Scattering Matrix Research Articles

Some Properties of Generalized Scattering Matrix Representations for Metallic Waveguides With Periodic Dielectric Loading

Some new results are presented on the properties of generalized scattering matrix representations for metallic waveguides with axially periodic dielectric loadings. A unified framework is given for describing the frequency dependence and for identifying the emergence of propagating, nonpropagating, and complex Floquet modes in single mode, as well as multimode, regions. Two new conservation relations are formulated for the generalized scattering matrix of the unit cell in lossless periodic structures. One of these relations provides a convenient means for checking the correctness of the values of calculated matrix elements, while the other relation yields accurate estimates for the stopband-passband transition frequencies located within single Floquet-mode regions.

Two-Particle Scattering Matrix of Two Interacting Mesoscopic Conductors

We consider two quantum coherent conductors interacting weakly via long range Coulomb forces. We describe the interaction in terms of two-particle collisions described by a two-particle scattering matrix. As an example we determine the transmission probability and correlations in a two-particle scattering experiment and find that the results can be expressed in terms of the density-of-states matrices of the noninteracting scatterers.

Efficient Technique for the Cascade Connection of Multiple Two-Port Scattering Matrices

There are several practical applications in microwave engineering that require the cascade connection of multiple two-port scattering matrices. Many microwave devices are analyzed by segmenting the structure into small building blocks (steps, resonators, lines, etc.) that are characterized by means of the generalized scattering matrix. In order to obtain the reflection and transmission parameters of the entire structure, the scattering matrices of all the building blocks must be cascaded. Traditionally, the conversion of the scattering matrices to ABCD or T matrices has been used in order to perform the cascade connection. An alternative to this procedure is to perform a recursive connection by pairs of the scattering matrices. In this paper, we present a new technique for the efficient cascade connection of N monomodal or multimodal scattering matrices that reduces the computation time by 35% when compared to the cascading by pairs, and by 75% when compared with the use of ABCD matrices.

On a solution to Improve the Object Detection Ability of Radars by Dynamic Polarization Method

One of the most important problems of modern radar is increasing object detection, object distinction ability. In the last years, the used traditional radar signal processing methods are seem to use up. For solving this question, specialists are interested in analyzing the fine structure of radar signal, and the first is polarization structure. The use of polarization information allows to raise the information ability of radar systems and provides high probability of radar objects detection, high contrast of small-scale man-made objects on the radar map and radar objects classification. The article deals with the detection of radar objects by exploiting the information on polarization based on the scattering matrix (SM) of the object. A solution to improve the object detection ability of radars by dynamic polarization method (to modify the polarization of radiative wave) is introduced. AJSTD Vol.23(1&2) pp.107-112 (2006)

Domain Decomposition Method Based on Generalized Scattering Matrix for Installed Performance of Antennas on Aircraft

We describe the factorization (FACTOPO) domain decomposition method based on the boundary element method (BEM) and the finite element method (FEM) applied to the analysis of antenna performance on aircraft. The benefits of the subdomain method are mainly the ability to deal with collaborative studies involving several companies, and the reduction of the computation costs by one or more orders of magnitude, especially in the context of parametric studies. Furthermore, this paper proposes global functions defined on fictitious surfaces surrounding radiating elements, to deal with the computation of antenna far field patterns in a multidomain mode. By masking the complexity of the antenna (wires, thin surfaces, materials, feeding network) the external domain of the aircraft can be closed so that the combined field integral equation can be used, which is better conditioned than the electric field integral equation and converges much faster. The accuracy and efficiency of this technique is assessed by directivity computations of VHF monopole antennas mounted on Fokker 100 and ATR42 scaled mock-up. Domain decomposition results obtained by combining two sets of subdomains are compared with measurements and the FEKO commercial method of moments code.

Erratum: Scattering matrix method for multimode electron transport through quantum wires under a local magnetic field modulation and spin-orbit interaction [Phys. Rev. B74, 195332 (2006)

Erratum: Scattering matrix method for multimode electron transport through quantum wires under a local magnetic field modulation and spin-orbit interaction [Phys. Rev. B<b>74</b>, 195332 (2006)

Analysis of Integrated Circuit System s by An Innovative Wavelet-Based Scattering Matrix Approach

This paper proposes the use of scattering parameters (S-parameters) in the wavelet domain for the analysis of coupled multiconductor transmission lines, high-speed integrated circuits, and interconnects. S-parameters-based computing techniques are widely used in the analysis of networks characterized by a large number of integrated devices and interconnects. The theoretical and practical definition of the wavelet-based S matrix is shown, and then some numerical examples of its use and potential in the analysis of systems with linear and nonlinear terminations is shown and compared with other numerical techniques. The computational costs and the memory requirements of the wavelet representation of scattering matrix are also addressed

A Novel Method of Mutual Coupling Matching for Array Antenna Design

By using the equivalent network model, this paper mainly analyses the relationship of impedance matrix and S-parameter matrix, coupling matching and gain respectively. It finds out that, assuming the gain keeps constant, the increase of |Smn |(m ≠ n) will sure lead to the decrease of |Smn | in the Scattering matrix. This relation can be used together with mutual coupling, and if used properly, it can improve the performance of antenna array. Under the guidance of this theory, a miniaturization circular array of four monopole antennas loaded disc is designed. Provided the antenna gain is invariable and pattern is correct, this design can improve the VSWR by using printed patch on the substrate of antenna top.

Principal Component Analysis (PCA) in the Context of Radar Polarimetry

Statistical and computational techniques for revealing the internal structure that underlies the set of random correlated data exists in a great variety at present; and target decomposition theorems, either in the coherent or incoherent formulation, are well established. In spite of this fact a rather innovative and new concept is presented in this contribution. In turn the Principal Component Analysis (PCA) is considered to possibly add value to existing approaches, and it allows for an interpretation of polarimetric synthetic aperture radar measurements using variables obtained via linear transformation. Starting with the Sinclair backscatter matrix S which will be further transformed into the so called target feature vector by stacking column elements of S and generating the covariance matrices averaged over a certain pixel array, we show, how the Sinclair backscatter matrix is decomposed into the sum of a maximum of four 2 x 2 elementary point scatter matrices which are weighted by the principal components, whereas the variances of these components agree with the eigenvalues of the covariance matrix. This mathematical development defines a decomposition which expresses scattering mechanism from distributed targets in terms of scattering matrices via an incoherent step.

311 スキャッタリングマトリックス法を用いた管路の音響解析に関する基礎研究

311 スキャッタリングマトリックス法を用いた管路の音響解析に関する基礎研究

Analysis of Slot Characteristics in Slotted Single-Mode Semiconductor Lasers Using the 2-D Scattering Matrix Method

We use the two-dimensional (2-D) scattering matrix method (SMM) to analyze the slot characteristics in slotted single-mode semiconductor lasers and compare the results with those calculated by the one-dimensional transfer matrix method (TMM). The analysis shows that the 2-D SMM is required to accurately account for the measured results. Using the 2-D SMM simulation, we find that there is almost no reflection at the interface from slot to waveguide while a large reflection exists at the interface from waveguide to slot, and the power loss is much larger than the power reflected. For a single slot, the slot width has little influence on the slot reflectivity, which coincides with the measured results. The reflection and transmission of the slot are found to be exponentially dependent on the slot depth

Basic Properties of the Generalized Scattering Matrix of Waveguide Transformers

This paper examines analytically the operator properties of the generalized scattering matrix of the H-(E-) plane waveguide transformer in an arbitrary shape. Four fundamental laws of electromagnetism are used to derive a new form of the generalized energy-conservation statement. The structure of spectrum of the generalized scattering matrix and the spectrum localization are established. A practical significance of the considered basic properties is illustrated by the example of matrix models of the waveguide bends. The obtained analytical results are useful for testing the correctness of numerical solutions, as well as for the mathematical justification of the methods based on modal analysis.

The energy and resonant properties of a longitudinal slot in a waveguide partially filled with dielectric

The paper considers a narrow longitudinal slot in the wide wall of a rectangular waveguide with a layer of dielectric arranged parallel to the waveguide narrow walls. The resonant properties of the slot and the behavior of its scattering matrix elements are investigated depending on physical dimensions and e of the dielectric.

A CAD-Oriented Method to Analyze and Design Radiating Structures Based on Bodies of Revolution by Using Finite Elements and Generalized Scattering Matrix

In this work, an efficient analysis of radiating structures based on bodies of revolution is dealt with. The procedure is a hybrid method based on a segmentation of the structure into two-dimensional regions, finite elements and a spherical computation domain surrounding the antenna, defining a boundary or port where a spherical mode expansion of the fields is used. A reduced order model is computed for a fast frequency sweep. To validate this method, some structures based on bodies of revolution as a rod dielectric antenna, conical dielectric-loaded horns, profiled horns and a monopole-dielectric resonator antenna are studied and results are compared with those demonstrated by other authors. The design of a smooth-walled horn by means of the optimization of the profile is also carried out.

Correlation Functions of Impedance and Scattering Matrix Elements in Chaotic Absorbing Cavities

Wave scattering in chaotic systems with a uniform energy loss (absorption) is considered. Within the random matrix approach we calculate exactly the energy correlation functions of different matrix elements of impedance or scattering matrices for systems with preserved or broken time-reversal symmetry. The obtained results are valid at any number of arbitrary open scattering channels and arbitrary absorption. Elastic enhancement factors (defined through the ratio of the corresponding variance in reflection to that in transmission) are also discussed.

Energy Invariants of Composition Rules for Scattering and Transfer Matrices of Propagating and Evanescent Electromagnetic Waves in Dielectric Structures

Energy Invariants of Composition Rules for Scattering and Transfer Matrices of Propagating and Evanescent Electromagnetic Waves in Dielectric Structures

ELECTROMAGNETIC SCATTERING BY A SET OF OBJECTS: AN INTEGRAL METHOD BASED ON SCATTERING OPERATOR

The paper presents the Scattering Operator Method, which is devoted to the problem of scattering from a set of N cylindrical objects. By contrast with the Scattering Matrix Method, which has been used by many groups in the last twenty years, it applies to any kind of cylinder shape, regardless of the relative location of the cylinders. The theory is based on a mathematical result: it is possible to define in the vicinity of the surface of each cylinder two complementary parts of the field: the total incident field and the field scattered by this cylinder. These two parts are the Calderon projectors of the values of the total fields on the surface of the cylinder. The validity of the method is checked on two examples. It is shown that the theory avoids some problems encountered in integral method like evaluations of singular or hypersingular integrals, or instabilities due to internal resonance of objects.

Tunable Fano resonance in photonic crystal slabs

A three dimensional analysis of a special class of anisotropic materials is presented. We introduce an extension of the Scattering Matrix Method (SMM) to investigate the behavior of anisotropic Photonic Crystal Slabs (PhCS) subject to external radiation. We show how the Fano effect can play a fundamental role in the realization of tunable optical devices. Moreover, we show how to utilize electron injection, electric field and temperature as parameters to control the Fano resonance shift in both isotropic and anisotropic materials as Si and Potassium Titanium Oxide Phosphate (KTP). We will see that because Fano modes are sensitive and controllable, a broad range of applications can be considered.

Statistics of Impedance and Scattering Matrices in Chaotic Microwave Cavities: Single Channel Case

We study the statistical properties of the impedance (Z) and scattering (S) matrices of open electromagnetic cavities with several transmission lines or waveguides connected to the cavity. In this paper, we mainly discuss the single port case. The generalization to multiple ports is treated in a companion paper. The model we consider is based on assumed properties of chaotic eigenfunctions for the closed system. Analysis of the model successfully reproduces features of the random matrix model believed to be universal, while at the same time incorporating features which are specific to individual systems as treated by the Poisson kernel of Mello et al. Statistical properties of the cavity impedance Z are obtained in terms of the radiation impedance (i.e., the impedance seen at a port with the cavity walls moved to infinity). Effects of wall absorption are discussed. Theoretical predictions are tested by direct comparison with numerical solutions for a specific system. (Here the word universal is used to denote high frequency statistical properties that are shared by the members of the general class of systems whose corresponding ray trajectories are chaotic. These universal properties are, by definition, independent of system-specific details.)

Statistics of Impedance and Scattering Matrices of Chaotic Microwave Cavities with Multiple Ports

The statistical model proposed in an accompanying paper is generalized to treat multiport scattering problems. Attention is first focused on two-port lossless systems and the model is shown to be consistent with Random Matrix Theory. The predictions are then tested by direct numerical simulation for a specific two-port cavity. Formulae are derived for the average transmission and reflection coefficients in terms of the port radiation impedance. The cases of cavities with multiple ports, and with a single port and distributed losses are compared.