Scattering Matrix Elements Research Articles

Polarization effects in 3D vectorial-induced current reconstructions

In tomography algorithms, the complex amplitude scattering matrix corresponds to the input parameter. When considering 3D targets, the scattering matrix now contains vectorial information. Thus, this scattering matrix might be calculated with various polarization projections. Moreover, when dealing with experimental data, we are almost every time faced with truncated data. We focus here on the impact of selecting parts of the amplitude scattering matrix elements versus others and in particular on the influence of the polarization choices on the imaging results. In order to better apprehend the physical content associated to each polarization term, the study is conducted with a simple vectorial-induced current reconstruction algorithm allowing reconstruction of qualitative maps of the scene. This algorithm is applied on scaled models of aggregates combined with experimental scattered fields acquired in the microwave frequency range.

Absorption and scattering by long and randomly oriented linear chains of spheres

This paper demonstrates that the scattering cross section per unit length of randomly oriented linear chains of optically soft spheres asymptotically converges toward those of randomly oriented and infinitely long cylinders with volume-equivalent diameter as the number of spheres increases. The critical number of spheres necessary to approximate the linear chains of spheres as infinitely long cylinders decreased rapidly as the size parameter of an individual sphere increased from 0.01 to 10. On the other hand, their absorption cross section per unit length was identical to that of an infinitely long volume-equivalent cylinder for any number of spheres. However, this approximation does not apply to the angle-dependent normalized Stokes scattering matrix element ratios.

Light transport in one-dimensional arrays of infinitesimal magnetoactive dielectric sheets: Theory and numerical simulations

We have provided a complete description of light propagation at an oblique angle of incidence in disordered one-dimensional (1D) ultrathin magnetophotonic crystals with an arbitrary number of sheets. We have shown that in the long-wavelength limit, when the parameter $\frac{d{\ensuremath{\epsilon}}_{L,R}}{\ensuremath{\lambda}}$ is much less than unity (${\ensuremath{\epsilon}}_{L,R}$ is the relative permittivity for left- and right-polarized light, $d$ is the thickness of the sheet, and $\ensuremath{\lambda}$ is the wavelength), the photon transport problem in a 1D magnetophotonic crystal is identical to Anderson's two-channel model. In our discussion we include mode conversion and derive exact and closed analytical expressions for all scattering matrix elements. We have calculated the Faraday and Kerr rotational angles for a periodic system. Our formulas predict correctly the main trends of magneto-optic effects in 1D systems. We also derived analytical expressions for photon localization lengths, in a weak disordered regime, for $s$ and $p$ modes and for circular polarized light. We demonstrate that the presence of coupling modes enhances ${\ensuremath{\xi}}_{s}$ and reduces ${\ensuremath{\xi}}_{p}$ with respect to the values ${\ensuremath{\xi}}_{s}(0)$ and ${\ensuremath{\xi}}_{p}(0)$ obtained when the coupling modes are absent. Presented analytical expressions for localization lengths are in good agreement with numerical calculations, exact up to order ${\ensuremath{\delta}}^{2}$ ($\ensuremath{\delta}$ being the disorder strength), and valid up to angles of incidence of $1.56$ rad.

Scattering and transport properties of tight-binding random networks

We study numerically scattering and transport statistical properties of tight-binding random networks characterized by the number of nodes N and the average connectivity α. We use a scattering approach to electronic transport and concentrate on the case of a small number of single-channel attached leads. We observe a smooth crossover from insulating to metallic behavior in the average scattering matrix elements <|S(mn)|(2)>, the conductance probability distribution w(T), the average conductance <T>, the shot noise power P, and the elastic enhancement factor F by varying α from small (α→0) to large (α→1) values. We also show that all these quantities are invariant for fixed ξ=αN. Moreover, we proposes a heuristic and universal relation between <|S(mn)|(2)>, <T>, and P and the disorder parameter ξ.

Distribution of Scattering Matrix Elements in Quantum Chaotic Scattering

Scattering is an important phenomenon which is observed in systems ranging from the micro- to macroscale. In the context of nuclear reaction theory, the Heidelberg approach was proposed and later demonstrated to be applicable to many chaotic scattering systems. To model the universal properties, stochasticity is introduced to the scattering matrix on the level of the Hamiltonian by using random matrices. A long-standing problem was the computation of the distribution of the off-diagonal scattering-matrix elements. We report here an exact solution to this problem and present analytical results for systems with preserved and with violated time-reversal invariance. Our derivation is based on a new variant of the supersymmetry method. We also validate our results with scattering data obtained from experiments with microwave billiards.

Electron scattering from gas phase cis-diamminedichloroplatinum(II): Quantum analysis of resonance dynamics

We present scattering calculations of electron collisions with the platinum-containing compound cis-diamminedichloroplatinum (CDDP), commonly known as cisplatin, between 0.5 eV and 6 eV, and the corresponding isolated Pt atom from 0.1 eV to 10 eV. We find evidence of resonances in e(-)-CDDP scattering, using an ab initio description of the target. We computed scattering matrix elements from equations incorporating exchange and polarization effects through the use of the static-exchange plus density functional correlation potential. Additionally, we made use of a purely local adiabatic model potential that allows Siegert eigenstates to be calculated, thereby allowing inspection of the possible resonant scattering wave functions. The total cross section for electron scattering from (5d(10)) (1)S Pt displays a large magnitude, monotonic decay from the initial collision energies, with no apparent resonance scattering features in any scattering symmetry. By contrast, the e(-)-CDDP scattering cross section shows a small feature near 3.8 eV, which results from a narrow, well localized resonance of b2 symmetry. These findings are then related to the possible electron-mediated mechanism of the action of CDDP on DNA replication as suggested by recent experiments.

Experimental and simulated scattering matrices of small calcite particles at 647 nm

We present measurements of the complete scattering matrix as a function of the scattering angle of a sample of calcite particles. The measurements are performed at 647nm in the scattering angle range from 3° to 177°. To facilitate the use of the experimental data we present a synthetic scattering matrix based on the measurements and defined in the full range from 0° to 180°. The scattering matrix of the calcite sample is modeled using the discrete-dipole approximation. Two sets of shapes, flake-like and rhomboid-like particles giving a total of 15 different targets are considered since both types of shapes have been found in our calcite sample. In our computations we use the measured size distribution of the calcite sample truncated at 1.2μm. We present a theoretical study of the impact of birefringence on the computed scattering matrix elements for both sets of shapes. Four different cases regarding the composition of the calcite particles are considered: two isotropic cases corresponding to the ordinary and extraordinary refractive index of calcite, respectively; one equivalent isotropic case analogous to internal mixing; and birefringence fully accounted for. Numerical simulations are compared with the experimental data. We find that birefringence has little impact on the calculated phase functions but it has a significant effect on the polarization-related elements of the scattering matrix. Moreover, we conclude that the shape of the targets (flakes or irregular rhomboids) has a much stronger effect on the computed scattering matrix elements than birefringence.

Generalized Lüscher formula in multichannel baryon-meson scattering

L\"uscher's formula relates the elastic scattering phase shifts to the two-particle energy levels in a finite cubic box. The original formula was obtained for elastic scattering of two massive spinless particles in the center of mass frame. In this paper, we consider the case for the scattering of a spin 1/2 particle with a spinless particle in multi-channel scattering. A generalized relation between the energy of two particle system and the scattering matrix elements is established. We first obtain this relation using quantum-mechanics in both center-of-mass frame and in a general moving frame. The result is then generalized to quantum field theory using methods outlined in Ref. \cite{Hansen:2012tf}. We verify that the results obtained using both methods are equivalent up to terms that are exponentially suppressed in the box size.

Using gate-modulated Raman scattering and electron-phonon interactions to probe single-layer graphene: A different approach to assign phonon combination modes

Gate-modulated and laser-dependent Raman spectroscopy have been widely used to study $q=0$ zone center phonon modes, their self-energy, and their coupling to electrons in graphene systems. In this work we use gate-modulated Raman of $q\ensuremath{\ne}0$ phonons as a technique to understand the nature of five second-order Raman combination modes observed in the frequency range of 1700--2300 cm${}^{\ensuremath{-}1}$ of single-layer graphene (SLG). Anomalous phonon self-energy renormalization phenomena are observed in all five combination modes within this intermediate frequency region, which can clearly be distinguished from one another. By combining the anomalous phonon renormalization effect with the double resonance Raman theory, which includes both phonon dispersion relations and angular dependence of the electron-phonon scattering matrix elements, and by comparing it to the experimentally obtained phonon dispersion, measured by using different laser excitation energies, we can assign each Raman peak to the proper phonon combination mode. This approach should also shed light on the understanding of more complex structures such as few-layer graphene (FLG) and its stacking orders as well as other two-dimensional (2D)-like materials.

Comparison of the performance of L-band polarimetric parameters for land cover classification

L-band fully polarimetric Synthetic Aperture Radar (SAR) data, acquired in April 2009 by the Japanese Advanced Land Observing Satellite over Tehran, were used to investigate the effect of various polarimetric descriptors on the accuracy of land cover classification. Particular attention was paid to evaluating the differences between polarimetric parameters in the image classification and understanding the type of information they contain. For this purpose, several polarimetric parameters were first derived from SAR complex analysis and target decomposition techniques including backscattering cross sections, ratios of scattering matrix elements, polarimetric coherencies, Pauli coefficients, Krogager coefficients, Freeman coefficients, Yamaguchi coefficients, H/A/Alpha parameters, and Eigenvalues of the coherency matrix. These parameters were then employed in Maximum Likelihood Classification (MLC), Minimum Distance Classification (MDC), and Parallelepiped classification for the land cover classification. The final accuracy assessment of the classification was performed using several statistical tests. This evaluation demonstrates that the performance and accuracy of the classification depend both on the selection of the polarimetric parameters and the type of classifier used. Polarimetric parameters extracted from target decomposition techniques in MLC produce the highest accuracies (a Kappa coefficient of greater than 90%) and the best discrimination of natural and man-made targets. Additionally, higher accuracies are generally obtained when the polarimetric parameters are derived from SAR complex analysis in a circular rather than linear basis. Thus, changing the polarization basis can significantly improve the result of classification.

T-matrix modeling of linear depolarization by morphologically complex soot and soot-containing aerosols

We use state-of-the-art public-domain Fortran codes based on the T-matrix method to calculate orientation and ensemble averaged scattering matrix elements for a variety of morphologically complex black carbon (BC) and BC-containing aerosol particles, with a special emphasis on the linear depolarization ratio (LDR). We explain theoretically the quasi-Rayleigh LDR peak at side-scattering angles typical of low-density soot fractals and conclude that the measurement of this feature enables one to evaluate the compactness state of BC clusters and trace the evolution of low-density fluffy fractals into densely packed aggregates. We show that small backscattering LDRs measured with ground-based, airborne, and spaceborne lidars for fresh smoke generally agree with the values predicted theoretically for fluffy BC fractals and densely packed near-spheroidal BC aggregates. To reproduce higher lidar LDRs observed for aged smoke, one needs alternative particle models such as shape mixtures of BC spheroids or cylinders.

Many-Channel Landauer-Like Conductance Formula in a Uniform Magnetic Field

For long time, it has been well recognized that transport in mesoscopic systems may relate to their scattering properties as it was originally proposed by Landauer [1, 2]. The single-channel conductance formula has been rst obtained heuristically as proportional to the ratio between transmission and re ection coe cients G = 2e 2 h T R [1]. Main attempts to derive this formula from linear-response theory (LRT) are known in the literature (see Ref. [3] and references therein). However, for long time, the generalization to a multichannel formula has been a great challenge for the physicists. The major di culty is that, in the LRT, the currentow in a sample is obtained as a response to an applied external perturbation inside the reservoirs in accordance to the Kubo viewpoint (KVP), whereas in the Landauer viewpoint (LVP) the current itself is considered as responsible for the induction of a position-dependent potential inside the sample. At this level, one has to note that it has been established heuristically that contacts between the reservoirs and the sample are at the origin of the di erence between the two points of view [4]. In recent works [5], a theory of transport that combines the LVP with the LRT and which does not consider the e ect of the contacts (called thereafter a self-consistent LRT) in order to calculate the relevant part of the density-operator for mesoscopic samples in the absence of an external magnetic eld, has been proposed. The obtained density-operator, necessary to evaluate all physical quantities, was used to derive a new and more plausible four-lead multichannel conductance formula that does not endure any of the inconsistencies cited in the literature for the other known formulae [3, 6]. This self-consistent LRT was recently extended to take into account the existence of a uniform magnetic eld [7, 8]. It has been shown that the density-operator may be written as a sum of two terms [7]: the rst represents the Kubo density-operator ρ [7 9] and the second denes the contribution of self-consistent e ects ρ [7, 8]: ρ = ρ + ρ. (1) Our aim in this work is the use of Eq. (1) to determine quantitatively the magnetoconductance of a four-lead mesoscopic measurement in terms of the scattering matrix elements whenever self-consistent e ects are relevant; that is, whenever the e ect of the contacts is neglected and the induced potential inside the sample is considered.

Electric field induced enhancement of multisubband electron mobility in strained GaAs/InGaAs coupled quantum well structures

We analyze the enhancement of multisubband electron mobility due to an external electric field in a pseudomorphic GaAs/InxGa1−xAs coupled double quantum well structure. An electric field, applied perpendicularly to the interface plane, changes the potential energy profile of the structure. This change alters the energy level, wave function as well as the occupation of a subband. By varying the field, the system can be transformed from double subband occupancy to single subband occupancy resulting in an enhancement of the mobility due to the suppression of the intersubband effects. We consider scatterings due to the ionized impurities, interface roughness and alloy disorder and study the variations in the intrasubband and intersubband scattering matrix elements as a function of the electric field. The novelty of our work is the analysis of the effect of structure parameters like well width, barrier width and doping concentration on the field dependent multisubband electron mobility. We show that a large enhancement in mobility can be achieved through application of an external electric field by suitably choosing the material parameters.

Scattering matrix of the boundary of a nonlocal metamaterial

We present a simple model of the interface between a local homogeneous medium and a potentially nonlocal metamaterial/photonic crystal. This model allows us to calculate the scattering matrix elements of the interface for a plane wave of light normally incident upon the interface from either direction. The resulting scattering matrix provides insight into the non-Maxwellian boundary conditions present at the interface between a homogeneous medium and a metamaterial/photonic crystal with strong spatial dispersion. We present the model mathematically. As an example, the model is used to calculate the scattering matrix of the interface between vacuum and a simple photonic crystal. Several tests of the calculated scattering matrix elements are presented. Finally, we used the results of the scattering model to postulate possible forms for the non-Maxwellian boundary conditions.

Effect of the orientation of the optic axis on simulated scattering matrix elements of small birefringent particles

We study how the orientation of the optic axis affects single-scattering properties for small, birefringent calcite particles simulated using DDSCAT 7.1.1. We consider two irregular model particles, a flake and a rhomboid, in either a (i) fixed or (ii) random orientation. Simulations are performed for three volume-equivalent radii of 0.1, 0.45, and 1.0 μm. For each target, we repeat the computations for three sets of orientations of the optic axis. When a fixed spatial orientation of the target is considered, the simulations are significantly affected by the orientation of the optic axis. However, the effect is considerably weaker when assuming the same targets in random spatial orientation.

Mie scattering by soft core-shell particles and its applications to ellipsometric light scattering

Through the use of Mie theory generalized to multiple spheres, the derivatives of the scattering matrix elements and ellipsometric scattering variables are found as a function of shell thickness and nonconcentricity for core-shell particles. In particular, for the case of a core-shell sphere system where the centers are not concentric, the derivatives are taken with respect to the line segment describing the distance between spherical centers. The derivatives of the scattering matrix elements can be used to calculate the changes in ellipsometric light scattering, allowing for sensitivity and precision in quantitative models of fluctuations in core-shell systems. Computed results giving model contrast for a variety of sizes and fluctuation modes are used to design and guide novel light-scattering experiments currently underway.

Identification of Terrain Cover Using the Optimum Polarimetric Classifier

A systematic approach for the identification of terrain media such as vegetation canopy, forest, and snow-covered fields is developed using the optimum polarimetric classifier. The covariance matrices for various terrain cover are computed from theoretical models of random medium by evaluating the scattering matrix elements. The optimal classification scheme makes use of a quadratic distance measure and is applied to classify a vegetation canopy consisting of both trees and grass. Experimentally measured data are used to validate the classification scheme. Analytical and Monte Carlo simulated classification errors using the fully polarimetric feature vector are compared with classification based on single features which include the phase difference between the VV and HH polarization returns. It is shown that the full polarimetric results are optimal and provide better classification performance than single feature measurements.

On the interpretation of gravitational corrections to gauge couplings

Several recent papers discuss gravitational corrections to gauge couplings that depend quadratically on the energy. In the framework of the background-field approach, these correspond in general to adding to the effective action terms quadratic in the field strength but with higher-order space–time derivatives. We observe that such terms can be removed by appropriate local field redefinitions, and do not contribute to physical scattering-matrix elements. We illustrate this observation in the context of open string theory, where the effective action includes, among other terms, the well-known Born–Infeld form of non-linear electrodynamics. We conclude that the quadratically energy-dependent gravitational corrections are not physical in the sense of contributing to the running of a physically-measurable gauge coupling, or of unifying couplings as in string theory.

Studies on the vibrational excitation differential cross sections of non-resonant e-N2 scattering using augmented polarization potentials

Distributed spherical Gaussian (DSG) correlation-polarization model potentials with higher-order terms and exact exchange effects in single-configuration Slater determinant are taken into account for low-energy vibrational excitation e-N2 scattering system. The integrodifferential coupled channel equations are solved using a combination of linear-algebraic and R-matrix-propagator algorithms. Analytic Born completion is used to calculate high-order scattering matrix elements in order to obtain convergent differential cross sections. The energy range is set to 4–15 eV which is not tested by the present theoretical method before. The overall agreement of theoretical results with the latest experiments emphasizes the importance of higher-order correlation-polarization potentials and rigorous exchange effects in vibrational excitation scattering.

Study of scattering and radiative properties of complex soot aggregates

The discrete dipole approximation (DDA) method is used to calculate the scattering matrix elements and optical cross-sections for a wide variety of complex soot aggregates in random orientation at a visible wavelength of 0.628 \mu m. The effects of the material composition and the size of the larger particle that is in touch with soot cluster on scattering and radiative properties of complex soot aggregates are analyzed. It is shown that the material composition and the size of the larger particle can strongly influence or even dominate the overall scattering and radiative properties of the aggregates.