Jones-matrix Formalism as a Representation of the Lorentz Group

Abstract

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.

RevTeX, 27 pages, no figures, to be published in J. Opt. Soc. Am. A

Cited by in corpus (15)

• Pattern Formation in Quantum Ferrofluids: from Supersolids to Superglasses
• Stokes Parameters as a Minkowskian Four-vector
• Wigner Rotations and Iwasawa Decompositions in Polarization Optics
• Iwasawa Effects in Multi-layer Optics
• Interferometers and Decoherence Matrices
• Optical finite representation of the Lorentz group
• Polarization Optics Analogy of Quantum Wavefunctions in Graphene
• Binary Representations of ABCD Matrices
• Generalized Formalisms of the Radio Interferometer Measurement Equation
• Lorentz group theory and polarization of the light
• Optical Activities as Computing Resources for Space-time Symmetries
• Poincaré Sphere and Decoherence Problems
• Understanding Squeezed States of Light Through Wigner's Phase-Space
• Transitivity in the theory of the Lorentz group and the Stokes -- Mueller formalism in optics
• Factorizations for 3-rotations and polarization of the light in Mueller-Stokes an Jones formalisms