Unified formalism for polarization optics with application to polarimetry on a twisted optical fiber

摘要

A unified formalism for polarization optics is presented. This formalism was developed to use the Stokes-Mueller matrix equation and the Lorentz group to provide a conceptual framework and a systematic method to model and understand complicated polarization phenomena in optical media (such as optical fibers, fiber systems, devices, and networks). Central to this approach is the utilization of operator and group theoretic techniques to exploit the analogy that exists between the dichroism and birefringence elements of the Mueller matrix of polarization optics and the boost and rotation generators, respectively, of the Lorentz transformations of special relativity. This formalism incorporates the other popular [i.e., the Jones, the coherency (or density), and the Mueller matrix] polarization approaches into a single unified formalism. To address polarization issues for complicated systems, we introduce several rudimentary deterministic Mueller matrices. First, the Mueller matrix for arbitrary birefringence and dichroism is given. Second, the Mueller matrix for arbitrary but uniform birefringence and dichroism is given. Third, the Mueller matrix for optical media with successive (series) birefringence and dichroism along the optical path are given. Fourth, the Mueller matrix for optical media with simultaneous (parallel) birefringences and dichro-isms along the optical path are given. Finally, the formalism is applied to a comparison between polarimetric data [for a short (～1 m) optical fiber with low internal linear birefringence under the influence of a constant external twist rate] and a theoretical model. The agreement between measurement and theory are excellent.