## Abstract

We extend the scope of the Mueller calculus to parallel that established by Jones for his calculus. We find that the Stokes vector **S** of a light beam that propagates through a linear depolarizing anisotropic medium obeys the first-order linear differential equation *d S*/

*dz*= m

**S**, where

*z*is the distance traveled along the direction of propagation and

**m**is a 4 × 4 real matrix that summarizes the optical properties of the medium which influence the Stokes vector. We determine the differential matrix

**m**for eight basic types of optical behavior, find its form for the most general anisotropic nondepolarizing medium, and determine its relationship to the complex 2 × 2 differential Jones matrix. We solve the Stokes-vector differential equation for light propagation in homogeneous nondepolarizating media with arbitrary absorptive and refractive anisotropy. In the process, we solve the differential-matrix and Mueller-matrix eigenvalue equations. To illustrate the case of inhomogeneous anisotropic media, we consider the propagation of

*partially*polarized light along the helical axis of a cholesteric or twisted-nematic liquid crystal. As an example of depolarizing media, we consider light propagation through a medium that tends to equalize the preference of the state of polarization to the right and left circular states.

© 1978 Optical Society of America

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