Spinors, matrix structures, and projective geometry in polarization optics

TL;DR

This paper explores the mathematical frameworks underlying polarization optics, focusing on spinor representations, matrix structures, and projective geometry to deepen understanding of Mueller and Jones formalisms.

Contribution

It introduces a comprehensive analysis of the mathematical structures, including SU(2) symmetry, Cartan 2-spinors, and SL(4,R), providing new insights into the classification and properties of Mueller matrices.

Findings

Classification of 1-parametric Mueller matrices

Analysis of semi-group structures in Mueller matrices

Connection between spinor formalisms and polarization optics

Abstract

The paper discusses the role played by Mueller and Jones formalisms in polarization optics, by addressing the following aspects: restriction to the SU(2) symmetry, non-relativistic Stokes 3-vectors; Cartan 2-spinors in polarization optics; Jones 4-spinors for partially polarized light; the linear group SL(4,R) and the classification of 1-parametric Mueller matrices; semi-group structure and classification of degenerate Mueller matrices.