propagation through optical media using metric contact geometry

TL;DR

This paper introduces a geometric framework using metric contact structures to analyze light propagation in optical media, revealing how boundaries cause aberrations and total internal reflection, with illustrative examples.

Contribution

It applies metric contact geometry to model light propagation and boundary effects in optical media, providing new insights into optical aberrations and internal reflection phenomena.

Findings

Orthogonality is expressed via metric contact structures.

Boundaries disrupt orthogonality, causing aberrations.

Examples demonstrate boundary effects on light propagation.

Abstract

In this work, we show that the orthogonality between rays and fronts of light propagation in a medium is expressed in terms of a suitable metric contact structure of the optical medium without boundaries. Moreover, we show that considering interfaces (modeled as boundaries) orthogonality is no longer fulfilled, leading to optical aberrations and in some cases total internal reflection. We present some illustrative examples of this latter point.