Differential matrix formalism for depolarizing anisotropic media

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.     

Forward and reverse product decompositions of depolarizing Mueller matrices

Because of the noncommutativity of the matrix product, the three factors into which a depolarizing Mueller matrix is decomposed, i.e., the diattenuator, the retarder, and the depolarizer, form six possible products grouped into two families, as already pointed out [J. Opt. Soc. Am. A13, 1106 (1996); Opt. Lett.29, 2234 (2004)]. We show that, apart from the generalized polar decomposition generating the first family of products, there exists a dual decomposition belonging to the second family. The mathematical procedure for this dual decomposition is given, and the symmetry existing between the two decompositions is pointed out. The choice of the most appropriate decomposition for a given practical optical arrangement is likewise discussed and illustrated by simple examples.     

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.     

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.     

Realizable free-electron lasers

We analyze the general class of constant period free-electron lasers (FELs) based on single-pass linear accelerator technology. The emittance and energy spread of the electron beam used to drive an FEL must be chosen to match the acceptance of the FEL wiggler. This acceptance determines the attainable current, and the current determines the gain and power output. For an optimized system in which the optical mode size in the interaction region is minimized, the gain is found to be independent of the laser length, while the efficiency and power output scale as the inverse and inverse cube of the length. Very high power output and good efficiencies are predicted.Work supported by the Office of Naval Research     

The transition operator for depolarizing collisions

The transition operator accounting for changes of the Zeeman sublevels of a¹ P-state or closely spaced² P-states has been derived using the classical-path approximation. In a first order approach to the problem thep-state atom is assumed to enter the range of a foreign atom non-adiabatically fast until reaching the point of the closest distance. There it is assumed to stop for the entire collision time. During this time the molecular σ and π states suffer phase-shifts due to the interaction with the molecular electric field. Subsequently thep-state atom leaves the range of the foreign atom again non-adiabatically fast. TheT-operator hence derived gives rise to the so-calledm _j-selection rule. In a better approach thep-state atom is assumed to stop twice when passing the range of the foreign atom. From this approximation additional terms to theT-operator arise which characteristically account for ‘molecular coupling’ phenomena during the collision. Consequently, these terms violate the afore-mentionedm _j-selection rule.     

Realizable high-order finite-volume schemes for quadrature-based moment methods

Dilute gas–particle flows can be described by a kinetic equation containing terms for spatial transport, gravity, fluid drag and particle–particle collisions. However, direct numerical solution of kinetic equations is often infeasible because of the large number of independent variables. An alternative is to reformulate the problem in terms of the moments of the velocity distribution. Recently, a quadrature-based moment method was derived for approximating solutions to kinetic equations. The success of the new method is based on a moment-inversion algorithm that is used to calculate non-negative weights and abscissas from the moments. The moment-inversion algorithm does not work if the moments are non-realizable, which might lead to negative weights. It has been recently shown [14] that realizability is guaranteed only with the 1st-order finite-volume scheme that has an inherent problem of excessive numerical diffusion. The use of high-order finite-volume schemes may lead to non-realizable moments. In the present work, realizability of the finite-volume schemes in both space and time is discussed for the 1st time. A generalized idea for developing realizable high-order finite-volume schemes for quadrature-based moment methods is presented. These finite-volume schemes give remarkable improvement in the solutions for a certain class of problems. It is also shown that the standard Runge–Kutta time-integration schemes do not guarantee realizability. However, realizability can be guaranteed if strong stability-preserving (SSP) Runge–Kutta schemes are used. Numerical results are presented on both Cartesian and triangular meshes.     

Solid-state active media based on dye-activated epoxypolymer matrices

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 50, No. 2, pp. 210–216, February, 1989.     

Realizable planar gradient-index solar lenses

The design of single element planar hemispherical gradient-index solar lenses that can accommodate the constraints of realistic materials and fabrication techniques are presented, and simulated with an extended and polychromatic solar source for concentrator photovoltaics at flux concentration values exceeding 1000 suns. The planar hemispherical far-field lens is created from a near-field unit magnification spherical gradient-index design, and illustrated with an f/1.40 square solar lens that allows lossless packing within a concentrator module.     

Coherence and polarization properties in speckle of totally depolarized light scattered by totally depolarizing media

When a totally unpolarized light is scattered by a medium that spatially totally depolarizes incident polarized light, the scattered field presents an increase of the order described by the temporal degree of polarization. We analyze the behavior of some polarization and coherence properties in such a physical situation.     

Measurements of diffuse backscattering Mueller matrices of turbid media

We report on the development of a method that records spatially dependent intensity patterns of polarized light that arise from illuminating a turbid media with a polarized laser beam and being diffusely backscattered. Our technique employs polarized light from a He-Ne laser () which is focused onto the surface of the scattering medium. A surface area of approximately 2×2 cm centered on the light input point is imaged through polarization analysis optics onto a CCD camera. The Mueller matrix is reconstructed by 49 intensity measurements with various orientations of polarizer and analyzer. The measured Mueller matrix of polystyrene spheres was compared with the theory result of incoherent scattering of light by spheres. The experimental and theory results are in excellent agreement. It appears that the azimuthal patterns of the Mueller matrix are determined by the symmetry of the turbid media.     

Circular differential double diffraction in chiral media

In an optically active liquid the diffraction angle depends on the circular polarization state of the incident light beam. We report the observation of circular differential diffraction in an isotropic chiral medium, and we demonstrate that double diffraction is an alternate means to determine the handedness (enantiomeric excess) of a solution.     

Off-specular neutron reflection from magnetic media with nondiagonal reflectivity matrices

The reflection of neutrons from magnetic substances is described using a reflection matrix including (in general) the off-diagonal matrix elements responsible for neutron spin reversal. In an external field the spin reversal is accompanied by changes in the neutron kinetic energy and, as a result, the reflection angle. An experiment to observe this new effect is described and the results are reported. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 12, 900–905 (25 June 1996) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Surface impedance matrices to model the propagation in multilayered media

The surface impedance matrices in stratified plates made of fluid layers and/or anisotropic absorbing solid layers link the particle velocity field to the stress field at any interface. A surface impedance matrix represents the impedance at a given interface of all the layers located between that interface and one boundary of the medium. For each interface, there are two surface impedance matrices, each one corresponding to one boundary. This notion simplifies the computations of the modal solutions. The number of elements in the matrices involved in the computations is divided by a factor of four in comparison to usual matrix methods. This paper describes the method and presents examples to illustrate its interests and its efficiency where other techniques fail, for instance in the case of modes possessing energy in layers embedded in the structure.     

Derivation of asymptotical formulas for resolution of systems of differential equations with symmetrical matrices

Abstract

Asymptotic formulae for resolution of L-diagonal systems of ordinary differential equations with symmetrical matrices are derived.     

可实现奇数通道滤波功能的光量子阱透射谱

针对光子晶体(AB)_m(CD)_n(BA)_m模型,选择适当的结构参数,通过传输矩阵法对其透射谱进行计算模拟发现,在归一化中心频率0.5(ωa/2πc)处,当光子晶体(CD)_n的导带处于光子晶体(AB)_m(BA)_m的禁带中,且两者均以中心频率处为对称中心时,构成镜像对称的光子晶体量子阱结构。在光量子阱透射谱的中心频率处及对称的两侧,分布着具有规律的奇数局域共振峰,出现明显的量子化效应,透射峰数目和位置都可以通过光子晶体(CD)_n的重复周期数n来调节,这一现象可用于设计可调性奇数通道滤波器。     

Local Statistics of Realizable Vertex Models

We study planar “vertex” models, which are probability measures on edge subsets of a planar graph, satisfying certain constraints at each vertex, examples including the dimer model, and 1-2 model, which we will define. We express the local statistics of a large class of vertex models on a finite hexagonal lattice as a linear combination of the local statistics of dimers on the corresponding Fisher graph, with the help of a generalized holographic algorithm. Using an n × n torus to approximate the periodic infinite graph, we give an explicit integral formula for the free energy and local statistics for configurations of the vertex model on an infinite bi-periodic graph. As an example, we simulate the 1-2 model by the technique of Glauber dynamics.     

Physically Realizable Broadband Acoustic Metamaterials with Anisotropic Density

Transformation acoustics are concentrated for the purpose of designing novel acoustic devices to tailor acoustic waves to achieve desirable characteristics. However, these devices require fluid or fluid-like materials with an anisotropic density that generally does not exist in nature. Therefore, we introduce pentamode metamaterials into an alternating multilayer isotropic medium model to build fluid-like metamaterials with an anisotropic density. A 2D acoustic bending based on transformation acoustics is established and investigated to verify our method. This idea provides a method to design broadband and physically realizable acoustic metamaterials with an anisotropic density and is meaningful for the design of acoustic metamaterials.