Azzam’s differential matrix formalism [J. Opt. Soc. Am. 68, 1756 (1978)], originally developed for longitudinally inhomogeneous anisotropic nondepolarizing media, is extended to include depolarizing media. The generalization is physically interpreted in terms of means and uncertainties of the elementary optical properties of the medium, as well as of three anisotropy absorption parameters introduced to describe the depolarization. The formalism results in a particularly simple mathematical procedure for the retrieval of the elementary properties of a generally depolarizing anisotropic medium, assumed to be globally homogeneous, from its experimental Mueller matrix. The approach is illustrated on literature data and the conditions of its validity are identified and discussed.

A product decomposition of a depolarizing Mueller matrix consisting in the sequence of five factors—a diagonal depolarizer stacked between two retarder and diattenuator pairs—is proposed. This novel “symmetric” decomposition allows for a straightforward interpretation and parameterization of an experimentally determined Mueller matrix in terms of an arrangement of polarization devices and their characteristic parameters: diattenuations, retardances, and axis azimuths. Its application is illustrated on experimentally determined Mueller matrices.

The paper addresses the polarization properties of tip enhanced Raman spectroscopy (TERS) through an experimental study on (001)- and (111)-oriented crystalline Si samples and quantitatively describes them by using a simple phenomenological model. The model, conceptually similar to that used in surface-enhanced Raman scattering (SERS), is based on the introduction of a phenomenological tip-amplification tensor accounting for the interaction of the tip with the electromagnetic field. It was found to be in a good agreement not only with our experimental data but also with the measurements and numerical simulations of other groups.

By applying the statistical definition of a depolarizing Mueller matrix we formally derive and physically interpret the differential matrix of a depolarizing homogeneous medium. The depolarization phenomenon being a direct consequence of the fluctuations of the six elementary polarization properties of the medium, the differential matrix contains the mean values and the variances of the properties, thus fully describing those from a statistical viewpoint. Similarly, the reduced coherency matrix associated with the G-symmetric component of the differential matrix has an immediate physical interpretation as being the covariance matrix of the three basic groups of polarization properties. The formal developments are illustrated on experimental examples.

It is shown that any depolarizing Mueller matrix can be reduced, through a product decomposition, to one of a total of two canonical depolarizer forms, a diagonal and a non-diagonal one. As a consequence, depolarizing Mueller matrices can be divided into Stokes diagonalizable and Stokes non-diagonalizable ones. Properties characteristic of the two canonical depolarizers are identified and discussed. Both canonical depolarizer forms are illustrated in experimental examples taken from the literature.