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A technique is described to measure the generalized scattering matrix (GSM) of a waveguide device whose ports are multimodal. The device-under-test is placed in between suitable converters, thereby transforming multimodal ports into monomodal ports. The needed data are then measured using a standard vector network analyzer. A dedicated algorithm is finally used to recover the multimode GSM of the device. The experimental validation is reported in this paper for rectangular and square waveguides showing excellent agreement between theory and measured results.

Tuning characteristics of the guided mode resonances in one- and two-dimensional (1- and 2-D) photonic crystal slab design using scattering matrix method are evaluated. This paper shows the superiority of 2-D design compared with 1-D design in terms of design flexibility considering that 2-D photonic crystal slab design requires a more mature and complex fabrication technology.

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.

We present a variation of the electric-field volume integral equation (VIE) for inhomogeneous media that is tailored for microwave S-parameter measurements. The kernel of the standard VIE is a dyadic Green's function that can relate fields in the object domain to observed scattered fields outside the object domain. Here, we derive a kernel we call a vector Green's function that gives, instead of observed fields, observed S-parameter measurements that would be obtained in a bistatic antenna setup. This formulation directly links the object properties to microwave measurements in a way that is useful to many microwave applications. This derivation uses an antenna model based on the source-scattering matrix formulation. We show how this vector Green's function can be obtained from simulation and validate this model with several experiments.

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.

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.

We show that the threshold of a photonic crystal surface-emitting laser can be calculated from first-principles by the method of rigorous coupled wave analysis (RCWA), which has been widely used to simulate the response spectra of passive periodic structures. Here, the scattering matrix (S-matrix) of a surface-emitting laser structure with added gain is calculated on the complex frequency plane using RCWA, and the lasing threshold is determined by the value of the gain for which the pole of the S-matrix reaches the real axis. This approach can be used for surface emitting laser structures in general and is particularly useful for those with complex in-plane structures.

A 60-GHz substrate integrated waveguide Butler matrix designed based on a systematic approach is fabricated by a standard single-layer print circuit board process, which is more economical for mass production than are the advanced processes such as low-temperature co-fired ceramic, thick-film process, etc. The systematic approach involves design equations, simulations, and measurements. Starting with a set of explicit design equations for the short-slot couplers, one calculates the structure dimensions. The calculated dimensions are then optimized with full-wave simulation to finalize the design of the key components, including the couplers and phase shifters. With the use of a noncoaxial multiport measurement technique, the characteristics of the components are acquired through a probe station and a two-port vector network analyzer. Measurement technique plays a critical role in the systematic design approach. By measuring at the intrinsic ports or the wave ports defined in the full-wave simulations, the components are unambiguously verified and then integrated to complete the design of the Butler matrix. The resulting Butler matrix is also verified by the measured eight-port S -matrix, which is shown in good agreement with the simulated one. As the measured results of the Butler matrix show, for the operating bandwidth from 58 to 62 GHz, the reflections and isolations are lower than -13.5 dB and the insertion losses are below 2.5 dB. Much like the measured results of the components, the measured eight-port S -matrix not only verifies the design of the Butler matrix, but also will facilitate the follow-on design of a switched-beam antenna array.

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

We present an S-matrix based model that provides a quantitative description over a wide range of realistic situations. The generation of radiation of very high harmonic frequencies is a relevant feature arising in the interaction of intense lasers with matter. Besides its theoretical interest as a paradigm of a non-perturbative phenomenon, it also conveys a number of technological applications (generation of coherent high frequency radiation, attosecond pulse generation, etc.).

Even in light of all the multiport vector network analyzers (VNAs) that appear to be on the market at present, the measurement of noncoaxial multiport devices remains a critical challenge due to the lack of a multiport counterpart of the two-port thru-reflect-line (TRL) calibration. Accordingly, based on the concept of virtual auxiliary termination and the two-port TRL calibration technique, a scattering matrix reconstruction procedure is developed for the use of a two-port VNA to characterize noncoaxial multiport devices up to the intrinsic ports located at the ends of the planar transmission lines such as microstrips, coplanar waveguides, and substrate integrated waveguides (SIWs). The four-port scattering matrix of a 60-GHz SIW 0-dB coupler for experimental validation is reconstructed. The final results are in agreement with not only the simulation results, but also the fully corrected TRL results.

Theory and experiments are presented of modal decomposition of scattering matrices of multiconductor transmission lines (TLs). In effect, n coupled TLs are decomposed into n independent ones. Its use is demonstrated by applying it to thru-only de-embedding of 4 coupled TLs (synthesized data) and 2 coupled TLs (measurement data from a 0.18 ?m-CMOS chip). The proposed de-embedding method could greatly facilitate accurate characterization of on-chip multiport networks.

The formulation of the generalized scattering matrix (GSM) of a finite array is revised to take into account the feeding network effects in the calculation of the external mutual coupling. It allows the analysis of finite arrays of externally coupled elements whose radiated field can be described by means of spherical waves on a ground plane, such as apertures, monopoles, cavity-backed patch antennas, or dielectric resonator antennas (DRAs), including rigorously the mismatching and internal coupling effects because of the feeding network.

This letter presents a flexible method to compensate the interelement mutual coupling (MC) effects that may degrade the field pattern of an array of real and coupled antennas. A closed-expression for a mutual coupling compensation matrix (MCCM) is derived. The MCCM is used to compensate the presence of the real individual elements' patterns and the interelement MC effects for any excitations obtained with an isotropic-based pattern synthesis method. The MCCM is calculated from the generalized scattering matrix (GSM) of an antenna array and the spherical mode expansion (SME) of its radiated field. For a given array, this MCCM has to be calculated only once since it only depends on the radiating and scattering characteristics of the antenna elements as well as on their location in the array. Conditions regarding null field pattern directions can also be reinforced in the MCCM. To compute the GSM of the array and the SME of the radiated field, a validated full-wave hybrid and modular methodology is used. Numerical results of synthesized patterns where the MC effects have been compensated are presented for arrays made up of dielectric resonator antennas.

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.

The conditions for the optimal non-reciprocal operation of longitudinally magnetised ferrite-coupled line (FCL) are obtained for the first time from the scattering-matrix treatment, and the necessary conditions for the multicomponent reciprocal network joint with a FCL section to be a circulator are specified. Using these optimal conditions, the minimum length of the FCL is also found. A self-biasing circulator with the minimum length of FCL at millimetre-wave frequency is reported and its scattering characteristics are simulated and discussed.

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 presents a method for the efficient analysis of multilayer frequency selective surfaces (FSSs) integrated with phased array of open-ended waveguides. The method is based on the assumption that all the periodic surfaces are arranged on the same spatial lattice (of arbitrary shape). The whole structure is represented as an equivalent multi-mode transmission line network, where each interface is characterized by an equivalent immittance matrix, computed through a full-wave analysis. To reduce the computational effort of the analysis a fast adaptive model-based interpolation algorithm for the scattering matrix entries is included. A software has been developed, which will provide an useful tool for the design of integrated FSS for phased array antennas.

This paper proposes a generalization of the Huynen theory to bistatic radar configurations for which the scattering matrices can no longer be assumed symmetrical. A set of parameters characterizing the physical mechanisms is extracted from the disoriented bistatic Kennaugh matrix. The distribution of amplitude between the parameters of the disoriented Kennaugh matrix is studied.

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.

Chain scattering parameters or T-parameters are a useful tool for calculating cascaded two-ports. With the increasing importance of mixed-mode S-parameters, a need for converting the T-parameters from their unbalanced form into a balanced form emerges for suiting both common and differential mode waves, as well as the mode conversion. This paper presents the derivation of the equations for transformations between mixed-mode S- and T-parameters for a mixed-mode two-port. Although derived in a way very similar to monomode T-parameters, no simplifications were necessary. Measurement results exemplify the quality of the T-parameter transformation under real-life conditions.

Almost all methods for measuring the scattering matrix of an n-port device with the use of a two-port vector network analyzer (VNA) require one to terminate the other n - 2 ports in the fully characterized auxiliary terminations and prefer auxiliary terminations with small or moderate reflection coefficients. In this paper, a technique is presented to measure the auxiliary terminations indirectly. It not only eases the measurement of auxiliary terminations, but also makes the concept of virtual auxiliary termination realizable. In practice, examples of virtual auxiliary terminations can be the inherent connectors or bonding pads of the test device. Also studied is the remedy for the numerical pitfall possibly coexisting with the use of strongly reflecting auxiliary terminations such as virtual auxiliary terminations. The scattering matrix of a four-port circulator is then acquired accordingly from measurements using a two-port VNA and virtual auxiliary terminations.

The properties of conservative symmetric polarimetric scatterer scattering matrices are examined. It is shown that the unambiguous rotation angle for "conservative" symmetric polarimetric scatterers is the interval (-pi/4,+pi/4] as compared with (-pi/2,+pi/2] for nonconservative symmetric scatterers. Errors relating to the Cameron decomposition, which are recently introduced into the literature, are discussed. It is demonstrated that these errors arise from a faulty symmetric scatterer scattering matrix distance measure. This, in turn, leads to an improper mapping of the symmetric scatterer unit disk to a hemisphere. The correct mapping of the symmetric scatterer unit disk to the symmetric scatterer unit sphere is described

The effect of square-wave propagation along coupled coplanar waveguides (C-CPWs) is presented in this paper. Developed numerical tools combining full-wave calculations of the frequency-dependent guided-mode parameters and the network theory formalism enable the determination of port voltages under specified linear termination conditions. Propagation constants and characteristic impedances of coupled lines have been determined for fundamental guided modes using the spectral domain technique combined with Galerkin's procedure. The scattering matrix of the four-port structure has further been used for the calculation of port voltages. Analysis has been performed by taking into account the bi-mode operation resulting from the assumption of the ideal electrical connection of distributed ground plane conductors. Simulation results have been compared with experimental data, and very good agreement has been found, proving the usefulness of the developed numerical tools

This paper presents a modeling technique to predict the output signal of an open-ended rectangular waveguide probe when scanning an arbitrary-shape crack in a lossy conductor with finite conductivity. The loss of the specimen is taken into account by using surface impedance at the surface. The technique discretizes the crack shape and applies the generalized scattering matrix technique to obtain the output signal. To validate the model proposed in this paper, the results of the proposed method are compared with the measurement results and those obtained using a finite-element code. The model is used to obtain appropriate inversion curves for determining crack depth measurement from the probe output signal

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.

This paper presents an efficient simulation algorithm-Scattering matrix method for investigation of the coated finite two-dimensional electromagnetic bandgap (EBG) structures. The method is derived to be capable to simulate the band properties of the coated cylinder photonic crystal with wave discontinuities. Numbers of photonic crystals with waveguide discontinuities are examined. The transmission characteristics of the EBG embedded with metal, dielectric, and various coated cylinders are analyzed. The results show that the tuned bandgap properties are able to provide an additional possibility to develop a novel device.

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.

This paper focuses on the multiport characterization of antennas. In particular, special attention is given to the cavity backed annular patch antenna (CABAPA) for multipolarization operations. We will show that the reflection coefficient is not the best representative parameter to determine the frequency response of the multiport antenna and its radiation performance. Therefore, we seek a new generalized parameter that conveys the frequency response of multiport antennas. The total active reflection coefficient (TARC) is introduced as the square root of the sum of all incident powers at the ports minus radiated power, divided by the sum of all incident powers at the ports. The TARC is a function of frequency and is a real number between zero and one. With this definition we can characterize the multiport antenna's frequency bandwidth and radiation performance. A method for calculating the TARC is detailed for different port excitations directly from the scattering matrix of the antenna and independent of the feeding network. First, the CABAPA is analyzed by the method of moments. Next, the corresponding scattering matrix is employed to calculate the TARC for different polarizations. The calculated results, when compared to the measured results, show good agreement. The measured -10 dB TARC bandwidth of the CABAPA is 30% compared with 68% as measured using only the s/sub 11/.

Describes the most straightforward method for accurately measuring the frequency response of optoelectronic devices. The method uses a calibrated optical reference receiver, a modulated optical source, and a calibrated electrical vector network analyzer.

Balun transformers are used in front of network analyzers to measure the balanced- and common-mode characteristics of transmission lines and electronic networks. The nonideal nature of real baluns will cause measurements made with this technique to be in error. This paper shows that by following a calibration procedure similar to the conventional network analyzer calibration of Kruppa and Sodomsky, where known standards are measured, and these measurements are used to correct measurements of unknown devices, one can compensate for the nonideal nature of the measurement baluns. In this procedure, a conventional two-port network analyzer is connected to the balun transformer and, without disconnecting the network analyzer, inaccuracies in the balun can be calibrated out. Balanced mode, common mode, and mode conversion parameters can be accurately measured. This paper applies the previously published method of Silvonen for conventional network analyzer calibration to correct the measurement errors when using balun transformers.

The theory of scattering in junction by posts consisting of a segment of conducting cylinder is developed using a combination of a modified iterative scattering procedure and an orthogonal expansion method. The multimode scattering matrix of the junction is obtained. The change of the post's configuration, as well as a simple rotation of the post, makes it possible to vary the electrical characteristic. The validity and accuracy of the method is verified by comparing the numerical results with those given in literature, received from finite-difference time-domain (FDTD) simulation and our own measurements. The proposed procedure is efficient and faster than alternative numerical solutions such as the FDTD method used for comparison.

A full-wave methodology for a broadband analysis of isolated cavity-backed and probe-fed arbitrarily shaped microstrip patch antennas is combined with an analytical method based on the properties of rotation and translation of spherical modes for obtaining an efficient scattering matrix description of the mutual coupling in a two-element array. The proposed procedure is validated and results are given for identical circular cavity-backed patch antennas.

Printed launchers are currently used to feed millimeter broad-band horn antennas. A time-domain procedure, based on the finite-difference time-domain method, is proposed to achieve an accurate model of the launching section. A scattering matrix approach is followed and unidirectional time-domain modal sources are developed for efficient generation of port modes.

A new scattering mechanism enhancement scheme has been developed for natural (distributed) targets based on the eigenvalues and corresponding eigenvectors of the covariance matrix in order to identify different scattering events. First, three new vectors (v/sub 1/, v/sub 2/, and v/sub 3/) were constructed from the eigenvectors of the covariance matrix with some modifications. Then, those modified vectors were weighted by the eigenvalues of the covariance matrix as a weighting function. Thus, three vertices (A, B, and C) could be obtained in the three-dimensional space. In order to utilize them equally, a triangle (/spl Delta/ABC) was constructed by connecting these three vertices. The shape of the triangle may be changed due to the different scattering mechanisms because the vertices are obtained from the combination of eigenvalues and eigenvectors. The result indicated that different scattering mechanisms can be represented by using an exterior angle derived from the interior angles of the triangle. Results obtained from the newly developed scattering enhancement scheme, when compared with the results derived from existing schemes, were in agreement in terms of the dominant scattering mechanisms, including surface scattering, double-bounce scattering, and volume scattering. The experimental results with the Spaceborne Imaging Radar version C (SIR-C) L-band full polarimetric data demonstrate the effectiveness of the new scattering enhancement scheme.

Measurements on an 11-GHz four-port microstrip ferrite-coupled-line (FCL) circulator, employing a broad-band hybrid coupler and an improved air bridge, confirm that only a weak biasing field of 3-4 kA/m (35-50 Oe) is required. By cascading the S-matrices of the FCL section and hybrid coupler using signal flow graphs, the measured and predicted bandwidth and losses are compared for the first time. Simulated results for stripline FCL sections exhibit broader bandwidths than those obtained with microstrip FCL sections. Using such a structure, the simulated performance of a three-port circulator indicates that, in principle, bandwidths of at least 3:1 or 4:1 may be possible.

We provide a comprehensive study of two- and three-dimensional discontinuities in chirowaveguides. The multimode coupled-mode method is an effective numerical approach to analyze this problem. After obtaining the coupled-mode equations, we diagonalize the coupling matrix to obtain a multimode scattering matrix rather than the usual two-mode approximation. We calculate the scattering properties of coaxial waveguides partially filled with lossy chiral media. Excellent agreement is observed between our results and those obtained by the mode-matching method. We also compare our results in the achiral case for dielectric material partially filled rectangular waveguide with experimental data and results obtained by the mode-matching method. Excellent agreement is again found. Based on our analysis, numerical and analytical results are displayed to provide physical insight into the problem. First, we discuss the effects of the chirality admittance on scattering properties and find that the sensitivity of the scattering parameters to chirality admittance increases as the chirality admittance increases. Second, we find the dielectric constant has a great influence on the scattering parameters. Third, we find the relative influence of height and width of chiral obstacles in rectangular waveguides.

A new class of multisection 180/spl deg/ hybrids is presented in this paper. It is based on the hybrid-ring coupler that has been reconfigured such that multiple sections can be conveniently cascaded together. The main limitations of the conventional hybrid-ring coupler are its limited bandwidth, large size, and the impracticably high-impedance levels required for large power-split ratios. These limitations are readily overcome using the multisection cascadable 180/spl deg/ hybrids. Simple design equations based on the scattering matrix and experimental verifications of the theoretical results for two-section 180/spl deg/ hybrids are presented.

A technique for converting baluns into 180/spl deg/ hybrids by adding an in-phase power splitter is presented in this paper. Incorporating the broad-band antiphase and in-phase power splitting characteristics of the balun and power splitter results in a 180/spl deg/ hybrid with broad-band characteristics. This technique also provides a means of achieving perfect matching and output isolation for three-port lossless baluns. Applying this technique to a Marchand balun will result in a broad-band impedance-transforming 180/spl deg/ hybrid. Simple design equations based on the scattering matrix are presented. These theoretical results are validated by an experimental 180/spl deg/ hybrid using a coupled line Marchand balun. It achieves amplitude balance of 0.5 dB and phase balance of less than 5/spl deg/ from 1.2 to 3.2 GHz.

This paper presents a robust formulation of SAW Green's functions for arbitrarily thick multilayers at high frequencies. The formulation is an alternative to that based on the transfer matrix method, which suffers from numerical instabilities when the frequency and/or thickness parameters become large. This numerical difficulty can be attributed to the mixture of exponentially growing and decaying terms during the transfer matrix calculations. To be more instructive, the numerical instability is delineated in terms of upward-bounded and downward-bounded waves within each layer. In accordance with such boundedness association, a recursive scheme not involving any growing terms is developed based on the scattering matrices to eliminate the instability. The resulting reflection matrix method is extremely concise and preserves the simplicity and convenience of the transfer matrix method. Using the reflection matrices, the generalized Green's functions that relate the particle velocity and the rate of electric potential change to the surface stress and charge are formulated succinctly. These Green's functions are useful for having incorporated the electrical properties of the vacuum above the surface. Numerical computations are exemplified to demonstrate the instabilities of the transfer matrix method and to justify the robustness of the reflection matrix formula.

This paper presents an adaptive technique to extract the signal of interest (SOI) arriving from a known direction in the presence of strong interferers using a single snapshot of data. The antenna elements in this method can be nonuniformly spaced and there can be mutual coupling between them. In addition, near-field scatterers can also be present. First, the voltages induced in the antenna elements of the array due to interferers, mutual coupling between the elements, and near-field scatterers is preprocessed by applying a transformation matrix to these voltages through a rigorous electromagnetic analysis tool. This electromagnetic preprocessing technique transforms the voltages that are induced in a nonuniformly spaced array containing real antenna elements to a set of voltages that will be produced in a uniform linear virtual array (ULVA) containing omnidirectional isotropic point radiators. In the transformation matrix we would like to include various electromagnetic effects like mutual coupling between the antenna elements, presence of near-field scatterers and the platform effects on which the antenna array is mounted. This transformation matrix when applied to the actual measured voltages yields an equivalent set of voltages that will be induced in the ULVA. A direct data domain least squares adaptive algorithm is then applied to the processed voltages to extract the SOI in the presence of interferers. Limited numerical examples are presented to illustrate the novelty of the proposed method.

An approach is presented to characterize a beamforming network by means of a single quantity. It is based on a comparison of the actual output signal vector to the desired output signal vector. The formulation can be concisely written in matrix notation and allows for a characterization over frequency, accounting for absolute offsets. By expressing the characteristics of a beamforming network by a single quantity, subsequent iterations of one network or different network implementations can be compared to each other. The formulation is applied to the evaluation of a 4 × 4 Butler matrix implemented in three different ways.

A rigorous modal analysis (MA) for the H-plane waveguide T-junction loaded with a partial-height conducting post is presented in this paper. The analysis is based on the classical resonator mode-matching technique for waveguide junction problems and a novel concept called extended eigenmode functions. The new concept can be used for constructing eigenmode functions of a complex resonator region as long as the modal solution for a subproblem is available. Particularly for the T-junction problem, the modal solution for the two-port in-line waveguide loaded with the post is used. The proposed MA has been extensively verified by a finite-element method software package. Excellent agreement can be observed. Numerical results obtained by the analysis reveal that by adjusting the dimension of the loading post, the usable band width of the T-junction for constructing a diplexer can be significantly expanded. Since the generalized scattering matrix is obtained, the proposed analysis can be integrated with other available waveguide key building-block models for system analysis.

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.

A 2-D T-shaped metal-insulator-metal plasmonic waveguide with a joint cavity is introduced. The field distribution of the structure is investigated by using the finite-difference time-domain (FDTD) method. It is found that the surface plasmon polaritons' splitting ratio changes periodically as the joint cavity is moved. The period and maximum for the splitting ratio increase with increasing the width of the joint cavity. The results of the splitting performance obtained by the FDTD agree well with our semi-analytic model based on the scattering matrix theory.

The rates of change of the scattering matrix of a microwave device with respect to geometric or material parameters are of interest to designers, and useful in automatic optimization. They are most efficiently calculated by the adjoint variable method, but this usually entails the additional cost of funding the adjoint solutions. In the finite-element formulation presented here, no new solutions are needed beyond those required to calculate the complete scattering matrix. Explicit expressions are given for the calculation of the required matrix for a tetrahedral edge element. Results are presented for three rectangular waveguide problems: a uniform length terminated in a short-circuit; an H-plane miter bend; and a two-step waveguide impedance transformer.

This paper introduces a new TLM (transmission line modeling method) three-dimensional cell model, based on a "/spl pi/-type" transmission-line. Using this new design, the main equations of this cell are demonstrated, as well as its scattering matrix for a time domain modeling. This new model is applied to the wave propagation analysis into resonators, and the results are compared to analytical results and to the results of other methods.

Other researchers have designed a symmetrical six-port microstrip coupler that yields a bandwidth of 7%. It has been found in this paper that a change of the design topology allows the coupler's bandwidth to be increased. A simple-to use computer model of the double-ring-with-star prototype has also been developed and tests have confirmed that good agreement can be expected between the predicted and measured results.

This paper presents a full four-port characterization for traveling-wave optoelectronic devices, in particular, traveling-wave photodetectors (TWPDs), resulting in a scattering matrix formalism, which can be used for passive as well as active devices. A set of coupled distributed equivalent circuits is proposed for modeling the device, taking into account the wanted detection and spurious emission of light. A scattering matrix formalism is established, predicting the performances of the device at microwaves, when a microwave signal is used either for modulating the intensity of the optical power (forward detection mode) or for biasing the p-i-n junction (reverse emission mode). Hence, the obtained four-port device is nonreciprocal. Some symmetry properties are induced by the physical symmetry of the device. It has matched inputs, when symmetric electrical and optical reference loads are used. The scattering matrix satisfies power conservation laws. The formalism may be used to optimize the designs of TWPD's by varying the loads at each of the four ports.