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Based on a pair of linear frequency modulation waveforms with opposite slopes, the mathematical model of the influence of intermediate frequency deviation (IFD) and sampling frequency deviation (SFD) on simultaneous polarisation measurement is derived. An IFD and SFD joint estimation and calibration method is proposed in this article. Simulation and real data results show that the radar frequency stability can change the position and phase of the polarisation scattering matrix (PSM) measurement. The approach proposed in this article can regulate the peak deviation effectively, compensate the phase error and accurately acquire the four elements of PSM.

The electron effective mobility analytical model without empirical parameters is investigated for uniaxial strained Si inversion layer, which can be conveniently applied by device and circuit designers. By one-dimensional inverse transform for the three-dimensional (3D) scattering matrix element along the vertical channel direction, three scattering (coulomb scattering, acoustic phonon scattering and intervalley scattering) rate models are researched. Then, the surface roughness scattering rate is taken into account to calculate the 2D inversion layer electron mobility. Based on the models, the simulations have been carried out by Matlab. The simulation results are in accord with the reference data, and the saturation phenomenon is brought to light.

A method is proposed that allows the computation of the continuous adjoint of a thermoacoustic network model based on the discretized direct equations. This hybrid approach exploits the self-adjoint character of the duct element, which allows all jump conditions to be derived from the direct scattering matrix. In this way, the need to derive the adjoint equations for every element of the network model is eliminated. This methodology combines the advantages of the discrete and continuous adjoint, as the accuracy of the continuous adjoint is achieved whilst maintaining the flexibility of the discrete adjoint. It is demonstrated how the obtained adjoint system may be utilized to optimize a thermoacoustic configuration by determining the optimal damper setting for an annular combustor.

We review a series of unitarization techniques that have been used during the last decades, many of them in connection with the advent and development of current algebra and later of Chiral Perturbation Theory. Several methods are discussed like the generalized effective-range expansion, K-matrix approach, Inverse Amplitude Method, Pad&eacute, approximants and the N / D method. More details are given for the latter though. We also consider how to implement them in order to correct by final-state interactions. In connection with this some other methods are also introduced like the expansion of the inverse of the form factor, the Omn&eacute, s solution, generalization to coupled channels and the Khuri-Treiman formalism, among others.

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.

International audience; A theoretical investigation of distributed microwave circuit built with Ti-shape topology is developed. The topology under study consists of neighbored T-and i-shape interconnect lines. The Ti-topology equivalent S-matrix is calculated as a function of crosstalk coupling coefficient and coupled line (CL) delay. To highlight the NGD modelling feasibility, parametric analyses with respect to the T-and i-element coupling and delay are introduced. More practical validation is carried out with designed, simulated and measured microstrip prototype. It is found that because of T-and i-crosstalk, the Ti topology can behave as a bandpass NGD function. A good NGD performance with NGD level of approximately −1 ns around the center frequencies 2.2 GHz with transmission coefficient of approximately −2.1 dB and reflection coefficient better than −14 dB. The measured results are in good agreement with calculated models and simulations. Two-cell Ti-NGD circuits were also investigated to illustrate the designability of the topology for multi-band and widened single band NGD responses. INDEX TERMS Crosstalk, distributed structure, Ti-topology, microwave theory, bandpass negative group delay (NGD), S-matrix theory.

In this study, the authors present an extended four-component model-based decomposition method by using a modified cross-scattering matrix. The scattering matrix of a rotated dihedral corner reflector is used to generate the modified cross-scattering matrix which accounts for the cross-polarisation power generated by the oriented dihedral structures. The orientation angles of the buildings are used to characterise this modified cross-scattering matrix which makes the proposed decomposition more feasible and effective. The effectiveness of the proposed decomposition method lies in its capability to discriminate between the cross-polarisation power generated by the oriented man-made structures and the vegetation. This makes the proposed method more suitable for the classification of oriented urban areas as compared with the existing model-based decomposition methods.

The reflection and transmission of polarized light for a cirrus cloud consisting of randomly oriented hexagonal columns were calculated by two very different vector radiative transfer models. The forward peak of the phase function for the ensemble-averaged ice crystals has a value of order 6 × 10 3 so a truncation procedure was used to help produce numerically efficient yet accurate results. One of these models, the Vectorized Line-by-Line Equivalent model (VLBLE), is based on the doubling–adding principle, while the other is based on a vector discrete ordinates method (VDISORT). A comparison shows that the two models provide very close although not entirely identical results, which can be explained by differences in treatment of single scattering and the representation of the scattering phase matrix. The relative differences in the reflected I and Q Stokes parameters are within 0.5% for I and within 1.5% for Q for all viewing angles. In 1971 Hansen [1] showed that for scattering by spherical particles the 3×3 approximation is sufficient to produce accurate results for the reflected radiance I and the degree of polarization (DOP), and he conjectured that these results would hold also for non-spherical particles. Simulations were conducted to test Hansen׳s conjecture for the cirrus cloud particles considered in this study. It was found that the 3×3 approximation also gives accurate results for the transmitted light, and for Q and U in addition to I and DOP. For these non-spherical ice particles the 3×3 approximation leads to an absolute error 2 × 10 − 6 for the reflected and transmitted I , Q and U Stokes parameters. Hence, it appears to be an excellent approximation, which significantly reduces the computational complexity and burden required for multiple scattering calculations.

Turbofan rotor–stator aeromechanic and aeroacoustics modeling has been traditionally developed by considering separately the aerodynamic and acoustic response of the fan and the stator to inflow nonuniformities. The present paper develops a model for the coupled fan–stator response for a realistic 3D geometry. The coupling mechanism is assumed to be mainly carried by scattered waves bouncing back and forth between the fan and the stator. The relationship between sources and state elements at three regions (inlet (1), in-between fan and stator (2), and exit (3)) is derived in terms of a scattering matrix S. The model is applied to two fan configurations: (1) a fully subsonic fan and (2) a transonic tip speed fan. The scattering matrix terms, up to the 5th blade passing frequency (BPF), are calculated by using CAAT, an Euler-based code. Results show coupling adds about 6 dB to the sound power level (PWL) of the transonic fan configuration but has a small effect for the subsonic fan configuration. The analysis of the propagating modes shows that, for the transonic configuration, the inlet mode at 1BPF propagates in regions 2 and 3 but is cut off in region 1. This reinforces the coupling process by trapping the acoustic mode 1BPF in region 2. Although this trapped energy is mainly due to the 1BPF of the fan wake, the fan scatters this energy into higher order acoustic modes and thus produces redistribution toward higher frequency of the acoustic spectra. Finally, adding a liner in region 2 reduces the energy of 1BPF mode propagating upstream and impinging on the fan. This mitigates the effect of the fan–stator coupling.

The purpose of this study is to demonstrate that the fully polarimetric radar can be effectively used to measure the insect orientation. First, the polarisation scattering matrix (PSM)-based orientation extraction method is reviewed. This method was proposed for traditional rotation polarisation radar, but is also applicable to fully polarimetric radar. Then, both anechoic chamber and field experiments were conducted to measure fully polarimetric insect PSMs and orientations, which verified the effectiveness of insect orientation extraction based on fully polarimetric measurement.

The half-life and the [Formula: see text]-value of alpha decay in several super heavy elements are calculated. The nuclear potential is computed using the double-folding method. Using the S-matrix theory, the alpha decay is treated as a scattering problem between alpha particle and the daughter nucleus. Nuclear potential was approximated by the parameterized Woods–Saxon potential. This idea has also been extended to predict the half-life and the [Formula: see text]-value of the heaviest elements of few other alpha chains.

Ionization of atoms in counter-rotating and co-rotating bicircular laser fields is studied using the S-matrix theory in both length and velocity gauges. We show that for both the bicircular fields, ionization rates are enhanced when the two circularly polarized lights have comparable intensities. In addition, the curves of ionization rate versus the field amplitude ratio of the two colors for counter-rotating and co-rotating fields coincide with each other in the length gauge case at the total laser intensity 5 × 1014 W/cm2, which agrees with the experimental observation. Moreover, the degree of the coincidence between the ionization rate curves of the two bicircular fields decreases with the increasing field amplitude ratio and decreasing total laser intensity. With the help of the ADK theory, the above characteristics of the ionization rate curves can be well interpreted, which is related to the transition from the tunneling to multiphoton ionization mechanism.

We provide a brief summary of a method to calculate improvements to the Veneziano Amplitude, creating sub-leading non-linearities in the Regge trajectory of states. We formulate it as an extension of a computation by Makeenko and Olesen. We begin in a confining gauge theory coupled to matter, rewriting the meson scattering amplitude as a specific path integral over shapes and sizes of closed Wilson loops using the worldline formalism. We then prescribe how to further the computation at strong coupling by employing holography, which provides a prescription for the expectation value of these Wilson loops in strongly coupled regimes. We find that the problem can then be thought of as a computation in an effective field theory of a string worldsheet sigma model, evolving in a broad class of holographic backgrounds. A convenient interaction picture presents itself naturally in this context, allowing us to draw Feynman diagrams corresponding to the first few corrections due to weaker coupling regimes. The answer we find has qualitatively the same features as other endeavours with the same objective., 24 pages, 7 figures, in preparation for submission to MPLA

In this paper we outline the recently derived Coulomb-Volkov (CV) S-matrix theory and present the results of calculations of the energy and the momentum spectra of the electrons emitted from ionisation of Ar atoms by an intense long-wavelength laser field. The results are compared with the corresponding calculations using the usual (plane-wave) SFA S-matrix theory, up to the second order of the series. We introduce a modified stationary phase method with a parametric integration to evaluate the high-dimensional integrals that occur in the second order of the ionisation amplitudes. The final-state Coulomb effect is found to be dominant at the lower energies, where the two theories differ greatly. In contrast, at high energies, the two theories produce qualitatively similar (in the logarithmic scale) distributions. It is found that despite the similarity of the positions of the 'forward rescattering' (or 'soft collision') peaks shown by the second order CV- and the SFA-amplitude, the line-shapes produced by them are qualitatively different. For example, the CV-spectrum shows a peak at 0.1 U-p with a characteristic line-shape that is convex on one side and steeply rising on the other side; this is qualitatively similar to the line-shape of the peak observed experimentally earlier at the same energy. In contrast, the SFA-spectrum shows at the same energy a pointed peak with a line-shape that is concave on both sides. The characteristic line-shape of the low energy LES-peak(s) thus appears to suggest itself as a signature of the final-state Coulomb interaction in strong-field ionisation processes.

Time-space modulated structures (or dynamic structures) possess properties modulated both in time and space. They have been extensively studied in diverse areas. This presented work theoretically studies the unusual wave propagation phenomena induced by elastic waves incident on time-space modulated beams. The scattering matrix is developed to predict the characteristics of the reflected and transmitted waves. It is shown that the scattering matrix directly indicates the non-reciprocal wave transmission and frequency splitting phenomena caused by the dynamic beam, it also reveals a frequency conversion phenomenon, which is rarely noticed by researchers but has very significant influence on the application of dynamic structures.

The identification of scattering matrix method is conducted using high fidelity Large Eddy Simulations. From a series of LES results, the scattering matrices of a plain orifice and a lean premixed nozzle are evaluated and compared with the corresponding experimental data. It is confirmed that LES simulations are capable of predicting the acoustic scattering matrix, with some limitations. The magnitude of the scattering matrices imply that the acoustic energy transfer across the orifice and mixer agree fairly well with that of the scattering matrices from the experimental data. Moreover, the phase angle of transmission/reflection elements for the traveling wave in the upstream region consistently follows the experimental trends. The phase angle of transmission/reflection elements for traveling waves in the downstream region, however, shows a significant discrepancy with the experimental measurements. For the direct use of the LES-based scattering matrix method, the accuracy of determination of the phase angle of reflection/transmission of the traveling wave in the downstream region needs further study.

By using the results of highly accurate T-matrix computations for randomly oriented oblate and prolate spheroids and Chebyshev particles with varying degrees of asphericity, we analyze the effects of a deviation of water-droplet shapes from that of a perfect sphere on the behavior of Lorenz-Mie morphology-dependent resonances of various widths. We demonstrate that the positions and profiles of the resonances can change significantly with increasing asphericity. The absolute degree of asphericity required to suppress a Lorenz-Mie resonance is approximately proportional to the resonance width. Our results imply that numerical averaging of scattering characteristics of real cloud droplets over sizes may rely on a significantly coarser size-parameter resolution than that required for ideal, perfectly spherical particles.

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.

We have determined a value for the 1S0 neutron-neutron scattering length (ann). The scattering length result is presented for the extended-soft-core (ESC04) interaction. The value obtained in the present work is ann = -18.6249 fm. The method of solution of the radial Schr?dinger equation with nonlocal potential for nucleonnucleon pairs is described and the result is consistent with previous determinations of ann = -18.63 ± 0.10 (statistical) ± 0.44 (systematic) ± 0.30 (theoretical) fm. The nonlocal potentials are of the central, spin-spin, spin-or-bital, and tensor type. The analysis from the ESC04 interaction is done at energies 0 ￡ Tlab ￡ 350 MeV. We compare the present result with experimental S-wave phase shifts analysis and agreement is found.

The method of time-dependent quantum wave packet dynamics has been successfully extended to study the charge transfer/exchange process in low energy two-body heavy particle collisions. The collision process is described by coupled-channel equations with diabatic potentials and (radial and rotational) couplings. The time-dependent coupled equations are propagated with the multiconfiguration time-dependent Hartree method and the modulo squares of S-matrix is extracted from the wave packet by the flux operator with complex absorbing potential (FCAP) method. The calculations of the charge transfer process 12Σ+ H-(1s2)+Li(1s22s)→22Σ+/32Σ+/12Π H(1s)+Li-(1s22s2l)(l=s,p) at the incident energy of about [0.3, 1.3] eV are illustrated as an example. It shows that the calculated reaction probabilities by the present FCAP reproduce that of quantum-mechanical molecular-orbital close-coupling very well, including the peak structures contributed by the resonances. Since time-dependent external interactions can be directly included in the present FCAP calculations, the successful implementation of FCAP provides us a powerful potential tool to study the quantum control of heavy particle collisions by lasers in the near future.

We develop a novel method based on sources and absorbers to examine quantum scattering in finite, nanoscale systems. We show that the Cauchy (mixed) boundary conditions (BCs) are required to put the scattering theory into an action integral formulation. These complex BCs are reduced to simpler Dirichlet BCs by introducing totally absorbing “stealth regions.” Material properties of these enclosing regions are optimized to give decaying solutions so that the scattering amplitudes vanish at the finite boundaries. With the active scattering region now surrounded by absorbers, we construct an “electron antenna” to provide incident waves. The method retains all the physical aspects of the conventional theory while providing new insights into “near-field” scattering effects. The action integral is discretized and evaluated to derive the local wavefunction everywhere. In two-dimensional quantum waveguides, we obtain the scattered wavefunction for geometrically complex scattering centers, showing the flexibility of our method. The modal decomposition of reflected and transmitted waves allows us to obtain transmission coefficients for both propagating and evanescent modes. Using group theory, we develop selection rules for the scattered modes depending on the symmetry of the potential. Our method outperforms the limitations of traditional perturbative estimates, transfer-matrix, S-matrix discretizations, and other schemes to provide a complete nonasymptotic variational description for electron transport in quantum waveguides.

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.

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.

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.

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.

Recently, it has been shown that on-shell scattering amplitudes can be constructed by the Feynman-tree theorem combined with the BCFW recursion relations. Since the BCFW relations are restricted to tree diagrams, the preceding application of the Feynman-tree theorem is essential. In this way amplitudes can be constructed by on-shell and gauge-invariant tree amplitudes. Here we want to apply this method to the electron-photon vertex correction. We present all the single, double, and triple phase-space tensor integrals explicitly and show that the sum of amplitudes coincides with the result of the conventional calculation of a virtual loop correction., 7 pages, 1 figure

An arrangement channel hyperspherical coordinate method for performing quantum scattering calculations on four-atom reactions is formulated. This method treats the vibrational and rotational states in different arrangement channels by a close-coupling expansion in nonorthogonal functions. The method is applied to the calculation of state-to-state probabilities for the OH+H2→H2O+H reaction. Good agreement is found with cumulative and state-selected reaction probabilities previously calculated by other methods. The major advantage of this general approach is that the whole S matrix can be obtained in a single calculation. © 1997 American Institute of Physics.

Scattering matrix theory is used to describe resonant optical properties of molecular monolayers. Three types of coupling are included: exciton-exciton, exciton-photon, and exciton-phonon coupling. We use the K-matrix formalism, developed originally to describe neutron scattering spectra in nuclear physics to compute the scattering of polaritons by phonons. This perturbation approach takes into account the three couplings and allows one to go beyond molecular exciton theory without the need of introducing additional boundary conditions for the polariton. We demonstrate that reflection, absorption, and extinction of light by 2D self-assembled monolayers of molecules containing quinque-thiophene chromophoric groups can be calculated. The extracted coherence length of the Frenkel exciton is discussed.

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.

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

The method of Gaussian weighted trajectories combines the classical description of gas-phase chemical reactions and Bohr quantization of final fragment vibrations. In practice, trajectories are assigned Gaussian statistical weights such that the closer the final vibrational actions to integer values, the larger the weights. This approach, called classical trajectory method with Gaussian binning (CT-GB) in the following, is a practical implementation of classical S matrix theory (CSMT) in the random phase approximation. However, CSMT is non unitary and consequently, the most utilized version of CT-GB is not strictly normalized to unity. In other words, the sum of product and re-formed reagent state populations is not exactly equal to one. The purpose of this work is to show that normalizing these populations to unity should significantly improve the quality of the predictions for indirect reactions. This finding is illustrated from calculations on the D+ + H2 reaction.

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.

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 expected resonance structure for the low-mass single diffractive states from a Regge-dual model elaborated paper by the present authors in a previous is predicted. Estimates for the observable low-mass single diffraction dissociation (SDD) cross sections and efficiencies for single diffractive events simulated by PYTHIA 6.2 as a function of the diffractive mass are given., 8 pages, 9 figures. Minor changes. To be published in the Modern Physics Letters A

S-matrix reconstruction transforms are based on two stages of matrix transformation to remove the mismatch-induced errors. Over the years, these transforms are widely used in measurements of multiport devices using a two-port vector network analyzer, especially for noncoaxial applications because high-quality matched loads are hardly accessible. In this paper, analytical error analysis of the S-matrix reconstruction transforms is performed to develop the accuracy criterion that is explicitly expressed in matrix form in terms of the S-matrix of the multiport device and the reflection coefficient matrix of the auxiliary terminations. The analytical insights in this paper can pave the way for using strongly reflecting auxiliary terminations. For noncoaxial measurements, strongly reflecting termination, such as a short-circuited or an open-circuited transmission line is more repeatable, reliable, and economical than terminations with loss like resistors. Consequently, the use of strongly reflecting auxiliary terminations is speculated to ease noncoaxial multiport measurements.

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.

The Q-values and half-lives of several heavy α decaying systems are calculated using the relativistic mean field (RMF) theory-based microscopic α-daughter nucleus potential. A unified procedure is adopted, using analytic S-matrix method and treating α-decay as the decay of the resonance state of the α-daughter nucleus system. The resonance parameters are obtained from the pole positions of the S-matrix in the complex k-plane and using these Q-values and half widths are evaluated. The calculation reproduces the experimental results well. We find that the present unified approach gives a good description of the data and compare well with those obtained by empirical formulae.

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.

Most of the decaying systems namely α-decay and proton radio activity have extremely narrow widths and hence are termed as quasi-bound states. There are three methods available for the computation of very narrow widths. First, the analytic S-matrix method which treats resonance as a pole in complex energy plane with its real part representing resonance energy and the imaginary part the half width. Another two methods namely (i) direct (D) method and (ii) distorted wave (DW) method are based on the property of the quasi-bound state wave function which is quite similar to a bound state wave function in the interior region and is matched with an outgoing spherical wave representing decaying behavior. We make a comparative study of these methods by applying them to the α-decay systems whose experimental results of Q-value and decay half-lives are known recently. It is observed that all the three methods give practically the same results for widths calculated at the same Q-value and explain the experimental results of Q-values and half-lives in several α-decaying nuclei quite well with a proper Coulomb nuclear interaction potential for the α+daughter nucleus system.

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

A multi-channel tunneling theory through a realistic hetero-junction barrier was developed using a mixed representation and studied within a few modes model. The transfer-matrix technique was employed to calculate spin-polarized transmission and reflection amplitudes between Bloch states in the semi-infinite leads. The transmission coefficients were used in Fisher and Lee’s formula for conductance. The multi-tunneling theory was applied within a real Fe/MgO/Fe hetero-junction barrier.

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.).

We present an accurate model for high-order harmonic generation beyond the Strong-Field Approximation which includes the field dressing of the bound state of the radiative transition. Our method does not imply the saddle point approximation. We demonstrate for a variety of parameters that our method gives better quantitative accuracy that the SFA calculations, performed either in velocity or length gauges. Comparisons have been made with the numerical solutions of the 3D single-active-electron time-dependent Schrodinger equation, that can be regarded as the exact description of this problem.

A theory of the evolution and collapse of pairs of resonances because of a change in the strength (thickness) of the inner barrier is developed in a model of effective masses and symmetric, square, potential barriers for an electron in a planar three-barrier structure. Analytical and numerical calculations of the spectral parameters (resonance energies and widths) are performed by the transmission coefficient and probability distribution function method using the transfer and S matrices. It is shown that the collapse of the resonance energies and widths of all quasistationary states in a symmetric three-barrier structure occurs for practically the same thicknesses of the inner barriers, somewhat greater than the total thickness of the outer barriers. It is established that with respect to the square-barrier model the δ model overestimates the resonance energies by 10% and the resonance widths by almost a factor of 2.