Scattering Matrix Research Articles

On the Construction of Scattering Matrices for Irregular or Elongated Enclosures Using Green’s Representation Formula

On the Construction of Scattering Matrices for Irregular or Elongated Enclosures Using Green’s Representation Formula

The study of water wave scattering by series of submerged elastic scatterers

A submerged flexible breakwater can be used to control waves in shallow water as an advanced alternative to traditional rigid submerged structures. Submerged flexible breakwaters not only cost less to build than conventional submerged breakwaters but also allow ships and marine life to bypass them if they are deep enough. These marine structures decrease the intensity of the shock wave and prevent standing waves from forming. We present a solution for transmission/reflection using a series of submerged identical elastic scatterers. Scattering and transfer matrices will be used to compute the transmission and reflection coefficients for N-submerged elastic scatterers. The behavior of the transmission for different values of physical parameters such as submergence depth, length of the scatterer, the gap between two successive scatterers, stiffness of the scatterer, and the number of submerged elastic scatterers is given. In doing so, we can achieve the frequencies and the incident amplitudes at which these submerged elastic scatterers can be effectively used as breakwaters in water of finite depth. We have looked at the transmission and reflection behaviors for a range of physical parameter values, such as the submergence depth, the length of the scatterer, the spacing between successive scatterers, the stiffness of the elastic scatterer, and the number of scatterers over a wide frequency range. We have given a spectrum of frequencies for which, given certain values of physical parameters, we can achieve zero transmission. Furthermore, even at high frequencies, we have demonstrated an incidence amplitude range for which zero propagation of transmission is feasible.

Feasibility of Model-Independent Reconstruction of the Amplitudes of the pp Elastic Scattering Matrix at the SPASCHARM Facility at U-70

Feasibility of Model-Independent Reconstruction of the Amplitudes of the pp Elastic Scattering Matrix at the SPASCHARM Facility at U-70

Generalization of the Method of Scattering Matrices to Problems in Nonlinear Dispersion Media

Generalization of the Method of Scattering Matrices to Problems in Nonlinear Dispersion Media

Scattering matrices of particle ensembles analytically decomposed into pure Mueller matrices

Scattering matrices of particle ensembles are analytically decomposed into sums of pure Mueller matrices. The ensembles are assumed to have equal numbers of particles and their mirror particles, both in random orientation. In the general case, there are four pure Mueller matrices in the decomposition. In the present spectral decomposition, of these four matrices, there is a single matrix that qualifies as a scattering matrix, whereas the remaining three matrices represent other classes of pure matrices. For ensembles of spherical particles, there are two pure Mueller matrices in the decomposition. Again, there is a single matrix qualifying as a scattering matrix. The analytical decomposition unveils the explicit dependencies of the pure Mueller matrices on the ensemble-averaged scattering matrix. Applications are identified in scattering by single particles and by random media of particles.

Majorana bound state in the continuum and Fano effect formed by the coupling of two Andreev-reflection channels

Majorana-induced Andreev reflection (AR) is theoretically investigated by considering the interplay between two AR channels, each of which is formed by the lead and its coupled topological-superconducting nanowire with Majorana bound states. By means of the Scattering matrix and nonequilibirum Green’s function technique, relevant observables are analyzed, including the differential conductance, the density of states, and shot-noise Fano factors. It is found that Majorana bound states in the continuum (MBIC) can be constructed, under the condition of two uniform nanowires and inter-channel couplings. Otherwise, the Fano effect is allowed to occur, which is manifested as the appearance of additional conductance dips. In particular, the Fano antiresonance can be induced by constructing the identical inter-channel couplings. All these results can be helpful in understanding the MBIC contributed by the Majorana-assisted ARs.

Model-Based Nine-Component Scattering Matrix Power Decomposition

Model-Based Nine-Component Scattering Matrix Power Decomposition

An Efficient Scheme for Quasi-Dynamic RCS Estimation of Multiple Targets Based on Polarization Scattering Matrices

An Efficient Scheme for Quasi-Dynamic RCS Estimation of Multiple Targets Based on Polarization Scattering Matrices

Nonlinear Scattering Matrix in Quantum Optics

It is well known that the scattering matrix plays an important role in quantum optics. This matrix converts the incoming characteristics of scattered radiation into output characteristics. Currently, only special cases of such a scattering matrix are known, which are determined by a specific problem. In this work, a general form of the scattering matrix is obtained, which can be applied to a wide range of problems. It is shown that previously well-known and widely used scattering matrices can be obtained from the resulting scattering matrix. The results obtained can be used to describe new quantum states, the scattering matrices of which have not yet been studied.

Universal Polarization Transformations: Spatial Programming of Polarization Scattering Matrices Using a Deep Learning-Designed Diffractive Polarization Transformer.

Controlled synthesis of optical fields having nonuniform polarization distributions presents a challenging task. Here, a universal polarization transformer is demonstrated that can synthesize a large set of arbitrarily-selected, complex-valued polarization scattering matrices between the polarization states at different positions within its input and output field-of-views (FOVs). This framework comprises 2D arrays of linear polarizers positioned between isotropic diffractive layers, each containing tens of thousands of diffractive features with optimizable transmission coefficients. After its deep learning-based training, this diffractive polarization transformer can successfully implement Ni No = 10 000 different spatially-encoded polarization scattering matrices with negligible error, where Ni and No represent the number of pixels in the input and output FOVs, respectively. This universal polarization transformation framework is experimentally validated in the terahertz spectrum by fabricating wire-grid polarizers and integrating them with 3D-printed diffractive layers to form a physical polarization transformer. Through this set-up, an all-optical polarization permutation operation of spatially-varying polarization fields is demonstrated, anddistinct spatially-encoded polarization scattering matrices are simultaneously implemented between the input and output FOVs of a compact diffractive processor. This framework opens up new avenues for developing novel devices for universal polarization control and may find applications in, e.g., remote sensing, medical imaging, security, material inspection, and machine vision.

A Domain Decomposition Method for the Analysis of Mutual Interactions Between Antenna and Arbitrary Scatterer Using Generalized Scattering Matrix and Translation Addition Theorem of SWFs

A Domain Decomposition Method for the Analysis of Mutual Interactions Between Antenna and Arbitrary Scatterer Using Generalized Scattering Matrix and Translation Addition Theorem of SWFs

Singularities of Scattering Matrices

Our main result is the analysis of singularities of the integrands of integrals representing the matrix elements of the scattering matrix and the inclusive scattering matrix in perturbation theory. These results are proven for any quantum field theory in any dimension.

Optical properties of polyaniline/modified graphene oxide nanocomposites

In this research, the complex refractive index of polyaniline (PANI)/hexamethylene diisocyanate-modified graphene oxide (HDI-GO) nanocomposites has been obtained. The PANI/HDI-GO nanocomposites were prepared via in situ polymerization of aniline monomer in the presence of HDI-GO nanofillers, and their crystalline structure and surface morphology were investigated via X-ray diffraction (XRD) and atomic force microscopy (AFM) measurements. Then, the experimental reflectance and transmittance for pure PANI and PANI/HDI-GO nanocomposite films with HDI-GO contents of 0.5, 1 and 2 wt% deposited on glass substrates were measured using UV-Vis spectrophotometry within the spectral region 300–900 nm. Then, the refractive index and extinction coefficient have been obtained using a novel method developed by the authors. The model is based on the generalized Scattering Matrix Method, which is used to obtain the theoretical values for the thin film/substrate reflectance and transmittance. Root mean square errors obtained are systematically lower than 0.21%, which corroborates the excellent accuracy of the model. The proposed method does not require sophisticated equipment, just a spectrophotometer, to obtain the complex refractive index of a thin film from transmittance and reflectance measurements.

Determining the Projected Crystal Structure from Four-dimensional Scanning Transmission Electron Microscopy via the Scattering Matrix.

We present a gradient-descent-based approach to determining the projected electrostatic potential from four-dimensional scanning transmission electron microscopy measurements of a periodic, crystalline material even when dynamical scattering occurs. The method solves for the scattering matrix as an intermediate step, but overcomes the so-called truncation problem that limited previous scattering-matrix-based projected structure determination methods. Gradient descent is made efficient by using analytic expressions for the gradients. Through simulated case studies, we show that iteratively improving the scattering matrix determination can significantly improve the accuracy of the projected structure determination.

A deep neural network for general scattering matrix

Abstract The scattering matrix is the mathematical representation of the scattering characteristics of any scatterer. Nevertheless, except for scatterers with high symmetry like spheres or cylinders, the scattering matrix does not have any analytical forms and thus can only be calculated numerically, which requires heavy computation. Here, we have developed a well-trained deep neural network (DNN) that can calculate the scattering matrix of scatterers without symmetry at a speed thousands of times faster than that of finite element solvers. Interestingly, the scattering matrix obtained from the DNN inherently satisfies the fundamental physical principles, including energy conservation, time reversal and reciprocity. Moreover, inverse design based on the DNN is made possible by applying the gradient descent algorithm. Finally, we demonstrate an application of the DNN, which is to design scatterers with desired scattering properties under special conditions. Our work proposes a convenient solution of deep learning for scattering problems.

On the Effect of Scalar Flux Weighting of Linearly Anisotropic Scattering Matrices in Higher-Order Transport Calculations

Most of the codes available for homogenized group constant generation for deterministic transport calculations apply the approximation of scalar flux weighting during energy group condensation of higher-order anisotropic scattering matrices. In this paper, we point out the bias caused by scalar flux weighting of linearly anisotropic scattering matrices in the result of SP3 and S12 calculations. An infinite pin cell was homogenized with Serpent 2 and ERANOS ECCO to compare group constants with different energy group condensation options. Serpent 2 applies scalar flux while ERANOS ECCO performs current weighting of the linearly anisotropic scattering matrices. Three simple reactor models were built assuming different core sizes using standard rectangular assemblies with 15 ×15 fuel pins to analyze the effect of the various weighting options. Diffusion, SP3, and S12 calculations were performed for the three models using group constants generated with Serpent 2 and ERANOS ECCO. The effect of scalar flux weighting of linearly anisotropic scattering matrices in higher-order transport calculations is shown by comparing the decrease in reactivity due to the decreased reactor size and the assembly power distribution to reference results obtained with Serpent 2 Monte Carlo calculations. Analogous results were observed during the extension of our investigations to a VVER-440 benchmark and the Budapest University of Technology and Economics (BME) Training Reactor. We also studied the effect of increasing the number of groups in these examples. Neglecting higher than linearly anisotropic scattering and indirect application of diffusion coefficients in higher-order transport calculations is advised with few-group structures if angular flux-moment spectra-weighted higher-order scattering matrices cannot be generated. Although in few-group calculations, it can lead to more accurate higher-order transport solutions than applying scalar flux–weighted linearly anisotropic scattering matrices, by increasing the number of energy groups, the distorting effect of scalar flux weighting can also be decreased.

Real Representation of the Polarimetric Scattering Matrix for Monostatic Radar

Synthetic aperture radar with polarimetric diversity is a powerful tool in remote sensing. Each pixel is described by the scattering matrix corresponding to the emission/reception polarization states (usually horizontal and vertical). The algebraic real representation, a block symmetric matrix form, is introduced to adopt a more comprehensive framework (non-restricted by reciprocity assumptions) in mapping the scattering matrix by the consimilarity equivalence relation. The proposed representation can reveal potentially new information. For example, its eigenvalue decomposition, which is itself a necessary step in obtaining the consimilarity transformation products, may be useful in characterizing the degree of reciprocity/nonreciprocity. As a consequence, it can be employed in testing the reciprocity compliance assumed with monostatic PolSAR data. Full-wave simulated polarimetric data confirm that oriented scatterers can present complex eigenvalues, even with the monostatic geometry.

Assessment of The Acoustic Scattering Matrix of a Heat Exchanger Using ssCFD-LNSE Simulation

The risk of thermoacoustic instability is present in any combustion appliance. The instability results from a closed loop feedback between unsteady combustion, heat-transfer and acoustic modes of the system. To predict the system acoustics all constituting elements of the appliance need to be modelled. A heat-exchanger is the element where the gas faces complex fluid dynamics and heat transfer processes. Therefore, modelling of (thermo)-acoustic properties of a heat exchanger is challenging. In this paper, a computational approach is proposed to characterize the acoustic properties of a generic heat exchanger in both laminar and turbulent flow regimes. A hybrid Computational Fluid Dynamics - Computational Aero-Acoustics (CFD-CAA) method is used based on full linearized Navier-Stokes equation, called ssCFD-LNSE. The fundamental idea in this approach is to efficiently model acoustic wave propagation with inclusion of mean flow and temperature fields. ssCFD-LNSE is performed by splitting the quantities of the total field into a mean part (obtained from CFD) and a (acoustic) perturbation part modelled within the LNSE solver. The goal of this research is to assess the two-port acoustic scattering matrix of an array of tubes, as a generic model of heat-exchanger, with a hot cross flow.

Polarization Scattering Matrix and Doppler Joint Estimation Based on Multichannel Spectrum Interpolation Clean

Polarization and micro-Doppler signatures are widely used for target detection and recognition in harsh sensing environments. However, accurately estimating polarization scattering matrices and Doppler frequencies of scattering centers remains challenging. This paper incorporates the multi-channel spectrum interpolation with the CLEAN algorithm. The proposed algorithm can estimate the Doppler frequencies and scattering matrices of target scattering centers from fully-polarized data with high precision. Compared with the traditional detection-after-imaging workflow, the proposed method takes an iterative suppression technique, which improves the estimation accuracy and reduces detection time. The effectiveness of the proposed method is verified based on the simulation and actual radar data. The estimation accuracy measured by polarized similarity is 99.9%, and the normalized root mean squared error of the estimated Doppler frequency is 4.8% in simulation.

Investigation of AFGSM Methods for Some Electromagnetic Bandgap Structures: From Analysis to Applied Antenna Design

Electromagnetic Bandgap (EBG) structures that exhibit various performances, such as preventing the electromagnetic wave propagation and reflecting an incident wave within the stopband, have unique electromagnetic characterization. Due to this reason, accurate analysis and design of the EBG structures are crucial to enhance the integrated system performance. This paper concentrates on the characterization of some planar EBGs using the Auxiliary Functions of Generalized Scattering Matrix (AFGSM) methods, with particular importance on an in-depth consideration of its bandgaps. The AFGSM method is applied to the planar EBG structures in the literature for the first time. The well-known kinds (symmetric and asymmetric cases) of mushroom type and multilayer EBG structures are considered to verify the presented method. Analysis results are compared with the Conventional Eigenvalue Equation (C-EIV) and the Generalized Scattering Matrix based Eigenvalue Equation (GSM-EIV) methods. Low computation load and accurate results are obtained to analyze the planar EBG structures with the AFGSM method due to using transmission line model. In addition, a design methodology is proposed for a chosen planar EBG structure using the AFGSM methods. Geometrical parameters of interested EBG problems are determined for acquiring the stopband frequency region of interest using the scattering parameters of unit cell configuration. The mushroom EBG model along one and two-dimensional axes is used in an antenna application to decrease mutual coupling between antenna elements. Three different scenarios are simulated in the HFSS electromagnetic simulation design environment to understand the effect of mutual coupling reduction in the antenna problem of the designed EBG structure via the AFGSM method. All designed antennas are manufactured, and the measurement results are in good agreement with the simulation results. The measurement results of the fabricated antenna application example including designed EBG using the proposed AFGSM method is compared with the existing similar problems with the same and different EBG models. It has been demonstrated that bandgap analysis, design of the planar EBG structures and integration of considered EBG model to a design application can be accurately and quickly achieved with the given methodology using the AFGSM method.