Differential and product Mueller matrix decompositions: a formal comparison

It is shown that the Mueller matrix logarithm and the Mueller matrix roots decompositions used for the extraction of the elementary polarization properties of a depolarizing medium, although being computationally different, are formally equivalent, being both based upon the differential representation of a continuously depolarizing medium. The common set of six elementary polarization properties provided by these two decompositions is generally different from that obtained from the various product decompositions summarized by the G-polar decomposition whereby the depolarization phenomenon is treated as being concentrated, and not uniformly distributed, within the medium. However, if the medium is weakly depolarizing, the two sets of elementary properties coincide to the first order in the depolarization and tend to the set of properties of the nondepolarizing estimate of the measured Mueller matrix obtained from its Cloude sum decomposition.     

Physical bounds to the entropy-depolarization relation in random light scattering

We present a theoretical study of multimode scattering of light by optically random media, using the Mueller-Stokes formalism which permits us to encode all the polarization properties of the scattering medium in a real 4 x 4 matrix. From this matrix two relevant parameters can be extracted: the depolarizing power D(M) and the polarization entropy E(M) of the scattering medium. By studying the relation between E(M) and D(M), we find that all scattering media must satisfy some universal constraints. These constraints apply to both classical and quantum scattering processes. The results obtained here may be especially relevant for quantum communication applications, where depolarization is synonymous with decoherence.     

Depolarizing differential Mueller matrices

The evolution of a polarized beam can be described by the differential formulation of Mueller calculus. The nondepolarizing differential Mueller matrices are well known. However, they only account for 7 out of the 16 independent parameters that are necessary to model a general anisotropic depolarizing medium. In this work we present the nine differential Mueller matrices for general depolarizing media, highlighting the physical implications of each of them. Group theory is applied to establish the relationship between the differential matrix and the set of transformation generators in the Minkowski space, of which Lorentz generators constitute a particular subgroup.     

Decomposition algorithm of an experimental Mueller matrix

This study deals with the interpretation of experimental Mueller matrices. The understanding of such a matrix is not straightforward in the case, in particular, of a strongly depolarizing medium, which is therefore disturbed and where relevant pieces of information are often distributed among its various elements. As a result, information data need to be extracted by a decomposition of any Mueller matrix into simple elements to uncouple the existing polarimetric effects. This led us to develop an algorithm in order to characterize any depolarizing, or not, polarimetric system. In addition to differentiating the experimental noise from the intrinsic depolarization of the optical system under study, this algorithm proved to: (i) separate depolarization from birefringence and dichroism and (ii) characterize the isotropic or anisotropic nature of the depolarization. At last, this algorithm was validated through the study of several optical systems with different polarimetric properties.     

Mueller matrix differential decomposition

We present a Mueller matrix decomposition based on the differential formulation of the Mueller calculus. The differential Mueller matrix is obtained from the macroscopic matrix through an eigenanalysis. It is subsequently resolved into the complete set of 16 differential matrices that correspond to the basic types of optical behavior for depolarizing anisotropic media. The method is successfully applied to the polarimetric analysis of several samples. The differential parameters enable one to perform an exhaustive characterization of anisotropy and depolarization. This decomposition is particularly appropriate for studying media in which several polarization effects take place simultaneously.     

Coupling effects between dichroism and birefringence of anisotropic media

The basic polarization properties of media are their dichroism and birefringence. In this work we report the possible consequences of the coupling effects between dichroism and birefringence of anisotropic media. Our analysis is based on a solution of the differential equation of the Stokes four-dimensional vector. It is shown that there exist three types of coupling effects between the components of the dichroism vector and birefringence vector of the medium. The conditions under which the polarization properties of a continuous medium can be calculated are identified. These results are helpful for any study involved an interpretation of the measured Mueller matrix of continuous anisotropic medium.     

Polarization of the light output from a weakly birefringent solid state laser

The output from a zero-degree ruby laser is shown to be fully elliptically polarized. Using a matrix formalism the eigenmodes of a Perot-Fabry cavity containing a partial polarizer and a weakly anisotropic medium are shown to be elliptically polarized.     

广义传播矩阵法分析分层各向异性材料对电磁波的反射与透射

在实验室坐标系下由Maxwell旋度方程出发构造了横向场的状态矢量和耦合矩阵,讨论了各 向异性介质中的特征波.通过引入横向场的传播矩阵,进而得到分层各向异性介质的反射系数和透射系数的解析表达式.该式可以适用于一般情况,包括分层单轴各向异性材料和回旋介质,以及半空间各向异性介质的反射和透射问题. 关键词： 广义传播矩阵 各向异性介质 反射与透射     

Theory of electromagnetic wave propagation in superlattices with optically anisotropic layers

A formalism is developed to find the photon dispersion relations in superlattice systems having layers with low optical symmetry or having magnetic layers. This formalism is an exact solution of the first order Maxwell's equations including all the information for the anisotropic optical response tensors and including the coupling of the TE and TM modes. Based on a 4×4 matrix approach for solving complicated reflection and transmission problems in stratified anisotropic media and employing a plane wave expansion of the field components to take into account the periodicity of the superlattices, the photon dispersion relation can be obtained numerically with a simple algorithm. This result is useful in predicting the absence of certain electromagnetic modes along the superlattice axis, and in identifying observed resonances with a particular excitations of the system.     

Generalized ellipsometry and the 4 × 4 matrix formalism

The 4 × 4 matrix formalism described by Berreman and others provides a method of determining the reflection and transmission properties of general stratified anisotropic materials. This formalism, when combined with the work of Azzam and Bashara and others on generalized ellipsometry, can be used to predict the extinction settings of a nulling ellipsometer for reflection of light from virtually any type of film covered surface provided that the surface is flat and that any films are uniform. In the present work the 4 × 4 matrix formalism is reviewed and combined with the equations necessary to predict the null settings of an ellipsometer. Examples of the application of these calculations to an optically active surface and a biaxial surface are also presented.     

cw Injection phase locking in homogeneously broadened media

A theory of cw injection phase locking in homogeneously broadened media is investigated using density matrix formalism to derive the interactions of three coherent fields with a two levels system. This powerful formalism leads to analytical expressions of the complex gain for each wave propagating inside the amplifier medium. Studies of the minimum signal intensity for single-frequency operation and power output are related.     

Generalization of the electromagnetic spinor formalism to anisotropic media

We generalize to magnetically isotropic but electrically anisotropic media the spinor formalism previously developed for isotropic media.     

Lekhnitskii’s formalism of one-dimensional quasicrystals and its application

By generalizing the complex potential approach developed by Lekhnitskii, plane problems of one-dimensional quasicrystals are solved first by using an octet formalism for which there are four pairs of complex roots. The approach uses a representation of stresses and proceeds by integration of the expressions for deformations and application of the anisotropic constitutive law and the compatibility of displacements. To illustrate its utility, the generalized Lekhnitskii??s formalism is used to analyse the coupled phonon and phason fields in an infinite quasicrystal medium containing an elliptic rigid inclusion.     

Product decompositions of depolarizing Mueller matrices with negative determinants

We show that the product decomposition of a depolarizing Mueller matrix (S.-Y. Lu, R.A. Chipman, J. Opt. Soc. Am. A 13 (1996) 1106) as well as the recently proposed reverse decomposition (R. Ossikovski, A. De Martino, Opt. Lett. 32 (2007) 689) need to be extended in order to account for Mueller matrices with negative determinants. The necessity of such an extension of the formalism is illustrated on experimentally determined Mueller matrices. The procedure of the modified decomposition formalism is explicitly described.     

Thermal shield effect with uniaxial crystals

A model describing radiative transfers inside uniaxial anisotropic media is presented. The transport equations for each electromagnetic mode supported by these media are derived in the limit of geometrical optics and an analytical solution is obtained from a ray tracing method. The temperature field inside such a medium illuminated on both sides by a blackbody radiation is calculated and compared to the temperature field of an isotropic medium submitted to the same conditions. We show that the temperature field in the anisotropic medium is drastically smaller than its counterpart, even for weak anisotropy.     

Electron spin polarization in a rotating triplet

The triplet model of electron spin polarization in fluid media is evaluated. The model consists of an initial singlet molecule rotating in a static, externally applied magnetic field. Intersystem crossing into different zero-field states is represented by a rate matrix diagonal in the molecular frame, and this matrix is expressed as an effective spin operator. The triplet rotates, and the motion affects the polarization in the laboratory frame, and also causes spin relaxation in the triplet manifold. The triplet is chemically quenched, and the polarization appears in the doublet fragments. The model is treated in a density matrix formalism and on the basis of anisotropic rotational diffusion of the triplet molecule. Explicit expressions are obtained in terms of the molecular parameters, the various rate constants, and the rotational correlation time.     

A density matrix approach to the Goldanskii-Karyagin effect

A density matrix formalism has been introduced to describe the perturbation of the Mössbauer line intensities caused by the anisotropic recoilless fraction in random absorbers. General properties of the matrix elements are discussed and relationships between thermal tensors and density matrices are investigated with the attention focused on the possibility to extract as much information about the thermal tensors as possible from the observed line intensities. It is shown, that quartic (anharmonic) anisotropy may be observable in quadrupolarly dominated transitions under favourable conditions.     

Optics of anisotropic nanostructures

The analytical formalism of Rokushima and Yamakita [J. Opt. Soc. Am. 73, 901–908 (1983)] treating the Fraunhofer diffraction in planar multilayered anisotropic gratings proved to be a useful introduction to new fundamental and practical situations encountered in laterally structured periodic (both isotropic and anisotropic) multilayer media. These are employed in the spectroscopic ellipsometry for modeling surface roughness and in-depth profiles, as well as in the design of various frequency-selective elements including photonic crystals. The subject forms the basis for the solution of inverse problems in scatterometry of periodic nanostructures including magnetic and magneto-optic recording media. It has no principal limitations as for the frequencies and period to radiation wavelength ratios and may include matter wave diffraction. The aim of the paper is to make this formalism easily accessible to a broader community of students and non-specialists. Many aspects of traditional electromagnetic optics are covered as special cases from a modern and more general point of view, e.g., plane wave propagation in isotropic media, reflection and refraction at interfaces, Fabry-Perot resonator, optics of thin films and multilayers, slab dielectric waveguides, crystal optics, acousto-, electro-, and magneto-optics, diffraction gratings, etc. The formalism is illustrated on a model simulating the diffraction on a ferromagnetic wire grating.     

The beam propagation method: an analysis of its applicability

Simple quantitative conditions for the applicability of the beam propagation method (BPM) in isotropic and anisotropic media are given. These conditions are derived using the operator formalism employed in the BPM in its conventional formulation. The basic limitations of the BPM are highlighted at the same time.