Minkowskian description of polarized light and polarizers

Mueller-Jones matrices as representing conformal Lorentz transformations

It is shown that Mueller-Jones matrices represent conformal Lorentz transformations. Thus the necessary and sufficient condition of a polarization device to be deterministic is to be describable by a conformal Lorentz transformation.

On a quasi-relativistic formula in polarization theory

In a pure operatorial (nonmatrix) Pauli algebraic approach, this Letter shows that the Poincaré vector of the light transmitted by a dichroic device can be expressed as function of the Poincaré vectors of the incoming light and of the device by a composition law of the same kind as the composition law of the noncolinear relativistic velocities. This is, in fact, a general law of composition for three-dimensional (3D) vectors remaining in the Poincaré ball (where they have a group-like structure). The differences between this problem and that of the composition law of two dichroic devices are pointed out and justified.

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.