Polarization nearness variation in an anisotropically absorbing medium

Azzam and Bashara have shown that a general, anisotropically absorbing, and retarding medium can be represented by a generalized form of the Jones matrix, whose first eigenstate is the polarization ellipse least attenuated by the medium, and whose second eigenstate (or eigenpolarization) is the one most absorbed. It is often convenient to represent a polarized beam incident to and departing from a medium as being in a state which is a linear combination of the two eigenstates. Successive slabs of the same material bring this state into ever greater Nearness to the low absorption eigenpolarization. An expression is developed to determine Nearness as a function of the optical depths of the two eigenstates and the state of the incident light.