Structure of matrices transforming Stokes parameters

Abstract

The structure of matrices that represent a linear transformation of the Stokes parameters of a beam of light into the Stokes parameters of another beam of light is investigated by means of the so-called Stokes criterion. This holds that the degree of polarization of a beam of light can never be changed into a number larger than unity. Several general properties are derived for matrices satisfying the Stokes criterion. These are used to establish conditions for the elements of such matrices. Conditions that are either necessary, or sufficient or both are presented. General 4×4 matrices are treated and a number of special cases is worked out analytically. Several applications are pointed out.