Unified formalism for polarization optics: further developments

We report further developments of the unified formalism for polarization optics. The unified formalism for polarization optics was designed to use the Stokes-Mueller matrix equation and the Lorentz group to provide a conceptual framework and a systematic method to model and to understand complicated polarization phenomena in optical media (like optical fibers systems, devices, and networks). To address polarization issues for complicated systems, we introduce several new Mueller matrixes. First, both the deterministic and the stochastic Mueller matrix for arbitrary but uniform dichroism and birefringence are given. Next, the Mueller matrixes for optical media with successive (series) and/or simultaneous (parallel) dichroism and birefringence along the optical path are given. Also, we report a comparison of measured Mueller matrix data with a theoretical model of a short (approximately 1 meter) optical fiber (with low internal linear birefringence) under the influence of a constant external twist. The agreement between measurement and theory are excellent. Finally, we argue that more complicated optical fiber systems and configurations with more than one source of dichroism and birefringence can be modelled or approximated by using combinations of the appropriate arbitrary (deterministic and/or stochastic), series, and/or parallel Mueller matrixes given above.