Transitivity in the theory of the Lorentz group and the Stokes -- Mueller formalism in optics

TL;DR

This paper applies Lorentz group theory to analyze polarization devices in optics, deriving explicit formulas for Mueller parameters from measurements and extending the analysis to Lorentzian devices.

Contribution

It introduces a group-theoretical framework for polarization device analysis, providing explicit formulas for Mueller parameters in both non-relativistic and Lorentzian cases.

Findings

Derived explicit formulas for Mueller parameters from polarization measurements.

Extended analysis from 3D orthogonal matrices to 4D Lorentzian matrices.

Established a group-theoretical basis for polarization device characterization.

Abstract

Group-theoretical analysis of arbitrary polarization devices is performed, based on the theory of the Lorentz group. In effective "non-relativistic" Mueller case, described by 3-dimensional orthogonal matrices, results of the one polarization measurement determine group theoretical parameters within the accuracy of an arbitrary numerical variable. There are derived formulas, defining Muller parameter of the non-relativistic Mueller device uniquely and in explicit form by by the results of two independent polarization measurements. Analysis is extended to Lorentzian optical devices, described by 4-dimensional Mueller matrices.