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Chapter 17 discusses the S-matrix theory of two-dimensional integrable models. From a mathematical point of view, the two-dimensional nature of the systems and their integrability are the crucial features that lead to important simplifications of the formalism and its successful application. This chapter deals with the analytic theory of the S-matrix of the integrable models. A particular emphasis is put on the dynamical principle of bootstrap, which gives rise to a recursive structure of the amplitudes. It also covers several dynamical quantities, such as mass ratios or three-coupling constants, which have an elegant mathematic formulation that is also of easy geometrical interpretation.

In this paper, we model multiple vias with irregular antipad in arbitrarily shaped 3-D integrated circuit and packaging system based on generalized Foldy-Lax equations method, boundary integral equation method, and generalized T matrix. We first obtain the impedance matrix for finite cavity, which includes the reflection features of the cavity boundaries. Then, the scattered field from a single via and a generalized T matrix, including the wall effects, are derived. The Foldy-Lax multiple scattering equations are generalized to include the wall effects using impedance matrix and the generalized T matrix. To obtain the incident field for the case of vias in the arbitrarily shaped antipad, we calculate the exciting and scattering field coefficients based on the transformation that converts surface integration of magnetic surface currents in antipad into 1-D line integration of surface charges on the vias and ground plane. The coupling among vertical vias are solved by applying Foldy-Lax multiple scattering equations. The scattering matrix of coupling among vias is calculated to make corresponding signal/power integrity analysis. Numerical results for the method are in a good agreement with a commercial full-wave numerical tool up to 50 GHz.

A uniform and closed-form spatial Green's function for finite dielectric structures is derived by using a combination of the characteristic Green's function (CGF) and rational function fitting method (RFFM). Employing the concept of quasi leaky waves, CGF-RFFM represents both of the discrete and continuous spectrum contributions efficiently by using the modified VECTFIT algorithm. The method is examined for 2-D truncated dielectric slab while it can be implemented for 3-D structure straightforwardly. An error of less than 0.2% is achieved compared with the direct numerical integration of the spectral integral. The derived Green's function is exact for separable structures while it is approximate for nonseparable structures like truncated dielectric substrates where the corner regions are replaced with fictitious materials. To obtain more accurate results, mode conversions due to the surface waves (SWs) incident on the end-facet are considered by employing the scattering matrix in the formulation for structures supporting several guided modes. The main advantage of this method lies in its speed as well as accuracy. Excellent agreements with the rigorous method of moments (MoM) are shown in several examples.

A method for determining the complete higher-order scattering matrix of an acoustic discontinuity is developed. The method is demonstrated for a right-angled waveguide bend, and the magnitude and phase of the reflection and transmission coefficients are extracted precisely. The procedure is straightforward and based on the solutions to the Helmholtz equation by the finite element method (FEM). The consistency of the scattering coefficients found by this method is verified by their properties of symmetry, and their accuracy is established by the conservation of energy. The reliability of the new technique is further proved by means of an arbitrary sound source and by comparing the direct FEM response to the reflection matrix calculation. Some features of the scattering matrix as a function of frequency are surprising, such as the steps and reversion of the phase evolution or the complete loss of transmission of the incoming wave. The methodology detailed in this paper can be extended to other multiport junctions, such as T-junctions or size discontinuities in ducts.

In this paper, a novel technique for cascading generalized scattering matrices based on a Krylov's iterative solver is presented. This new technique is fully general, since it can be applied to solve the connection of an arbitrary number of networks, each one with an arbitrary number of ports, and it is easy to implement. This technique is able to compute, not only the modal spectra at the free ports of the global network, but also the modal spectra at the connected ports, so that the field inside the full network can be computed for an arbitrary incidence. In addition, this technique can also be used to evaluate the scattering parameters of the global network.

An efficient approach is presented to compute the eigensolutions of closed and open radiating periodically loaded waveguides by modal series expansion. The eigensolutions of the homogeneous background waveguides serve as basis functions for the fields in the periodic boundaries. The corresponding scattering matrix of an isolated periodic unit cell is determined by commercial software solvers. The scattering matrix is transformed into the transfer matrix, which can be used to formulate an eigenproblem. Open field problems are converted into a closed equivalence while the characteristics of the original open configurations are preserved, even for radiating (leaky) waveguiding structures. Consequently, the original continuous spectrum of modes is represented by a discrete and proper set of modes. An eigenproblem must still be solved but it is considerably reduced in size and complexity for configurations where relatively few expansion modes are sufficient.

A full-wave antenna modeling method by means of elementary sources described in terms of colocalized infinitesimal dipoles is presented in this paper. The procedure provides a generalized scattering matrix (GSM) in terms of equivalent infinitesimal dipoles from the GSM of the antenna by using rotation and translation of spherical modes. The number of equivalent infinitesimal dipoles and their positions are optimized by using a genetic algorithm. The application to the full-wave analysis of arrays is also presented, providing very accurate results even when the minimum spheres of the antennas in the array environment overlap considerably, which cannot be solved by the direct coupling of generalized scattering matrices in terms of spherical waves. Some examples of antenna modeling and their application to the analysis of arrays of antennas on a metallic plane will be shown.

Arrays of volumetric antennas whose minimum spheres overlap are efficiently analyzed by means of translational addition theorems for spherical modes in this letter. For this purpose, an improved model of the isolated antenna in terms of elementary sources of infinitesimal dipoles is used. The model provides a generalized scattering matrix (GSM) in terms of infinitesimal dipoles that allows synthesizing the whole behavior of the isolated antenna and enables its precise application to array environments by using translational addition theorems. The search region for the optimization procedure that finds the positions of the elementary sources to model the isolated antenna has been extended to the volume occupied by the antenna, so that the model becomes very precise. As a consequence, even when the minimum spheres of the array elements are strongly overlapped, it provides accurate results since the equivalent models will never overlap. Additionally, the optimization procedure is carried out only once for a wide band. The proposed approach has been validated by means of two different radiating elements such as monopoles and dielectric resonator antennas (DRAs), with good agreements obtained in comparison to the full-wave results simulated by commercial software.

The combination of the generalized transverse resonance technique, a field-matching method, and the generalized scattering matrix (GSM) concept is proposed in this paper as an efficient, versatile, and accurate method for the analysis of laterally open periodic waveguides. The proposed method accounts for both open and periodic boundary conditions without any approximation. Its only drawback is its restriction to the analysis of structures that can be segmented in the Cartesian coordinate system. How ever, a staircase approach has been successfully applied to over come this basic limitation. The segmentation of the waveguides, the field expansions for TMp,qz Bloch modes in each partition, and a modification of the well-known GSM cascading procedure for the analysis of a particular type of structure are detailed. In order to demonstrate the capabilities of the proposed approach, four structures, similar to the substrate integrated waveguide, have been analyzed, built, and measured. These examples include single-row square-post and circular-post waveguides, and displaced-row and multiple-row square-post waveguides. The computations and measurements confirm the efficiency, accuracy, and great versatility of this method.

A different and useful approach is presented for detecting new events in a scene, such as the presence or absence of landmines or perhaps the movement of people, vehicles, or structures. The approach rests on the radar examination of an area several times, once, before there are targets present, and the other (or others) after. The change detection algorithm notices if there are any changes after the first view. In the present approach the prospective target is represented, not in terms of three complex elements of a scattering matrix, but in terms of phenomenologically-based Huynen parameters. Each element of the Huynen parameter set conveys a different type of physical and geometrical attribute about the scatterers, thus the potential for significant false-alarm mitigation is increased. We provide results of the application of this approach on fully polarimetric signatures of simulated pairs of buried cylindrical targets. These results indicate the following. 1) Huynen parameters are more effective for change detection than the scattering matrix elements because of their ability to generate higher unambiguous autocorrelation peaks and fewer dominating cross-correlation curves. 2) A large number of symmetries are observed in the plots of the Huynen parameters for both one and two buried cylinders. These symmetries may eventually lead to further classification insights. 3) By using standard Prony methods, relevant resonance frequencies are extracted from the parameter plots, from which the height of either one of the cylinders is estimated. 4) The diameter of either cylinder can also be obtained by a simple procedure based on ray-tracing and time delays. Numerical calculations substantiate all the above assertions.

A new hybrid mode matching and method of moments formulation based only on electric currents is presented in this paper. The use of only one equivalent current allows the introduction of a new set of unknowns. The chosen new unknowns are the weights related to the scattered modes that emerge from the ports to the waveguides that feed the problem. Applying this new formulation, the matrices that must be inverted are smaller and the generalized scattering matrix can be obtained directly from the solution of the resulting system of equations, so that no additional projection is needed to obtain the scattering parameters, as happens with traditional approaches with two equivalent currents. As a result, certain efficiency improvement is obtained, as can be seen when this technique is applied to the solution of H plane problems in rectangular waveguide

By characterizing the condition number as an indicator of accuracy, an error analysis is performed to determine how different auxiliary terminations affect the accuracy of the scattering matrix renormalization transform. Such an error analysis plays an essential role in enhancing the accuracy and widening the applicability of the port renormalization method for measuring multiport devices with a two-port vector network analyzer.

This paper presents an efficient and robust algorithm for passivity enforcement of S -parameter-based macromodels. The method computes updated values of the model residues by least squares fitting of nonpassive residuals of the scattering matrix. Several examples show that the proposed method yields accurate passive macromodels at a limited computational cost.

We propose a generalized T -matrix definition that facilitates the conversion between the S-parameter and T-parameter for multiport networks based on the well understood and mathematically simple two-port relations. This approach generalizes all multiport networks into two cases: balanced and unbalanced. Balanced networks have the same number of entrance and exit ports and are symmetric to the two-port network. Unbalanced networks generate a nonsquare T -matrix and do not have the same number of entrance and exit ports. Through careful selection of the T -matrix, this method extends two-port symmetry to multiport networks and provides an engineering implementable relationship between the S-parameter and T-parameter for multiport networks. This symmetry extension allows a practical means to cascade and de-embed such networks.

Most of the existing methods for the analysis of meanderline polarizer assume that the embedded metallic grids are infinitely thin. A modal procedure is presented here for treating meanderline grids with finite thicknesses. The space between the metallic grids in a unit cell is considered as a meanderline waveguide with a stepped cross-section and length given by the grid thickness. The modes of this guide are obtained using the transverse resonance technique. A generalized scattering matrix characterization of the grid is obtained by field matching of the modes of the meanderline guide and the free space Floquet guide. The accuracy of this approach is verified by the very good agreement obtained between predicted and measured transmission phases of polarizer grids.

Simple and compact rectangular waveguide 90deg twist is proposed. The twist transformer region is a square waveguide section with two square corner cuts. The twist full-wave model is based on the mode-matching and generalized S-matrix techniques. It is found that the optimized twists can provide the bandwidths of no less than 30% at the 30-dB return-loss level or 16% at the 40-dB level over a lower, middle, or higher part of the rectangular waveguide operating band. The twist lengths are five times less than the rectangular waveguide wavelength at the central frequency of the chosen operating band. Role of evanescent modes in the interaction of two small-distanced twist transitions is discussed. The design results are confirmed by the results of real device measurements.

This paper introduces a general multigrid-subgridding formulation aimed at improving the efficiency of the transmission line matrix method. The rigorous algebraic procedure, based on Hilbert space formulation, leads to the definition of a general boundary scattering matrix, which interfaces 3-D regions of uniform computational mesh with different spatial resolution, thus allowing the modeling of objects of very disparate geometrical or electrical scale, e.g., such occurring in nanodevices. Computational acceleration and accuracy are measured by comparing the run time of simulations performed with subgridding to the run time of simulations without any subgridding.

The S matrix theory with use of the effective Hamiltonian is sketched and applied to the description of the transmission through double quantum dots. The effective Hamilton operator is non-hermitian, its eigenvalues are complex, the eigenfunctions are bi-orthogonal. In this theory, singularities occur at points where two (or more) eigenvalues of the effective Hamiltonian coalesce. These points are physically meaningful: they separate the scenario of avoided level crossings from that without any crossings in the complex plane. They are branch points in the complex plane. Their geometrical features are different from those of the diabolic points.

The analytic structure of the S-matrix of singular quantum mechanics is examined within a multichannel framework, with primary focus on its dependence with respect to a parameter (Ω) that determines the boundary conditions. Specifically, a characterization is given in terms of salient mathematical and physical properties governing its behavior. These properties involve unitarity and associated current-conserving Wronskian relations, time-reversal invariance, and Blaschke factorization. The approach leads to an interpretation of effective nonunitary solutions in singular quantum mechanics and their determination from the unitary family., Instituto de Física La Plata, Consejo Nacional de Investigaciones Científicas y Técnicas

This paper derives, in the exact framework of multiple scattering theory for point targets, a noniterative analytical formula for the nonlinear inversion of the target scattering strengths from the scattering or response matrix that can be applied after the target positions have been estimated in a previous step via, e.g., time-reversal multiple signal classification or another approach. The new formula provides a noniterative analytical alternative to the iterative numerical solution approach for the same problem presented in a recent paper [A. J. Devaney, E. A. Marengo, and F. K. Gruber, "Time-reversal-based imaging and inverse scattering of multiply scattering point targets," J. Acoust. Soc. Am. 118, 3129-3138 (2005)]. The two methods (noniterative versus iterative) are comparatively investigated with two numerical examples.

In this paper, we present an efficient cascading procedure for analyzing frequency selective surface (FSS) systems consisting of multiple FSS screens of unequal periodicity embedded in multiple dielectric layers. In this procedure, we first find a global period for the FSS system by studying the composite in its entirety. Next, we compute the scattering matrix [S] of each of the FSS subsystems for the global Floquet harmonics by applying a relationship we establish that maps the [S] matrix of the subsystem for the individual Floquet harmonics to that for the global harmonics. This mapping-cum-filling process substantially reduces the effort needed to compute the [S] matrix of a subsystem. Finally, we compute the [S] of the entire system by applying a modified cascading formulation, in which one matrix inversion step is eliminated, resulting in a reduction in the total computing resource requirement as well as time. Two numerical examples are given to illustrate the efficiency and effectiveness of the technique.

A generalized scattering matrix (GSM) approach, which utilizes finite-difference time-domain (FDTD) with a modified unsplit PML (perfectly matched layer) and mode matching techniques, is used to analyze spatial power combiners/dividers with hard horn feeds. The simulation results are experimentally verified for a 1:9 spatial power dividing system. Furthermore, the effects of various design parameters on the overall performance of a 1:9 divider is investigated.

In standard quasiclassical trajectory calculations, each trajectory has the same statistical weight. Alternately, the Gaussian weighting method is an ad hoc procedure which consists in weighting each trajectory by a Gaussian-like coefficient such that the closer the final actions to integer values, the larger the coefficient. The goal of the present note is to justify such a method in the framework of classical S matrix theory.

This paper discusses the application of model-order reduction in the optimization of microwave devices. It focuses on the direct optimization of the scattering matrix poles and zeros, yielding an advanced reliability and universality at a computational cost that is comparable to a surrogate model optimization. The scattering matrix poles and zeros are computed from a state-space model that is obtained from a finite-integration discretization and then optimized to match a set of target poles and zeros.

The use of current probes for the injection of wide-band disturbance in electromagnetic compatibility applications requires their accurate characterization up to few gigahertz. While the representation of the current probe with a simple transformer is acceptable at low frequencies, the spectral content of fast signals requires models which are accurate even at gigahertz frequencies. This can be accomplished directly by measurements in the frequency domain (FD), making use of a S-matrix representation of the probe, or in the time domain (TD), recovering the transfer functions from the impulse responses measurement. Both techniques suffer limitations due to numerical and experimental problems; in particular, the FD approach leads to the solution of an inverse problem, with numerical instabilities in the high-frequency range, whereas the TD approach is not so accurate in the low-frequency range of the sought transfer function. The paper combines the two techniques to overcome these difficulties and achieve a better accuracy across the overall bandwidth. The characterization of a commercially available current probe allows comparison of numerical results with experimental measurements.

For noncritical energies, the asymptotic behavior of the scattering phase and of the time-delay are known to be described by a Weyl type formula and the Breit–Wigner formula, respectively. We consider here the case of critical energy levels in dimension 1. We obtain the semiclassical asymptotics of the scattering phase and of the time-delay, uniformly with respect to the energy in a neighborhood of a critical value.

Digital waveguides are generalized to the multivariable case with the goal of maximizing generality while retaining robust numerical properties and simplicity of realization. Multivariable complex power is defined, and conditions for "medium passivity" are presented. Multivariable complex wave impedances, such as those deriving from multivariable lossy waveguides, are used to construct scattering junctions which yield frequency dependent scattering coefficients which can be implemented in practice using digital filters. The general form for the scattering matrix at a junction of multivariable waveguides is derived. An efficient class of loss-modeling filters is derived, including a rule for checking validity of the small-loss assumption. An example application in musical acoustics is given.

A method is presented for full-wave modeling of vertical vias in multilayered circuits. The analysis of the interior problem is based upon the cylindrical wave expansion of the magnetic field Green's function. The multiple interaction among vertical vias is modeled by the Foldy-Lax scattering formula. Multilayered effects are included by using cascaded network of the single-layer components. The exterior problem of the via and the transmission line is analyzed using the method of moments approach. The exterior and interior problems are combined into a system of equations to facilitate the solution of a large number of vias. Using this approach, the scattering matrix of problems of several thousand vias can be calculated with moderate CPU and memory requirement. Numerical results have been obtained for different via configurations and for a large range of frequency. Also illustrated are results for common and differential mode in differential signaling with surrounding idle and shorting vias.

A new and efficient hybrid mode-matching method is presented for the analysis of arbitrarily shaped inductive obstacles and/or discontinuities in a rectangular waveguide. The irregular region with obstacles and/or discontinuities is characterized using a full-wave hybrid spectral/numerical open-space technique expanding the fields in cylindrical wave functions. Next, a full-wave mode-matching procedure is used to match the cylindrical wave functions to guided modes in all ports and a generalized scattering matrix for the structure is finally obtained. The obstacles can be metallic or dielectric with complex permittivities and arbitrary geometries. The structure presents an arbitrary number of ports, each one with different orientation and dimensions. The accuracy of the method is validated comparing with results for several complex problems found in the literature. CPU times are also included to show the efficiency of the new method.

We consider perturbative quantum field theory in the causal framework. Gauge invariance is, in this framework, an identity involving chronological products of the interaction Lagrangian; it express the fact that the scattering matrix must leave invariant the sub-space of physical states. We are interested in generalizations of such identity involving Wick sub-monomials of the interaction Lagrangian. The analysis can be performed by direct computation in the lower orders of perturbation theory; guided by these computations we conjecture a generalization for arbitrary orders., Comment: 23 pages. arXiv admin note: text overlap with arXiv:1508.02183

A new derivation is given for the representation, under certain conditions, of the integral dispersion relations of scattering theory through local forms. The resulting expressions have been obtained through an independent procedure to construct the real part, and consist of new mathematical structures of double infinite summations of derivatives. In this new form the derivatives are calculated at the generic value of the energy $E$ and separately at the reference point $E=m$ that is the lower limit of the integration. This new form may be more interesting in certain circumstances and directly shows the origin of the difficulties in convergence that were present in the old truncated forms called standard-DDR. For all cases in which the reductions of the double to single sums were obtained in our previous work, leading to explicit demonstration of convergence, these new expressions are seen to be identical to the previous ones. We present, as a glossary, the most simplified explicit results for the DDR's in the cases of imaginary amplitudes of forms $(E/m)^\lambda[\ln (E/m)]^n$, that cover the cases of practical interest in particle physics phenomenology at high energies. We explicitly study the expressions for the cases with $\lambda$ negative odd integers, that require identification of cancelation of singularities, and provide the corresponding final results., Comment: The final publication is available at http://scitation.aip.org/content/aip/journal/jmp

The sufficient conditions under which the S-matrix orthogonal part U(k) is real and even are proved. These conditions are required for generalization of the projection matrices method in the N×N Riemann–Hilbert boundary value problem, N=2,3,…,N

A full-wave analysis of an inhomogeneous waveguide region with both planar and circular cylindrical boundaries is presented in this paper. Circular cylindrical modal functions are used to represent the fields. Field matching on the planar walls and apertures is rigorously achieved by the finite plane-wave series expansion of each modal field, whereas the addition theorem for cylindrical waves is used for rigorous field matching on the circular cylindrical boundaries. Numerical results are given for rectangular waveguides with 90/spl deg/ bends and rounded outer corners.

We have carried out the optimization of the simplest dual-mode horn that does not include the special cylindrical phasing section. Calculation of the horn characteristics has been performed by using a stepped representation of the conical section, with a subsequent application of the method of generalized scattering matrices, which more accurately accounts for all of the effects taking place when exciting the horn, The objective of the optimization has been the minimization of the maximum crosspolar level. The optimum horn parameters obtained as a result, and the corresponding radiation characteristics, can serve as additional reference information in the development of antenna systems using dual-mode horns.

The excitation of hybrid modes by discontinuities in rectangular waveguide can often be decomposed into separate LSE/LSM or TE/TM mechanisms, so that each component can be analyzed with the most suitable modal base. Correct interfacing, however, is required. We report the scattering matrices representing all the possible transformations of modal bases in rectangular waveguide. Such matrices provide an useful tool to simulate complex circuits made up of components strongly interacting, without requiring the use of a common modal base for the characterization of each element. Since the transformation matrices can easily include pieces of transmission lines, their use does not require any additional computation effort.

In a co- or cross-polarized channel, the polarization states of the transmitting and receiving antennas are the same or orthogonal, and the corresponding target nulls (i.e., the co-pol nulls or x-pol nulls) are defined as the polarization states of the transmitting antenna such that the received power equals zero. However, no systematic studies have been carried out to solve the problem of the corresponding target nulls if the polarization states of the transmitting and receiving antennas are independent. In this paper, the target null theory is extended to the case of two independent polarization states. For two arbitrary independent symmetric scattering matrices, it is proved that there exists only one pair of polarization states such that both of the received powers equal zero. This polarization states' pair is called the co-null of the two targets, which can easily be obtained by solving an eigenvalue problem. Based on this concept and algebraic theory, the concept of the co-null space is introduced for the symmetric scattering matrix case, and many important results are presented, e.g., the relations between the co-null and the co-pol/x-pol nulls, the properties of the co-null space, and the relation between the co-null and target decomposition. Finally, the co-null for the asymmetric scattering matrix case is studied. The concepts of the mono-co-null space and the bi-co-null space are introduced, and the relations between both spaces are presented.

Kern's plane-wave scattering-matrix formulation is extended to treat the case of two interfaces plus a scatterer imbedded in the second region. This formulation can treat different shapes for the scatterer and only requires two different evaluations depending upon the location of the observer: 1) in the near field, a two-dimensional (2-D) fast Fourier transform (FFT) (one-dimensional (1-D) FFT is treated by an analytical integration), and 2) in the far-field an asymptotic evaluation of the integral. These two regimes are in contrast to the Sommerfeld integral approximations where different approximations are required for various parameter ranges (quasistatic, saddle-point evaluation for the radiation field, saddle point evaluation for the surface field when the saddle point is near a pole, and the lateral wave field evaluated using a uniform asymptotic evaluation for the integrals).

In this paper, we reconsider the question of the definition of the generalized scattering matrix (GSM) of a lossless device, and show the conditions that the GSM must satisfy in order to correctly represent a lossless device, independently of the method used for its calculation. Moreover, starting from circuit theory, possible choices are considered, and among them the one is examined that seems to be the most meaningful when dealing with modes below cutoff. When the circuit is lossless, in fact, the resulting GSM is unitary, even when modes below cutoff are taken as accessible. This property provides an immediate check of the correctness of the computational implementation of actual problems. Finally, a practical example of the usefulness of the conditions provided is shown.

The present state of quantum field theory (QFT) is analyzed from a new viewpoint whose mathematical basis is the modular theory of von Neumann algebras. Its physical consequences suggest new ways of dealing with interactions, symmetries, Hawking–Unruh thermal properties and possibly also extensions of the scheme of renormalized perturbation theory. Interactions are incorporated by using the fact that the S matrix is a relative modular invariant of the interacting—relative to the incoming—net of wedge algebras. This new point of view allows many interesting comparisions with the standard quantization approach to QFT and is shown to be firmly rooted in the history of QFT. Its radical “change of paradigm” aspect becomes particularly visible in the quantum measurement problem.

In this paper, we present a multidomain and multi-method coupling scheme called FACTOPO, based on generalized scattering matrix computations on three-dimensional (3-D) subdomains. The global target /spl Omega/ is split in N/sub V/ subdomains (V/sub i/)(i=1, N/sub V/), separated by N/sub I/ fictitious surfaces (/spl Gamma//sub j/)(j=1,N/sub I/). We use a modal representation of the tangent fields on the interfaces. In each domain, the generalized scattering matrix S/sub i/ is computed with different methods such as the 3-D finite-element method (FEM) or the electric field integral equation (EFIE). This coupling scheme leads to an important reduction in computational resources, especially for cavities with one dimension much larger than the other two. The advantages of this formulation for parametric studies is illustrated by two cases: computing the RCS of an air-intake terminated with a flat PEC or a fan (CHANNEL) and of an antenna structure coupled to an electronic feed with a varying parameter (DENEB). Numerical as well as experimental results are presented.

In this paper, a finite-difference time-domain numerical dispersion relation for evanescent waves is derived, and its impact on the modeling accuracy is studied. The numerical evanescent constant is found to differ from the analytical one. As a result, a correction must be used to compute discontinuity parameters. This influences the reference plane chosen for the analysis of propagating modes. Moreover, on calculating multimode transmission and reflection coefficients, the dispersion for evanescent higher order modes is determinant. The dispersive relation is derived, discussed, and used to correct the evanescent constants for the multimode analysis of a waveguide discontinuity.

This paper presents a general procedure to analyze a multilayer array structure, where each layer may have different periodicities, different lattice structures, and/or the array axes between the layers may be nonparallel. The procedure involves the determination of a global cell with a global coordinate system, then computations of local generalized scattering matrices (GSMs) of individual layers followed by modal mapping from local to global GSMs. The global GSMs for individual layers are then combined to characterize the entire structure. The mapping relations are derived for two layers with different lattice structures, different periodicities, and array-axes orientations. Three examples of practical importance are considered to demonstrate the methodology. The first example is a two-layered patch array with different periodicities. The second example is an array of subarrays with several patch elements within a subarray. It is shown that a subarray can be characterized rigorously by characterizing only one element of a subarray instead of analyzing all the elements of the subarray simultaneously. Consequently, the analytical and computational complexities reduce considerably. The last example is a patch array loaded with a multilayer meander-line polarizer. The patch array and the meander-line array have two different periodicities and the axes are nonparallel. Detailed radiation characteristics of the structure are presented and compared with that of a strip-grid polarizer. The computational advantages of this method are discussed.