Mathematics for Polarization Analysis

A vast amount of knowledge on the mathematical treatments of polarization issues have been accumulated since Malus' early investigation on the topic, especially since optical fiber communications became a reality in the early 1970s. This chapter describes mathematical methods for polarization analysis, including detailed derivations of almost all major polarization related formulae or conclusions for interested readers to have a “one‐stop shop” to find out not only what they are, but also how they are arrived at, without having to search for the answers scattered in dozens of publications. It introduces two quantitative methods to describe the polarization state of light and its evolution: the Jones calculus and the Mueller calculus. The chapter introduces the matrix representation of an optical fiber. It then introduces two mathematic methods to describe partial polarization. One is the coherency matrix introduced by Emil Wolf, and another is the Stokes parameters introduced by Stokes.