Jones-matrix Formalism as a Representation of the Lorentz Group

It is shown that the two-by-two Jones-matrix formalism for polarization optics is a six-parameter two-by-two representation of the Lorentz group. The attenuation and phase-shift filters are represented respectively by the three-parameter rotation subgroup and the three-parameter Lorentz group for two spatial and one time dimensions. It is noted that the Lorentz group has another three-parameter subgroup which is like the two-dimensional Euclidean group. Possible optical filters having this Euclidean symmetry are discussed in detail. It is shown also that the Jones-matrix formalism can be extended to some of the non-orthogonal polarization coordinate systems within the framework of the Lorentz-group representation.