The Polar Decomposition And Vector Parametrization Of The Mueller Matrices

It was demonstrated that presentation of the coherent matrix (polarization density matrix) of the electromagnetic beams as biquaternion corresponding to the four-vector of the pseudo Euclidean space with intensity and Stokes parameters as components gives the possibility for introducing of the group transformations of such values isomorphic to the S(3.1) group. These transformations are the subset of the set of polarization Mueller matrices creating algebraic structure of semigroup. Reduction of the semigroup of Mueller matrices to the group of transformations make it possible to use the vector parameterization of transformations of the group SO(3.1) for interpretation of polar decomposition of the Mueller matrices. In this approach in particular the elements of Mueller matrices corresponding to retarders and polarizers are more simple and natural connected with there eigenpolarizations.