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 dimensions and one time dimension. The Lorentz group has another three-parameter subgroup, which is like the two-dimensional Euclidean group. Optical filters that may have this Euclidean symmetry are discussed in detail. It is shown that the Jones-matrix formalism can be extended to some of the nonorthogonal polarization coordinate systems within the framework of the Lorentz-group representation.
© 1997 Optical Society of America
Original Manuscript: July 31, 1996
Revised Manuscript: January 15, 1997
Manuscript Accepted: January 15, 1997
Published: September 1, 1997
D. Han, Y. S. Kim, and Marilyn E. Noz, "Jones-matrix formalism as a representation of the Lorentz group," J. Opt. Soc. Am. A 14, 2290-2298 (1997)