Maxwell-Schroedinger Equation for Polarized Light and Evolution of the Stokes Parameters

TL;DR

This paper derives a Maxwell-Schroedinger equation for polarized light in anisotropic media, linking classical electromagnetism with quantum techniques to describe polarization evolution via Stokes parameters.

Contribution

It introduces a quantum-inspired approach to model polarization changes, providing a unified framework for optical phenomena like Faraday effect and magnetic resonance analogs.

Findings

Derived a Schroedinger-like equation for polarization states

Connected polarization evolution to pseudospin dynamics on the Poincare sphere

Applied the model to simulate Faraday effect and optical magnetic resonance

Abstract

By starting with the Maxwell theory of electromagnetism, we study the change of polarization state of light transmitting through optically anisotropic media. The basic idea is to reduce the Maxwell equation to the Schroedinger like equation for two levels (or states) representing polarization. By using the quantum mechanical technique, the density matrix, and path integral, the evolution of the Stokes parameters results in the equation of motion for a pseudospin representing a point on the Poincare sphere. Two typical examples relevant to actual experiments are considered; the one gives the generalized Faraday effect, and the other realizes an optical analog of magnetic resonance.