Information structure and general characterization of Mueller matrices.

Linear polarimetric transformations of light polarization states by the action of material media are fully characterized by corresponding Mueller matrices, which contain, in an implicit and intricate manner, all measurable information on such transformations. The general characterization of Mueller matrices relies on the positive semi-definiteness of the associated coherency matrix, which can be mathematically formulated through the nonnegativity of its eigenvalues. The enormously involved explicit algebraic form of such formulation prevents its interpretation in terms of simple physical conditions.

Unraveling the physical information of depolarizers.

The link between depolarization measures and physical nature and structure of material media inducing depolarization is nowadays an open question. This article shows how the joint use of two complementary sets of depolarizing metrics, namely the Indices of polarimetric purity and the Components of purity, are sufficient to completely describe the integral depolarizing properties of a sample. Based on a collection of illustrative and representative polarimetric configurations, a clear and meaningful physical interpretation of such metrics is provided, thus extending the current tools and comprehension for the study and analysis of the depolarizing properties of material media.

Algorithm for the numerical calculation of the serial components of the normal form of depolarizing Mueller matrices.

The normal form of a depolarizing Mueller matrix constitutes an important tool for the phenomenological interpretation of experimental polarimetric data. Due to its structure as a serial combination of three Mueller matrices, namely a canonical depolarizing Mueller matrix sandwiched between two pure (nondepolarizing) Mueller matrices, it overcomes the necessity of making a priori choices on the order of the polarimetric components, as this occurs in other serial decompositions. Because Mueller polarimetry addresses more and more applications in a wide range of areas in science, engineering, medicine, etc.

Characterization of passivity in Mueller matrices.

Except for very particular and artificial experimental configurations, linear transformations of the state of polarization of an electromagnetic wave result in a reduction of the intensity of the exiting wave with respect to the incoming one. This natural passive behavior imposes certain mathematical restrictions on the Mueller matrices associated with the said transformations. Although the general conditions for passivity in Mueller matrices were presented in a previous paper [ J.

Arbitrary decomposition of a Mueller matrix.

Mueller polarimetry involves a variety of instruments and technologies whose importance and scope of applications are rapidly increasing. The exploitation of these powerful resources depends strongly on the mathematical models that underlie the analysis and interpretation of the measured Mueller matrices and, very particularly, on the theorems for their serial and parallel decompositions. In this Letter, the most general formulation for the parallel decomposition of a Mueller matrix is presented, which overcomes certain critical limitations of the previous approaches, particularly the unnecessary exigency that the Mueller matrices of all parallel components have to be normalized in order to have equal transmittances for unpolarized light.

Invariant quantities of a nondepolarizing Mueller matrix.

Orthogonal Mueller matrices can be considered as corresponding either to retarders or to generalized transformations of the polarization basis for the representation of Stokes vectors, so that they constitute the only type of Mueller matrices that preserve the degree of polarization and the intensity of any partially polarized input Stokes vector. The physical quantities that remain invariant when a nondepolarizing Mueller matrix is transformed through its product by different types of orthogonal Mueller matrices are identified and interpreted, providing a better knowledge of the information contained in a nondepolarizing Mueller matrix.

Singular Mueller matrices.

Singular Mueller matrices play an important role in polarization algebra and have peculiar properties that stem from the fact that either the medium exhibits maximum diattenuation and/or polarizance or because its associated canonical depolarizer has the property of fully randomizing the circular component (at least) of the states of polarization of light incident on it. The formal reasons for which the Mueller matrix M of a given medium is singular are systematically investigated, analyzed, and interpreted in the framework of the serial decompositions and the characteristic ellipsoids of M. The analysis allows for a general classification and geometric representation of singular Mueller matrices, which are of potential usefulness to experimentalists dealing with such media.

Explicit algebraic characterization of Mueller matrices.

A general explicit algebraic characterization of Mueller matrices is presented in terms of the non-negativity of a set of leading principal minors of the coherency matrix C(A) associated with the arrow form M(A) of a given Mueller matrix M. This result is also formulated through a set of four characteristic Stokes vectors. The particular cases of Mueller matrices with zero degree of polarizance and symmetric Mueller matrices are analyzed.

Polarimetric subtraction of Mueller matrices.

A general formulation of the additive composition and decomposition of Mueller matrices is presented, which is expressed in adequate terms for properly performing the "polarimetric subtraction," from a given depolarizing Mueller matrix M, of the Mueller matrix of a given nondepolarizing component that is incoherently embedded in the whole system represented by M. A general and comprehensive procedure for the polarimetric subtraction of depolarizing Mueller matrices is also developed.

Poincaré sphere mapping by Mueller matrices.

By using the symmetric serial decomposition of a normalized Mueller matrix M [J. Opt. Soc.

Serial-parallel decompositions of Mueller matrices.

The algebraic methods for serial and parallel decompositions of Mueller matrices are combined in order to obtain a general framework for a suitable analysis of polarimetric measurements based on equivalent systems constituted by simple components. A general procedure for the parallel decomposition of a Mueller matrix into a convex sum of pure elements is presented and applied to the two canonical forms of depolarizing Mueller matrices [Ossikovski, J. Opt.