Scattering Matrix Research Articles

Bandwidth Limitations for Scattering of Higher Order Electromagnetic Spherical Waves With Implications for the Antenna Scattering Matrix

Various physical limitations in electromagnetic theory and antenna theory have received considerable attention recently. However, there are no previous limitations on the scattering of higher order electromagnetic vector spherical waves, despite the widespread use of spherical wave decompositions. In the present paper, bandwidth limitations on the scattering matrix are derived for a wide class of heterogeneous objects, in terms of their electrical size, shape and static material properties. In particular, it is seen that the order of the dominating term in the Rayleigh limit increases with the order of the spherical wave. Furthermore, it is shown how the limitations place bounds on the antenna scattering matrix, thus introducing a new approach to physical limitations on antennas. Comparisons to other types of antenna limitations are given, and numerical simulations for two folded spherical helix antennas and a directive Yagi-Uda antenna are included to illuminate and validate the theory. The results in this paper are derived using a general approach to derive limitations for passive systems: First, the low-frequency asymptotic expansion of the scattering matrix of a general scatterer is derived. This gives a set of sum rules, from which the limitations follow.

The Spectral Density of the Scattering Matrix for High Energies

We determine the density of eigenvalues of the scattering matrix of the Schrödinger operator with a short range potential in the high energy asymptotic regime. We give an explicit formula for this density in terms of the X-ray transform of the potential.

Wave Propagation in Discontinuous Media by the Scattering Matrix Method

Propagation of elastic waves in discontinuous media is studied in this paper by the scattering matrix method (SMM). An electromagnetic transmission line analogy is also used to set up the mathematical model. The SMM operates in the frequency domain and allows for all wave polarizations (P, SV and SH). Rock masses are examples of discontinuous media in which the discontinuities (fractures or joints) influence wave propagation. Both elastic and viscoelastic joints are considered and the latter are described by Kelvin–Voigt, Maxwell and Burgers models. Rock joints with Coulomb slip behavior are also analyzed, by applying the averaging principle of Caughy (J Appl Mech 27:640–643, 1960). The evaluation of the effects of periodic discontinuities in a homogeneous medium is presented by introducing the concept of Bloch waves. The dispersion curves of these waves are useful to explain the existence of frequency bands of strong attenuation, also in the case of lossless (perfectly elastic) structures. Simple expressions of transmission and reflection coefficients are obtained. Finally, the SMM results are compared with those computed via the distinct element method (DEM). The comparisons are performed on a medium with joints with Coulomb slip behavior and the agreement is satisfactory, although the SMM must be applied in conjunction with the equivalent linearization technique. Even if the DEM is much more general, the SMM in these simple cases is extremely faster and provides a higher physical insight.

Numerical Methods for Calculating Poles of the Scattering Matrix With Applications in Grating Theory

Waveguide and resonant properties of diffractive structures are often explained through the complex poles of their scattering matrices. Numerical methods for calculating poles of the scattering matrix with applications in grating theory are discussed. A new iterative method for computing the matrix poles is proposed. The method takes account of the scattering matrix form in the pole vicinity and relies upon solving matrix equations with use of matrix decompositions. Using the same mathematical approach, we also describe a Cauchy-integral-based method that allows all the poles in a specified domain to be calculated. Calculation of the modes of a metal-dielectric diffraction grating shows that the iterative method proposed has the high rate of convergence and is numerically stable for large-dimension scattering matrices. An important advantage of the proposed method is that it usually converges to the nearest pole.

Asymptotic simplifications for hybrid BEM/GO/PO/PTD techniques based on a Generalized Scattering Matrix approach

In this paper we describe a new hybrid weak coupling of asymptotic GO/PO/PTD techniques, Boundary Element Methods (BEM) and Finite Element Method (FEM) based on the FACTOPO Domain Decomposition Methodology (DDM). Thus, the modular domain decomposition approach already assessed with exact techniques such as BEM and FEM is conserved, with the utilization of GO/PO/PTD techniques, resulting in an important reduction of CPU time during parametric studies. As the coupling scheme between asymptotic and exact methods is based on the Lorentz reciprocity theorem, the external structure of the large object is considered perfectly conducting. The accuracy and efficiency of this technique is assessed by performing the computation of the diffraction and radiation by several test-objects in a multi-domain way, cross compared with reference integral equation results.

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.

Analysis of Multilayered Periodic Structures Using a Hybrid FDTD/GSM Method

An efficient algorithm for computing the scattering properties of multilayered periodic structures using a hybrid Finite-Difference Time-Domain/Generalized Scattering Matrix (FDTD/GSM) technique is described. In this technique, the constant-horizontal-wavenumber approach is used to compute the scattering parameters of each periodic layer. A complete Floquet harmonic analysis of the periodic structure is presented, where propagation and evanescent behaviors of Floquet harmonics are studied. In addition, guidelines for selection of higher-order harmonics for a certain layer separation are provided. The scattering matrix of each layer, including proper Floquet harmonics, is then cascaded together with those of the other layers to obtain the generalized scattering matrix of the entire structure. The validity of this algorithm was verified through several numerical examples, including frequency-selective surfaces (FSS) with different periodicities and under different incidence angles. The numerical results showed good agreement with the results obtained from the FDTD simulation of the entire structure, while the new procedure saved computational time and storage.

Inter-Reciprocity Principles for Linear Network- Waveguides Systems Based on Generalized Scattering, Admittance and Impedance Matrices

Inter-reciprocity principles for linear <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$n$</tex></formula> -ports with connected waveguides are presented which are based on a formalism using generalized scattering, admittance and impedance matrices. The definitions of these matrices are kept as general as possible, so that any <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$n$</tex> </formula> -port of dimensionality <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$n$</tex> </formula> composed of linear media can be represented, and least assumptions on the transmission lines or waveguides connected to the network ports are necessary. In particular, the formalism allows for anisotropic media in the <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$n$</tex></formula> -port, as well as in the waveguides. Also intricate situations may be covered by this approach, where the usual description by ordinary scattering, impedance and admittance matrices fails. It is shown that the waveguides have to be taken into account as integral parts of the whole network-waveguides system, because the inter-reciprocity relations which are derived for the <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$n$</tex> </formula> -port depend on the waveguide modes. It is further investigated under which conditions these general relations coincide with the equations used to define abstract inter-reciprocity in network theory.

Discussion around the Scattering Matrix Realization of a Microwave Filter using the Bond Graph Approach and Scattering Formalism

Problem statement: Further to research works made previously and which use collectively the scattering formalism and bond graph technique for the modeling of a physical systems often working in high frequencies, we propose, in this article, a comparative study (discussion) for the scattering matrix realization of a high-frequency physical system. Approach: This discussion is based, on the one hand, on a non-causal (acausal) bond graph model which represents the starting model for the determination of the scattering parameters. On the other hand, we shall use a causal bond graph model richer in information and to which we shall apply what we called in former articles: the analytical procedure of the scattering parameters exploitation with the aim of showing the importance of the causality notion in the physical systems study by the bond graph approach, as well as the importance of the ways and causal loops notion. Results: We will, initially, apply this discussion, to an elementary transmission line; in the second place, the application is carried out on the equivalent circuit of a band pass filter based on localized elements often used like microwave filters in high frequencies studies. Conclusion: We will finish this discussion by realizing the scattering bond graph model of a quadruple by pointing out the procedure used for the construction of this new type of bond graph model.

Graphene-Based Normal/Ferromagnetic/Normal Junction as a Polarizer

Scattering matrix formalism is employed to calculate the conductance in a graphene-based N/F/N/F/N junction in the ballistic regime. The manipulation of spin transport for any number of N/F junctions is investigated by both the electrode gate and magnetic barriers. Kronig-Penney model is applied to consider the effects of barriers on spin transport in graphene. By considering a sequence of N/F junctions we have proposed that N/F/N junction could act like a polarizer. In this way, unpolarized charge carriers while traversing through the consecutive N/F/N junctions turn into polarized charge carriers.

J101032 向かい合う開口部の間を伝播する音波のスキャッタリングマトリックス

J101032 向かい合う開口部の間を伝播する音波のスキャッタリングマトリックス

Effect of the uncertainty of the shape of a distribution on its parameters retrieval using the scattering matrix of quartz suspension

Scattering matrices of an aqueous suspension of quartz were measured at a wavelength of 0.63 μm in the scattering angle range of 10°–150°. The angular dependences of matrix elements were measured with a laser polarimeter the optical scheme of which contained two electro-optical modulators. The results of measurements were compared with the data of calculation for scatterers having the shape of prolate ellipsoids. It was shown that, under conditions of wide distribution of particles by size and at a dimensional parameter value of 2.1, the uncertainty of the shape of the distribution leads to an increase in the error of the retrieval of the parameters of the suspension particle distribution.

Fast Computation of the Scattering Matrix of Lined Ducts Containing Passive Components

Fast Computation of the Scattering Matrix of Lined Ducts Containing Passive Components

Spherical-Wave-Based Shaped-Beam Field Synthesis for Planar Arrays Including the Mutual Coupling Effects

An analytical method to synthesize shaped-beam patterns with planar arrays, based on the handling of spherical waves, is proposed. Translational Addition Theorems will be used here for two different purposes: (1) relating the spherical modes produced by each element in the array to calculate the mutual coupling effects, and (2) expressing the field radiated by each element in terms of spherical modes corresponding to the whole array, to carry out a spherical-wave synthesis procedure based on the orthogonal properties of spherical modes. This field synthesis method is based on the fact that any antenna radiated field can be expressed as a discrete series of weighted spherical vector wave functions and it only requires the a priori knowledge of the Generalized Scattering Matrix of each array element considered as isolated from the rest of the array elements.

Performance of the Scattering Matrix Arc Detection System on the JET ITER-like ICRF antenna

Ion Cyclotron Radio Frequency (ICRF) antennas operating under high voltage to couple high power to fusion plasmas are at risk of electrical arcing. The standard Voltage Standing Wave Ratio (VSWR) system does not protect low impedance areas, which are used in antennas to achieve load tolerance to variations in plasma loading during Edge Localised Modes (ELMs). The Scattering Matrix Arc Detection System (SMAD) was designed to create additional protection for these areas, and 4 complete systems were implemented and tested on the ITER-like antenna (ILA) on JET. This paper describes the performance under relevant experimental conditions of load tolerance and/or high voltage and electrical arcing causing generator trip events.

Ferrite Based Non-Reciprocal Radome, Generalized Scattering Matrix Analysis and Experimental Demonstration

A non-reciprocal antenna radome based on the Faraday rotation effect in a ferrite slab is proposed and analyzed. This radome allows transmission in one direction and attenuates the signal in the opposite direction. It includes two layers of strip gratings on each side of the ferrite slab, consisting of highly conductive strips for proper reflection, and thin highly lossy strips for reflection/dissipation, and three dielectric layers for matching. The radome is analyzed rigorously by the generalized scattering matrix (GSM) method and its performance experimentally demonstrated between two broadband antennas. The measured results show 21 dB and 0.85 dB loss in the isolation and transmission directions, respectively.

Efficient design of multituned transmission line NMR probes: The electrical engineering approach

Transmission line-based multi-channel solid state NMR probes have many advantages regarding the cost of construction, number of RF-channels, and achievable RF-power levels. Nevertheless, these probes are only rarely employed in solid state-NMR-labs, mainly owing to the difficult experimental determination of the necessary RF-parameters. Here, the efficient design of multi-channel solid state MAS-NMR probes employing transmission line theory and modern techniques of electrical engineering is presented. As technical realization a five-channel ( 1H, 31P, 13C, 2H and 15N) probe for operation at 7 Tesla is described. This very cost efficient design goal is a multi port single coil transmission line probe based on the design developed by Schaefer and McKay. The electrical performance of the probe is determined by measuring of Scattering matrix parameters (S-parameters) in particular input/output ports. These parameters are compared to the calculated parameters of the design employing the S-matrix formalism. It is shown that the S-matrix formalism provides an excellent tool for examination of transmission line probes and thus the tool for a rational design of these probes. On the other hand, the resulting design provides excellent electrical performance. From a point of view of Nuclear Magnetic Resonance (NMR), calibration spectra of particular ports (channels) are of great importance. The estimation of the π / 2 pulses length for all five NMR channels is presented.

基于散射矩阵方法的金属光子晶体薄膜异常光学透射研究

基于散射矩阵方法的金属光子晶体薄膜异常光学透射研究

Scattering by an Array of Rods using the Gaussian Beam Formalism Coupled to the Scattering Matrix Method

We present in this paper a technique to compute the two-dimensional scattering of an arbitrary and regular incident field by an array of circular cylinders. Firstly, a rigorous semi-analytical technique is introduced for the electromagnetic scattering of an array of rods due to an incident gaussian beam in two dimensions. Then, the principle of decomposition of an arbitrary incident field in terms of elementary gaussian beams is outlined. The combination of these tools lead the way to the computation of the electromagnetic scattering of a 2D array of cylinders illuminated by an arbitrary incident field. Some results are presented in order to prove the validity of the method.

基于散射矩阵方法的金属光子晶体薄膜异常光学透射研究

基于散射矩阵方法的金属光子晶体薄膜异常光学透射研究