On the symplectic structures arising in Optics

TL;DR

This paper explores the symplectic geometry underlying geometric optics, deriving the symplectic structure of light rays in media with varying refractive index and providing explicit coordinates and physical applications.

Contribution

It introduces a presymplectic geometric framework for geometric optics and derives the symplectic structure of light rays in non-uniform media, including explicit Darboux coordinates.

Findings

Derived the symplectic structure of light rays in media with variable refractive index.

Provided explicit Darboux coordinates for the symplectic structure.

Illustrated the theory with practical examples and applications.

Abstract

Geometric optics is analysed using the techniques of Presymplectic Geometry. We obtain the symplectic structure of the space of light rays in a medium of a non constant refractive index by reduction from a presymplectic structure, and using adapted coordinates, we find Darboux coordinates. The theory is illustrated with some examples and we point out some simple physical applications