Maxwell fish eye for polarized light

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.

Integrable isotropic profiles for polarized light

“…In this paper, following [5] we propose a general scheme of the deformation of isotropic refraction index profiles. It allows us to restore the initial symmetries of the system after one takes the light polarization into consideration.…”

Basic Notions of Poisson and Symplectic Geometry in Local Coordinates, with Applications to Hamiltonian Systems

“…If we have only one function Φ(z), we assume that it has a non vanishing gradient, rank (∂ i Φ) = 1. Taking c α = 0 in (21), we have the surface of level zero…”