This paper demonstrates that numerous calculations involving polarization transformations can be condensed by employing suitable geometric algebra formalism. For example, to describe polarization mode dispersion and polarization-dependent loss, both the material birefringence and differential loss enter as bivectors and can be combined into a single symmetric quantity. Their frequency and distance evolution, as well as that of the Stokes vector through an optical system, can then each be expressed as a single compact expression, in contrast to the corresponding Mueller matrix formulations. The intrinsic advantage of the geometric algebra framework is further demonstrated by presenting a simplified derivation of generalized Stokes parameters that include the electric field phase. This procedure simultaneously establishes the tensor transformation properties of these parameters.
© 2014 Optical Society of America
Original Manuscript: March 3, 2014
Revised Manuscript: May 31, 2014
Manuscript Accepted: July 12, 2014
Published: August 11, 2014
George Soliman, David Yevick, and Paul Jessop, "Geometric algebra description of polarization mode dispersion, polarization-dependent loss, and Stokes tensor transformations," J. Opt. Soc. Am. A 31, 1956-1962 (2014)