Relativistic kinematics formulation of the polarization effects of Jones-Mueller matrices

The polarization of a partially coherent, transverse electric, electromagnetic plane wave is commonly represented by a Stokes vector. The similarity between Stokes vectors and four-momentum vectors in special relativity (SR) is studied in depth. The set of Stokes vectors naturally possesses a Euclidean and a Lorentzian geometry. The latter is used to express the polarization-altering properties of Jones-Mueller matrices in a simple and elegant way. In particular, it is shown that the action of a diattenuator on a Stokes vector can be understood in terms of the addition law for velocities from SR. An important simplification in the resulting mathematical expressions further arises if the degree of polarization of a Stokes vector is represented by a hyperbolic polarization angle. This then allows us to demonstrate that the output hyperbolic polarization angle is related to a diattenuator hyperbolic polarization angle and the input hyperbolic polarization angle by the hyperbolic law of cosines holding in a hyperbolic triangle.