The spinorial representation of polarized light and Berry phase

TL;DR

This paper presents a spinorial framework for polarized light using relativistic concepts, demonstrating how the Berry phase can be computed via matrix methods on the Poincare sphere, linking polarization and quantum phase.

Contribution

It introduces a novel spinorial representation of polarized photons and a matrix-based method to calculate Berry phase, bridging relativistic and quantum descriptions of polarization.

Findings

Polarized photons can be described by two-component spinors.

Berry phase can be computed through matrix methods on the Poincare sphere.

The approach links relativistic and quantum polarization phenomena.

Abstract

From relativistic point of view it has been shown here that a polarized photon can be visualized to give an equivalent spinorial description when the two-component spinor is the eigenvector of $2\times2$ Hermitian, Polarization matrix. The Berry phase of the initial state can be calculated by matrix method as it complete one rotation over a closed path on the Poincare's sphere.