Depolarization by aerosols: Entropy of the Amsterdam light scattering database

In this paper we apply an entropy analysis to measured scattering matrices from the Amsterdam light scattering database. We select examples of mineral aerosols from the database and use them to demonstrate differences in polarization behavior between the particle clouds using a new coherency matrix formulation. These differences are further investigated by analyzing the polarized component of the matrices via two new eigenvector parameters, which can be mapped conveniently onto the surface of a sphere, analogous to the Poincaré sphere used for wave states. We conclude by considering the potential for discriminating different aerosols on the basis of their entropy/eigenvector signatures by solving the contrast optimization problem for clouds with different scattering matrices by using a novel generalized coherency eigenvalue formulation.     

Cutoffs and shadows in classical scattering of atoms from surfaces

A commonly used model for the scattering of atoms from crystalline surfaces is that of a classical hard sphere interacting with a hard, corrugated surface. This model is simple enough to permit the study of the effect on the scattering of variation of parameters of the model. We examine here how changes in the amplitude and symmetry of the corrugations, the size of the sphere, and the depth of an attractive well near the surface modify the scattering. We show, in particular, how edge effects due to shadowing of parts of the surface and second hits by the sphere distort the classical rainbow structure. We show the results as topological and intensity plots for special cases. The edge effects give new information on the structure of the surface. For suitable real systems, experimental measurement of the angular and energy dependence of the fraction of the scattering that is elastic may show some of the features described.     

Transformation matrices for the Mueller-Jones formalism

The Mueller-Jones (MJ) or pure Mueller matrix formulation has been reported by using two different matrix transformations in a condensed representation. The possibility to find other transformation matrices is explored. A complete set of unitary operators (R) is found to be closely related with the MJ matrices and with the evolution of pure states on the Poincaré sphere surface. We propose an alternative deduction for the condensed representation of the MJ matrices, obtained by using the Kronecker product operation and use of R unitary matrices as a tool to combine different Mueller matrices and changes of polarized states on the Poincarè sphere surface. Finally, it is shown explicitly that the columns of the transformation matrices are the eigenvectors of the MJ matrix associated to a non-depolarizing optical system and a corollary is established as a criterion to differentiate a Mueller matrix from an MJ matrix.     

On Factorization of Coupled Channel Scattering S Matrices

We investigate the problem on how to factorize a coupled channel scattering S matrix into a product of simple S matrices. Simple S matrix solntions are found, respecting unitarity, analyticity and being real analytic. The phase shift and its physical meaning produced by these simple S matrices are discussed.     

Light scattering by small feldspar particles simulated using the Gaussian random sphere geometry

The single-scattering properties of Gaussian random spheres are calculated using the discrete dipole approximation. The ensemble of model particles is assumed to be representative for a feldspar dust sample that is characteristic for weakly absorbing irregularly shaped mineral aerosol. The morphology of Gaussian random spheres is modeled based on a statistical shape analysis using microscope images of the dust sample. The size distribution of the dust sample is based on a particle sizing experiment. The refractive index of feldspar is estimated using literature values. All input parameters used in the light scattering simulations are thus obtained in an objective way based on the true properties of the mineral sample. The orientation-averaged and ensemble-averaged scattering matrices and cross sections of the Gaussian random spheres are compared with light scattering simulations using spheroidal shape models which have been shown to be applicable to the feldspar sample. The Gaussian random sphere model and the spheroidal shape model are assessed using the measured scattering matrix of the feldspar dust sample as a reference. Generally, the spheroidal model with strongly elongated prolate and strongly flattened oblate shapes agrees better with the measurement than the Gaussian random sphere model. In contrast, some features that are characteristic for light scattering by truly irregular mineral dust particles are rendered best by the Gaussian random sphere model; these features include the flat shape of the phase function and a minimum in the scattering matrix element F₂₂/F₁₁ as a function of the scattering angle.     

Determining Transport Properties of Complex Multiterminal Systems: S‐Matrix of General Tight‐Binding Periodic Leads

Calculation of the scattering matrix (S‐matrix) of a system allows direct determination of its transport properties. Within the scattering theory, S‐matrices relate amplitudes of incoming and outgoing waves in semi‐infinite leads attached to a scattering region. Recently, an assembly method to calculate S‐matrices of arbitrary tight‐binding systems connected to atomic chains has been proposed, were the S‐matrices of subsystems are used to obtain S‐matrix of the total system. In this paper, a new efficient method to obtain S‐matrices of general periodic leads is established, which can be used in the mentioned assembly method, allowing to address coherent quantum transport of arbitrary multiterminal systems with complex geometries trough Landauer‐Büttiker formalism. In addition, a new method to determine extended‐state band structures of general infinite periodic wires is presented, which exploits properties of the S‐matrix. Finally, these methods are used to obtain band structure of graphene arm‐chair and zig‐zag nanoribbons and transmission functions in three terminal Z‐shaped graphene nanoribbon structures.     

Mueller Matrix Analysis of PDL Components

A detailed Mueller-Stokes analysis of an arbitrary elliptical dichroic polarizer is presented. Explicit expressions for the Jones matrix, the Stokes parameters, and the Mueller matrix for a distributed and localized dichroic polarizer acting as a polarization-dependent loss (PDL) element are derived. Application to wavelength-dependent PDL elements is discussed. The Poincare sphere representation and the application of the Mueller matrices for the study of randomly oriented concatenated PDL elements and PDL vector measurement are addressed.     

On the separability of relativistic electron propagators

In this contribution we examine the separability of relativistic electron propagators. Both, magnetic and non-magnetic systems are studied on the basis of the Kohn-Sham-Dirac equation. We find a Dirac-Green's function in excellent agreement with recent calculations utilizing the left and right-handed solutions to the Dirac equation. Starting from these Dirac-Green's functions we re-derive a rotation matrix formalism that was shown to result in separable scattering matrices in the non-relativistic case. It turns out, that spin-dependent scattering matrices can be formulated which are closely related to their non-relativistic counterparts. These matrices incorporate spin-flip and non spin-flip processes on an equal footing, but are irreducible to sums over composite rotation matrices. The latter result is a major drawback for numerical applications since electron scattering in terms of composite rotations had drawn a lot of attention recently. Received 1st July 1997     

Exact solution for the scattering and absorption properties of sphere clusters on a plane surface

A formulation and computational scheme are presented for predicting the scattering and absorption cross-sections, and the scattering matrix elements, of clusters of non-intersecting spheres that are lying on or above an infinite plane surface and exposed to plane-wave radiation. The formulation provides an exact solution to Maxwell's equations and the associated boundary conditions on the spheres and the plane surface, and is applicable for arbitrary refractive indices for the spheres and the surface. A simplified strategy is presented for the calculation of the surface reflection matrix, which transforms the reflected scattered field from one sphere into a regular vector spherical harmonic expansion centered about another sphere. The calculation results are presented for the clusters of one, two, and four polystyrene spheres, with size parameters of one and 10, lying on a silicon substrate, and are compared with the predictions from the normal incidence approximation (NIA) in which the reflectance of the surface is assumed constant at the normal incidence value. The results show that the accuracy of the NIA is highly dependent on the extent of the sphere cluster, the angle of incidence, and the particular quantity (cross-sections, scattering matrix elements) under examination.     

Calculations of Backscattering Mueller Matrices for Turbid Media with a Sphere Queue Model

A sphere queue model is introduced to calculate Mueller matrices of turbid media. Combined with the single scattering approximation, the backscattering Mueller matrices of turbid media can be computed rapidly by Mie theory. The numerical results agree with the azimuthal dependences of backscattering Mueller matrices＇ patterns from turbid media, which indicates that the major contribution to the Mueller matrices＇ patterns comes from the single scattering of the sphere queue, and the multiple scattering considered as a high-order correction does not change the patterns. The numerical analysis reveals that the contrast of Mueller matrices＇ patterns will decrease with increase of the concentration of media and the distance from the incident point.     

原子受激态的Stokes参数分析

根据密度矩阵理论,导出了受激原子态P态密度矩阵元和P态退激辐射的光子密度矩阵元的Stokes参数,它们之间存在一种非常简单直接的关系,说明在电子-光子符合散射实验中,通过测量光子的Stokes参数,就可以描述受激P态电荷云分布和散射过程的动力学。According to the density matrix theory, the density matrix of photon emitted from excited atom P state and of P state were introdued in this paper. There were a simple direct relation between the two density matrices, which shows that the electron cloud shape of excited atomic state and scattering dynamics can be described through the observable Stokes parameters of photon in electron-photon coincidence experiment.     

Scattering matrices of Lamb waves at irregular surface and void defects

Time-harmonic solution of Lamb wave scattering in a plane-strain waveguide with irregular thickness is investigated based on stair-step discretization and stepwise mode matching. The transfer relations of the transmission matrices and reflection matrices are derived in both directions of the waveguide. With these, an explicit expression of the scattering matrix is derived. When the scattering region of an inner irregular defect is geometrically divided into several parts composed of sub-waveguides with variable thicknesses and void regions with vertical free edges corresponding to the plate surfaces, the scattering matrix of the whole region could then be derived by modal matching along the artificial boundaries, as explicit functions of all the scattering matrices of the sub-waveguides and reflection matrices of the free edges. The effectiveness of the formulation is examined by numerical examples; the calculated scattering coefficients are in good accordance with those obtained from numerical simulation models.     

Effect of detailed cell structure on light scattering distribution: FDTD study of a B-cell with 3D structure constructed from confocal images

Human B-cells play an important role in the immune system, and because of their relatively simple structures with a nearly spherically shaped cell membrane and a large nucleus, they provide a good case to study on how the details of cell structure affect light scattering properties. A finite-difference-time-domain (FDTD) method is used to calculate angle-resolved light scattering distributions from a B-cell. Published FDTD simulations to date have used a smooth shape with a certain degree of symmetry to approximate the actual cell shape. In contrast, for this work, the shapes of the cell and its nucleus were determined from confocal microscopy measurements. An automated procedure was developed to construct a realistic three-dimensional structure of a B-cell from a stack of two-dimensional confocal images. The angle-resolved Mueller matrix elements of the B-cell were calculated and averaged for 30 different angles of incidence using a parallel FDTD code. These results were compared with those from a homogeneous and a coated sphere. Scattering from the two sphere models and the B-cell were very similar for scattering angles less than 5°, and the coated sphere and B-cell agreed well for scattering angles up to 20°. However, at larger angles, the scattering from the B-cell was a much smoother function of angle than scattering from either sphere model. Additionally, the homogeneous sphere results were the most similar to the B-cell results for most angles between 120° and 150°, and at angles greater than 150°, the B-cell scattered more light than either of the spheres. These results yield strong evidence that accurate modeling of light scattering by biological cells requires not only the high accuracy of the employed numerical method but the realistic cellular structure as input information as well.     

Study of the sensitivity of size-averaged scattering matrix elements of nonspherical particles to changes in shape, porosity and refractive index

Studies of the physical parameters that influence the single scattering properties of a size distribution of small particles in random orientation are fundamental in understanding the origin of the observed dependence of the scattering matrix elements on the scattering angle. We present results of extensive calculations of the single scattering matrices of small nonspherical particles performed by a computational model based on the Discrete-Dipole Approximation. We have particularly studied the sensitivity of the size-averaged scattering properties at visible wavelengths of nonspherical, randomly oriented absorbing particles considering changes in shape, porosity and refractive index. These studies have importance regarding the inversion of physical properties of small particles as measured in the laboratory and the dust properties in various astrophysical and atmospherical environments. We have found that size distributions of randomly oriented irregular particles of different shape, including large aspect ratio particles, show similar scattering matrix elements as a function of the scattering angle, in contrast with the pattern found for regularly shaped particles of varying axis ratios, for which the scattering matrix elements as a function of the scattering angle show much larger differences among them. Regarding porosity, we have found a very different pattern in the scattering matrix elements for an ensemble of compact and porous particles. In particular, the linear polarization for incident unpolarized light produced by compact and absorbing particles of large size parameter tend to mimic the pattern found for large absorbing spheres. For porous particles, however, the linear polarization for incident unpolarized light tends to decrease as the size of the particle grows, with the maximum being displaced towards smaller and smaller scattering angles.     

Atomic-force microscopy and spectral characteristics of hybrid nanosystems for photodynamic therapy in oncology

The structural-morphological parameters of hybrid nanosystems, which are promising as photosensitizers (PS) for photodynamic therapy (PDT), are comparatively studied by atomic force microscopy (AFM), ultraviolet (UV) spectroscopy, photoluminescence (PL) and dynamic light scattering. The nanosystems are nanoparticles of zinc selenide (ZnSe) prepared using the hydrothermal synthesis method, stabilized by various polymer matrices: bovine serum albumin (BSA), polymethacrylic acid (PMAA) and, the second generation PS, photoditazin (PD). Comparison of the nanostructure size characteristics in ZnSe nanoparticles/polymer + PD systems (in a solution by means of the molecular optics and PL, and on a surface of a silicon wafer in air by means of AFM) at the same concentration of reagents in the reaction mixture shows that nanocluster sizes in the solution are two times larger than those in a thin film prepared on the substrate surface. When the order of the BSA and PD introduction into the system is changed, the nanosystem morphology changes strongly (nanocluster sizes and shape), which is due to the competition of the polymer stabilizers during complex formation with ZnSe nanoparticles. Analysis of the photoluminescence excitation and emission spectra of PD and the triple-system aqueous solutions shows that the ZnSe/BSA nanostructures do not suppress PD photoluminescence in the triple system ZnSe/BSA + PD, i.e., do not affect their ability to generate active forms of oxygen and make them promising as the basis for the creation of photosensitive compounds for PDT in oncology.     

Polarimetric scattering from a two-dimensional improved sea fractal surface

This paper studies the influence of wind parameters and fractal dimension from an improved two-dimensional sea fractal surface on the polarimetric scattering by using facet integration.A two-dimensional improved sea surface simulated is discretized into three matrices of sea surface facets including a height matrix and two slope matrices on orthogonal directions.Based on the Kirchhoff approximation,the polarimetric scattered field is derived in the Cartesian coordinate system by integration of three matrices mentioned above.Finally,the fully polarised radar cross section is numerically simulated and the dependence of the polarimetric scattering on the sea fractal surface,such as the wind speed,the wind direction,as well as the fractal dimension,is discussed in detail.     

Influence of the order of the constituent basis matrices on the Mueller matrix decomposition-derived polarization parameters in complex turbid media such as biological tissues

The influence of the multiplication order of the constituent basis matrices on the Mueller matrix decomposition-derived polarization parameters in complex tissue-like turbid media exhibiting simultaneous scattering and polarization effects are investigated. A polarization sensitive Monte Carlo (MC) simulation model was used to generate Mueller matrices from turbid media exhibiting simultaneous linear birefringence, optical activity and multiple scattering effects. Mueller matrix decomposition was performed with different selected multiplication orders of the constituent basis matrices, which were further analyzed to derive quantitative individual polarization medium properties. The results show that for turbid medium having weak diattenuation (differential attenuation of two orthogonal polarization states), the decomposition-derived polarization parameters are independent of the multiplication order. Importantly, the values for the extracted polarization parameters were found to be in excellent agreement with the controlled inputs, showing self-consistency in inverse decomposition analysis and successful decoupling of the individual polarization effects. These results were corroborated further by selected experimental results from phantoms having optical (scattering and polarization) properties similar to those used in the MC model. Results from tissue polarimetry confirm that the magnitude of diattenuation is generally lower compared to other polarization effects, so that the demonstrated self-consistency of the decomposition formalism with respect to the potential ambiguity of ordering of the constituent matrices should hold in biological applications.     

Solving the hypersingular boundary integral equation in three-dimensional acoustics using a regularization relationship

Regularization of the hypersingular integral in the normal derivative of the conventional Helmholtz integral equation through a double surface integral method or regularization relationship has been studied. By introducing the new concept of discretized operator matrix, evaluation of the double surface integrals is reduced to calculate the product of two discretized operator matrices. Such a treatment greatly improves the computational efficiency. As the number of frequencies to be computed increases, the computational cost of solving the composite Helmholtz integral equation is comparable to that of solving the conventional Helmholtz integral equation. In this paper, the detailed formulation of the proposed regularization method is presented. The computational efficiency and accuracy of the regularization method are demonstrated for a general class of acoustic radiation and scattering problems. The radiation of a pulsating sphere, an oscillating sphere, and a rigid sphere insonified by a plane acoustic wave are solved using the new method with curvilinear quadrilateral isoparametric elements. It is found that the numerical results rapidly converge to the corresponding analytical solutions as finer meshes are applied.