Maxwell fish eye for polarized light

TL;DR

This paper investigates how polarization affects light propagation in Maxwell fish eye media, revealing symmetry violations and proposing a modified profile that restores symmetry and ensures closed ray trajectories.

Contribution

It introduces a polarization-dependent Maxwell fish eye profile that maintains symmetries and produces closed light trajectories, advancing understanding of polarized light in complex media.

Findings

Polarization breaks the symmetry of Maxwell fish eye medium.

A modified, polarization-dependent profile restores symmetry.

Explicit solutions for polarized ray trajectories are provided.

Abstract

We consider the propagation of polarized light in the medium with Maxwell fish eye refraction index profile. We show that polarization violates the additional symmetries of medium, so that ray trajectories no longer remain closed. Then we suggest a modified, polarization-dependent Maxwell fish eye refraction index which restores all symmetries of initial profile and yields closed trajectories of polarized light. Explicit expressions for the polarization dependent integrals of motion and the solutions of corresponding ray trajectories are presented.