ABSTRACT
This chapter presents introduction of the differential Jones and Mueller matrices, expressed in terms of the phenomenological elementary polarization properties of the medium. It aims to develop differential decomposition of depolarizing Mueller matrices; namely, the mathematical existence, the physical realizability, and addresses the multiplicity of the Mueller matrix logarithm. The chapter introduces the model of the homogeneous depolarizing medium, allowing for immediate physical interpretation of polarimetric experimental data in terms of mean values and variances–covariances of the elementary polarization properties. The differential formalism describes phenomenologically the polarimetric response of a continuous medium, measured in transmission, in terms of the six elementary polarization properties. Being a special, continuous kind of matrix product decomposition, the differential formalism considers the sequential propagation of the electromagnetic wave through the medium along a definite path length; however, unlike the product decompositions, it characterizes the sample in terms of simultaneously, not sequentially, occurring polarization properties.
