an efficient closed form derivation of spatial green s function for finite dielectric structures using characteristic green s function rational function fitting method 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

an accurate and systematic surface wave pole location method for multilayered media finding the surface wave modes in multilayered media is a problem that is of great importance in many full wave numerical electromagnetic solvers in this communication an efficient and systematic method is proposed to locate all of the surface wave poles for general multilayered structures it is observed that the characteristic equations can be cast into a function composed of eri kz i and ti tan kz i di where the ti occur for the substrates that have finite thicknesses the pole location method is carried out in the complex kzm plane where kzm represents the wave number along the z axis for the substrate with the maximum permittivity two sets of critical points are determined in the kzm plane according to the parameters of the structure since there is at most one pole between two consecutive critical points these critical points establish proper limits for the zero search algorithm muller s method can thus be applied to find the pole between the two consecutive critical points if it exists the proposed method is validated by means of several numerical examples

a fast analysis of scattering from large scale finite periodic microstrip patch arrays arranged on a non orthogonal lattice using sub entire domain basis functions a sub entire domain sed basis function method which was first introduced for modeling large scale finite periodic pec structures in free space has been extended for fast characterization of electromagnetic scattering from an electrically large planar finite periodic microstrip patch array the microstrip array may have a nonrectangular layout and non orthogonal lattice configurations e g hexagons or quadrangles based on the mixed potential integral equation and utilizing the proposed sed basis function algorithm the original large scale finite periodic array of microstrip patches can be efficiently simulated by decomposing it into two problems with matrix equations of small dimensions the first is to construct the sed basis functions for the corresponding microstrip arrays with orthogonal non orthogonal lattices three kinds of the sed basis functions are constructed including those related to the edge patch elements the interior patch elements and the corner patch elements the second is to solve the system equation with significantly reduced problem dimension as compared to the original larger problem based on the obtained sed basis functions the reduced matrix equation of small size can be generated by the galerkin procedure and solved by use of the lu lower upper decomposition based direct solver which results in a fast solution the accuracy and efficiency of the developed algorithms are demonstrated by numerical tests that include the scattering from several large scale finite periodic arrays of microstrip patches with rectangular non orthogonal lattices

efficient determination of the poles and residues of spectral domain multilayered green s functions that are relevant in far field calculations in this work the total least squares algorithm tlsa is applied to the determination of the proper and improper poles of spectral domain multilayered green s functions that are closer to the branch point and to the determination of the residues at these poles the introduction of an adequate transformation in the spectral domain permits that the tlsa provides accurate values of the poles and residues regardless of the proximity of the poles to the branch point it is shown that the poles and residues supplied by the tlsa can be used to write the far field of the spatial domain green s functions in terms of closed form expressions that are reliable in a wide variety of scenarios

unbounded and scattered field representations of the dyadic green s functions for planar stratified bianisotropic media this paper presents a rigorous formulation of the spectral domain dyadic green s functions for planar stratified bianisotropic media the media may consist of any number of layers bounded by optional impedance admittance walls both electric and magnetic dyadic green s functions for arbitrary field and source locations are derived simultaneously based on the principle of scattering superposition these dyadics are decomposed into unbounded and scattered parts the scattered dyadic green s functions are determined without cumbersome operations using the concepts of effective reflection and transmission of outward bounded and inward bounded waves the scattering coefficient matrices are expressed in compact and convenient forms involving global reflection and transmission matrices corresponding to the impedance admittance boundary walls the global reflection matrices are related directly to the wall impedance admittance dyadics for illustration the general expressions of dyadic green s functions are applied to the configuration of a grounded bianisotropic slab embedded in isotropic halfspace

arbitrarily oriented perfectly conducting wedge over a dielectric half space diffraction and total far field complex scattering targets are often made by structures constituted by wedges and penetrable substrates which may interact at near field in this paper we describe a complete procedure to study this problem with possible developments in radar technologies like gpr antenna development or electromagnetic compatibility tips near substrates the diffraction of an incident plane wave by a perfectly conducting pec wedge over a dielectric half space is studied using generalized wiener hopf equations gwhes and the solution is obtained using analytical and numerical analytical approaches that reduce the wiener hopf wh factorization to integral equations ies the mathematical aspects are described in a unified and consistent theory for angular and layered region problems the proposed procedure is valid for the general case and the paper focuses on e polarization at normal incidence the solutions are given in terms of geometrical uniform theory of diffraction gtd utd diffraction coefficients and total far fields for engineering applications this paper presents several numerical test cases that show the validity of the proposed method

closed form uniform asymptotic expansions of green s functions in layered media far field closed form expressions are derived for spatial domain multilayered green s functions gf for the derivation of these far field expressions the spectral domain multilayered gf are approximated by means of the total least square algorithm tlsa in terms of the spectral variable u0 k 2 k02 1 2 and uniform asymptotic expansions are determined for the sommerfeld integrals of the resulting tlsa approximations numerical results show that the far field asymptotic expressions are accurate within 0 1 for distances between source and field points larger than one free space wavelength also it is shown that the hybrid use of the discrete complex image method and the tlsa in terms of the spectral variable k leads to near field closed form expressions of multilayered gf that are typically accurate within 0 1 for distances between source and field points smaller than one free space wavelength therefore the combination of the novel far field asymptotic expressions and the well known near field expressions makes it possible to compute multilayered gf with a great accuracy in the whole range of distances between source and field points and in a wide range of frequencies

interaction of electromagnetic waves with 3 d arbitrarily shaped homogeneous chiral targets in the presence of a lossy half space the interaction of electromagnetic waves with an arbitrarily shaped three dimensional 3 d homogeneous chiral object located above a lossy half space is investigated using the method of moments mom via the coupled mixed potential integral equations mpies based on the surface equivalence principle the equivalent surface electric and magnetic currents are used to replace the homogeneous chiral target in the presence of the half space two coupled mpies are developed for the unknown equivalent surface electric and magnetic currents by utilizing the continuity condition of the tangential total electric and magnetic field components on the chiral body s surface the well known galerkin procedure with rao wilton glisson rwg basis functions is applied to solve this problem the spatial domain half space green s functions are obtained from the corresponding spectral domain green s functions via the discrete complex image method dcim combined with the generalized pencil of function gpof technique the reciprocity theorem is employed to calculate the far zone scattered field numerical results are presented for characterizing electromagnetic scattering by a 3 d arbitrarily shaped homogenous chiral object located above a lossy half space so as to demonstrate the accuracy and efficiency of the proposed technique

accurate approximation of green s functions in planar stratified media in terms of a finite sum of spherical and cylindrical waves a robust and computationally expedient methodology is presented for accurate closed form approximation of the green s functions used in the mixed potential integral equation statement of the electromagnetic boundary value problem in planar stratified media the proposed methodology is based on the fitting of the spectrum of the green s function after the extraction of the quasistatic part making use of rational functions the effectiveness and robustness of the proposed methodology rely upon the proper sampling of the spectrum in order to improve the accuracy of the rational function fit the resulting closed form approximation is in terms of both spherical and cylindrical waves thus high accuracy is obtained in the approximation of the green s function irrespective of the distance of the observation point from the source the methodology is validated through its application to the approximation of the green s function for a multi layered planar dielectric stack

efficient computation of 1 d periodic layered mixed potentials for the analysis of leaky wave antennas with vertical elements an efficient mixed potential integral equation formulation is proposed for the analysis of one dimensional 1 d periodic leaky wave antennas lwas based on planar stratified configurations with inclusions of arbitrarily oriented metallic or dielectric perturbations both the transverse and vertical components of the mixed potential green s functions due to a 1 d phased array of dipoles in a layered medium are accelerated using suitable homogeneous medium asymptotic extractions from the standard spectral series of floquet harmonics a novel acceleration procedure is applied for the computation of the vertical potentials whose extracted terms can be expressed as potentials from a 1 d phased array of half line sources in a homogeneous medium their numerical calculation requires a suitable modification of the ewald method thus resulting in new modified spectral and spatial series having gaussian convergence even in the case of complex modes and improper harmonics numerical comparisons for the 1 d periodic potentials both in the case of bounded and unbounded e g leaky harmonics validate the efficiency and accuracy of the proposed acceleration technique the method is illustrated and verified by determining the dispersion behavior of both bound and leaky modes for several lwa test cases

a hybrid 2 d 3 d multilevel green s function interpolation method for electrically large multilayered problems the multilevel green s function interpolation method has been implemented to solve the general electrically large multilayered problems a new hybrid 2 d and 3 d h2 d 3 d multilevel interpolation method and a cross level translation scheme are devised for the specific problems from which a quad tree is constructed the interpolation of the multilayered medium green s function using radial basis function is then studied to further accelerate the computation a subdomain fast fourier transform scheme and a sparse approximated inverse preconditioner with a new discarding strategy are also incorporated into the algorithm as numerical examples typical microstrip antenna arrays a metasurface antenna and electromagnetic bandgap integrated antenna arrays are analyzed with the proposed method and excellent performance is observed in both accuracy and efficiency

numerical integration of related hankel transforms by quadrature and continued fraction expansion an algorithm is presented for the accurate evaluation of hankel or bessel transforms of algebraically related kernel functions defined here as the non bessel function portion of the integrand that is more widely applicable than the standard digital filter methods without enormous increases in computational burden the algorithm performs the automatic integration of the product of the kernel and bessel functions between the asymptotic zero crossings of the latter and sums the series of partial integrations using a continued fraction expansion equivalent to an analytic continuation of the series the integrands may be saved to allow the rapid computation of related transforms without recalculating the kernel or bessel functions and the integration steps use interlacing quadrature formulas so that no function evaluations are wasted when it is necessary to increase the order of the quadrature rule the continued fraction algorithm allows very slowly divergent or even formally divergent integrals to be computed quite easily the local error is controlled at each step in the algorithm and accuracy is limited largely by machine resolution the algorithm is written in fortran and is listed in an appendix along with a driver program that illustrates its features the driver program and subroutine are available from the seg business offtce

direct rational function fitting method for accurate evaluation of sommerfeld integrals in stratified media the current work proposes a direct rational function fitting method employing cylindrical waves alone for the accurate evaluation of sommerfeld integrals for planar multilayered structures three are the key points of the effort 1 until now relative works require the extraction of the quasi static asymptotic terms and branch cut continuous wave contribution explicitly in the current one the explicit treatment of those terms is avoided the proposed methodology is based on the direct fitting of the spectrum of the green s function by rational functions thus it provides the spatial green s function solely in terms of cylindrical waves 2 the effectiveness robustness and accuracy improvement of the rational function fit rely upon the proper sampling of the spectrum this accurate fitting is possible because instead of avoiding large variations of the spectral kernel we introduce proper paths to include more variation and thus more spectrum information before we apply the modified vectfit algorithm 3 furthermore proper weighting of the vectfit is proposed in order to guide the algorithm in providing increased accuracy in specific desired areas of the horizontal distance between the source and observation points armed with the above the direct rational function fitting method provides accurate results both for the near and far field regions various examples among them the correct treatment of a two branch case are given that prove the excellent performance and robustness of the proposed approach

full wave analysis of antennas containing horizontal and vertical metallizations embedded in planar multilayered media the paper presents an efficient way of evaluating green s functions arising in planar stratified media in the spectral domain the components are split into a singular and a regular part the latter is expressed in terms of exactly four boundary coefficients whose computation is extracted from the numerical kernel of the method and the former is evaluated analytically via the sommerfeld identity the spatial counterparts are then evaluated by a method which combines the advantages of the complex image method cim and the direct numerical evaluation of the sommerfeld integral while trying to avoid their respective drawbacks the result is an efficient technique to treat horizontal and vertical metallizations embedded in multilayered media results for a three dimensional 3d planar inverted f antenna are obtained with this technique and successfully compared to measurements

a fast volume integral equation solver for electromagnetic scattering from large inhomogeneous objects in planarly layered media a newly developed iterative method the stabilized biconjugate gradient fast fourier transform bcgs fft method is applied to simulate electromagnetic scattering from large inhomogeneous objects embedded in a planarly layered medium in this fast solver the weak form formulation is applied to obtain a less singular discretization of the volume electric field integral equation several techniques are utilized to speed up the dyadic green s function evaluation to accelerate the operation of the dyadic green s function on an induced current i e the green s operation the green s function is split into convolutional and correlational components so that fft can be applied the cpu time and memory cost of this bcgs fft method is o nlogn and o n respectively where n is the number of unknowns significantly more efficient than the method of moments mom as a result this method is capable of solving large scale electromagnetic scattering problems in a planarly layered background a large scale scattering problem in a layered medium with more than three million unknowns has been solved on a sun ultra 60 workstation with 1 2 gbytes memory

an efficient perfectly matched layer based multilevel fast multipole algorithm for large planar microwave structures an efficient multilevel fast multipole algorithm mlfma formalism to model radiation and scattering by from large planar microwave structures is presented the technique relies on an electric field integral equation efie formulation and a series expansion for the green dyadic based on the use of perfectly matched layers pml in this way a new pml mlfma is developed to efficiently evaluate matrix vector multiplications arising in the iterative solution of the scattering problem the computational complexity of the new algorithm scales down to o n for electrically large structures the theory is validated by means of several illustrative numerical examples

accelerated macro basis functions analysis of finite printed antenna arrays through 2d and 3d multipole expansions an efficient technique is presented for the analysis of finite printed antenna arrays made of identical elements it is based on a closed form expression for the spatial domain green s function gf given as a finite sum of cylindrical waves obtained through rational function fitting plus one spherical wave from there a multipole expansion can be obtained for planar layered medium gfs the macro basis function mbf technique is applied to the method of moments mom solution of a mixed potential integral equation this reduces the size of the mom impedance matrix and allows for a direct solution however the evaluation of the entries of this reduced matrix becomes the dominant contribution to the total computation time the aforementioned multipole expansion is exploited to provide a fast construction of the reduced mom matrix whose elements are the reaction integrals between the mbfs considered to characterize the currents on the array element the complexity of evaluating the interactions between mbfs is found to be dominated by the calculations related to the spherical wave term thus taking into account the layered medium does not increase the order of the complexity with respect to a multipole accelerated computation of reaction integrals in a homogeneous medium

an efficient numerical evaluation of the green s function for the helmholtz operator on periodic structures abstract numerical methods which are based on boundary integral formulations require the numerical evaluation of the green s function associated with the problem in the case of periodic structures the green s function is often an infinite series this infinite series may converge slowly making numerical evaluation expensive here we present a practical computer implementation of a technique which dramatically speeds up the convergence of the infinite series green s function associated with the helmholtz operator to show the consequences of using this technique we include some numerical examples

treatment of singularities and quasi static terms in the efie analysis of planar structures this paper reports on some mathematical and numerical details of the application of the electric field integral equation efie method to the analysis of planar structures printed on multilayered substrates closed form expressions for singular and hypersingular terms of the transverse electric field green s dyadic tefgd are identified so that they can be explicitly extracted out before solving the efie the problems due to the presence of the hypersingular contribution usually argued to preclude the application of the efie to planar structures are solved in addition a low frequency expansion of the tefgd corresponding to a single layer substrate is carried out to recognize nonsingular electrostatic type contributions that can eventually become very important for computational purposes

analysis of an infinite periodic array of slot radiators with dielectric loading an efficient numerical procedure for determining the radiation characteristics of an infinite periodic array of slots in a conducting screen is presented the procedure employs a novel mixed potential integral equation formulation and is solved by the method of moments subdomain type basis functions are used to provide the flexibility to model arbitrarily shaped slots analysis is carried out to account for dielectric layers ground planes or cavities placed on either side of the slot series acceleration techniques are employed to reduce significantly the computation time required to sum the series representing the periodic green s function the numerical scheme developed is applied to obtain quantities such as the slot field distribution and input admittance as a function of the array scan angle where possible numerical results obtained are compared with data available in the literature data for the half space case are found to agree with those of a y grinev et al 1978 except for the case of multilayer dielectric loading

the weighted averages algorithm revisited the classic weighted averages wa algorithm for the evaluation of sommerfeld like integrals is reviewed and reappraised as a result a new version of the wa algorithm called generalized wa is introduced the new version can be considered as a generalization of the well established holder and cesaro means used to sum divergent series generalized wa exhibits a more compact formulation devoid of iterative and recursive steps and a wider range of applications it is more robust as it provides a unique formulation valid for monotonic and oscillating functions the implementation of the new version is easier and more economical in terms of basic operations preliminary numerical examples show that generalized wa also outperforms in terms of accuracy the classic wa algorithm which is currently recognized as the most competitive algorithm to evaluate sommerfeld integral tails

a fast analysis of scattering and radiation of large microstrip antenna arrays an accurate and efficient method that combines the precorrected fast fourier transform fft method and the discrete complex image method dcim is presented to characterize the scattering and radiation properties of arbitrarily shaped microstrip patch antennas in this method the mixed potential integral equation mpie is discretized in the spatial domain by means of the discrete complex image method the resultant system is solved iteratively using the generalized conjugate residual method gcr and the precorrected fft technique is used to speed up the matrix vector multiplication the precorrected fft eliminates the need to generate and store the usual square impedance matrix and thus leads to a significant reduction in memory requirement and computational cost numerical results are presented for arbitrarily shaped microstrip antenna arrays to demonstrate the accuracy and efficiency of this technique

a complex image reduction technique using genetic algorithm for the mom solution of half space mpie the discrete complex image method dcim has been widely used to analytically approximate the sommerfeld integrals sis of green s functions in layered media this method has been greatly improved in accuracy and generality in the past years but has resulted in a large amount of complex images it is found that using so many complex images for si approximation in method of moment mom applications is redundant and inefficient to reduce the number of complex images a technique by means of genetic algorithm is proposed and applied to the mom solution of the half space mixed potential integral equation mpie

analysis of a plane wave excited subwavelength circular aperture in a planar conducting screen illuminating a multilayer uniaxial sample a spectral domain analysis is presented of a plane wave excited subwavelength circular aperture in a planar perfectly conducting screen in close proximity to a multilayer stack which may comprise uniaxially anisotropic slices the formulation employs the bethe bouwkamp aperture model for the general case of oblique incidence and it combines the hankel transform method with a transmission line network analogue of the medium which facilitates the inclusion of any number of material layers the electromagnetic fields are expressed in terms of one dimensional 1 d hankel transform integrals which are efficiently evaluated by a numerical quadrature along a suitably selected path with convergence acceleration by extrapolation sample numerical results are presented to demonstrate the validity of the method and its utility in the modeling of multilayer near field lenses and aperture type probes of near field optical microscopy

critical distance for grating lobe series estimating a transition or critical distance above a planar periodic array of point sources radiating into an unbounded medium is considered it is shown that as an observation point approaches a periodic planar phased array of point sources the corresponding spectral domain green s function or grating lobe series converges much more slowly than an equivalent mixed domain representation exhibiting gaussian convergence for a given argument of the green s function the critical transition distance above the array for which both representations take the same time to compute can be estimated numerically since phased array antenna structures with cavity or waveguide type backings often have dimensions that fall well below the critical distance investigations of such structures would seem to benefit significantly from formulations incorporating such hybrid green s functions

an accurate derivation of spatial green s function for finite dielectric structures using characteristic green s function perfectly matched layer method a closed form spatial green s function for a truncated dielectric slab is derived by using a combination of the characteristic green s function cgf and perfectly matched layer pml method the original structure is terminated by pml that is backed by perfect electric conductor pec in semi infinite layer at the top and or bottom the eigenmodes of the closed structure by pml construct the continuous spectrum contribution of the original structure efficiently derived green s function is exact for separable finite structure while it is approximate for nonseparable one especially in the corners generalized scattering matrix gsm of truncating surface which contains possible conversions between all modes is computed with mode matching method it is demonstrated that by importing gsm in cgf formulation more exact results for nonseparable structures can be obtained the source and observation points dependence is analytically available in derived expression and allows very efficient computation and storage of the spatial green s function very close to the source where the large number of modes must be considered shank s transform is used to preserve the efficiency of the method the main advantage of the method lies in its accuracy and low dependency of the result to the pml parameters excellent agreements with the rigorous method of moments mom are shown in several examples

accelerating the convergence of series representing the free space periodic green s function a method for improving the convergence of the series representing the doubly periodic free space green s function is presented the method consists of successively applying three different transformations to the green s function spectral representation kummer s transformation is first applied to convert the slowly converging spectral representation into the sum of a rapidly converging series and a slowly converging series the latter series is recognized as the spectral representation of the original periodic source distribution radiating in a medium with an imaginary wavenumber application of the poisson transformation to this series renders it exponentially convergent since it effectively represents propagation of point source contributions through a medium with imaginary wavenumber finally shanks transform is plotted versus the number of terms taken in the series numerical results confirm that an improvement in the convergence rate of the series is achieved for a particular convergence criterion

a homotopy method for locating all the poles of a parallel plate waveguide with the pml in this paper a homotopy method for locating all the poles of a parallel plate waveguide with the perfectly matched layer is proposed as is well known the green s functions for an open multilayered medium can be approximated by those for a parallel plate waveguide with the perfectly matched layer while the latter green s functions can be theoretically expressed into series expansions of their own eigenmodes without involving any numerical integrations the homotopy method here is applied for finding the desired mode poles in this method the newton raphson iteration is employed to solve every node equation except the start node equation while the dichotomy method is used to solve the start node equation the roots of the end node equation are just the desired mode poles with the proposed method the green s functions for a lossy or lossless multilayered medium can be efficiently calculated by the corresponding series expansions some numerical examples are provided to examine the robustness and accuracy of the proposed method

gaussian ring basis functions for the analysis of modulated metasurface antennas this paper presents a novel type of basis functions whose spectral and space domain properties can be exploited for the efficient method of moments mom analysis of planar metasurface mts antennas the effect of the homogenized mts is introduced in the integral equation as an impedance boundary condition ibc the proposed basis functions are shaped as gaussian type rings with small width and linear azimuthal phase the analytical form of the spectrum of the gaussian ring basis allows for a closed form evaluation of the mom impedance matrix s entries moreover these basis functions account for the global evolution of the surface current density in an effective manner reducing the size of the mom system of equations with respect to the case of subdomain basis functions these features allow one to carry out a direct solution for problems with a diameter of up to 15 wavelengths in less than 1 min using a conventional laptop the applicability on practical antennas has been tested through the full wave analysis of mts antennas implemented with small printed elements

electromagnetic modeling of three dimensional bodies in layered earths using integral equations we have developed an algorithm based on the method of integral equations to simulate the electromagnetic responses of three dimensional bodies in layered earths the inhomogeneities are replaced by an equivalent current distribution which is approximated by pulse basis functions a matrix equation is constructed using the electric tensor green s function appropriate to a layered earth and it is solved for the vector current in each cell subsequently scattered fields are found by integrating electric and magnetic tensor green s functions over the scattering currents efficient evaluation of the tensor green s functions is a major consideration in reducing computation time we find that tabulation and interpolation of the six electric and five magnetic hankel transforms defining the secondary green s functions is preferable to any direct hankel transform calculation using linear filters a comparison of responses over elongate three dimensional 3 d bodies with responses over two dimensional 2 d bodie

regularized integral equations and curvilinear boundary elements for electromagnetic wave scattering in three dimensions the boundary integral equations bies in their original forms which govern the electromagnetic em wave scattering in three dimensional space contain at least a hypersingularity 1 r sup 3 or a cauchy singularity 1 r sup 2 usually both thus obtaining reliable numerical solutions using such equations requires considerable care especially when developing systematic numerical integration procedures for realistic problems regularized bies for the numerical computation of time harmonic em scattering fields due to arbitrarily shaped scatterers are introduced two regularization approaches utilizing an isolation method plus a mapping are presented to remove all singularities prior to numerical integration both approaches differ from all existing approaches to em scattering problems both work for integral equations initially containing either hypersingularities or cauchy singularities without the need to introduce surface divergences or other derivatives of the em fields on the boundary also neither approach is limited to flat surfaces nor flat element models of curved surfaces the muller linear combination of the electric and magnetic field integral equations efie and mfie is used to avoid the resonance difficulty that is usually associated with integral equation based formulations some preliminary numerical results for em scattering due to single and multiple dielectric spheres are presented and compared with analytical solutions

waveguide excited microstrip patch antenna theory and experiment an arbitrarily shaped microstrip patch antenna excited through an arbitrarily shaped aperture in the mouth of a rectangular waveguide is investigated theoretically and experimentally the metallic patch resides on a dielectric substrate grounded by the waveguide flange and may be covered by a dielectric superstrate the substrate and superstrate if present consists of one or more planar homogeneous layers which may exhibit uniaxial anisotropy the analysis is based on the space domain integral equation approach more specifically the green s functions for the layered medium and the waveguide are used to formulate a coupled set of integral equations for the patch current and the aperture electric field the layered medium green s function is expressed in terms of sommerfeld type integrals and the waveguide green s function in terms of floquet series which are both accelerated to reduce the computational effort the coupled integral equations are solved by the method of moments using vector basis functions defined over triangular subdomains the dominant mode reflection coefficient in the waveguide and the far field radiation patterns are then found from the computed aperture field and patch current distributions the radar cross section rcs of a plane wave excited structure is obtained in a like manner sample numerical results are presented and are found to be in good agreement with measurements and with published data

a new approach to dyadic green s function in spectral domain a new method is proposed to derive the dyadic green s function for stratified dielectric layers from the wave equation in spectral domain the result is a clear equivalent circuit of the whole structure which combines the te and tm modes by hybrid block matrices it is simple to apply and evaluate the relation to the conventional immittance approach is shown by means of a similarity transform which diagonalizes the submatrices the simplicity of the method is demonstrated in the application to the well known example of a single microstrip patch on a grounded dielectric layer as well as structures with multiple layers and metallizations in arbitrary interfaces

acceleration of mixed potentials from vertical currents in layered media for 2 d structures with 1 d periodicity an original acceleration procedure is proposed for the efficient calculation of the vertical components of the dyadic and scalar mixed potential layered media periodic green s functions the extraction of suitable asymptotic terms i e quasi static images is performed in order to speed up the convergence of the relevant spectral series this procedure well known for planar green s functions is here generalized to treat the off diagonal dyadic components and the corrective scalar potential arising from the vertical currents the extracted terms are homogeneous medium green s functions due to a periodic phased array of half plane currents computed through a modified ewald method leading to a pair of gaussian convergent series the highly improved convergence rate of the relevant series is shown and the reduction of the computation time is numerically tested and discussed the algorithm is implemented in eiger an open source code based on the method of moments several periodic structures are analyzed and fully validated through numerical comparisons the proposed formulation has been proven very efficient accurate and stable

generalized ray theory for time domain electromagnetic fields in horizontally layered media generalized ray theory for time domain electromagnetic fields in a horizontally layered medium is developed it can be considered as the time domain equivalent of the intensively studied green s function formulation in frequency domain after introducing appropriate integral transformations and source type field representations the solution is written out in terms of generalized ray constituents whose space time counterparts are constructed with the aid of the cagniard dehoop technique the formulation lays the foundation to rigorously study time domain field behavior in numerous practical topologies where a stratified multilayer is involved such as planar antennas and circuits but also electromagnetic compatibility emc and propagation problems illustrative numerical results are presented

application of dcim to mpie mom analysis of 3d pec objects in multilayered media the formulation c green s functions for multilayered media are reformulated in this paper to extract z dependent part when the source and observation points are in different layers the discrete complex image method dcim is applied to obtain complex images independent on z but dependent on z spl acute for simulation of three dimensional 3 d perfectly electrical conduction pec objects penetrating two or more layers tables of complex images are built in a z spl acute grid during the matrix filling stage of the mixed potential integral equation together with method of moments mpie mom the spatial domain green s functions are interpolated from values in the z spl acute grid while these values are calculated from complex images in the z spl acute grid this interpolation scheme is more efficient than those directly storing the spatial domain green s functions numerical examples are given for analyzing a dipole in a two layered media

computation of the sommerfeld integral tails using the matrix pencil method the oscillating infinite domain sommerfeld integrals si are difficult to integrate using a numerical procedure when dealing with structures in a layered media even though several researchers have attempted to do that generally integration along the real axis is used to compute the si however significant computational effort is required to integrate the oscillating and slowly decaying function along the tail extrapolation methods are generally applied to accelerate the rate of convergence of these integrals however there are difficulties with the extrapolation methods such as locations for the breakpoints in this paper we illustrate a simplified approach for accurate and efficient calculation of the integrals dealing with the tails of the si in this paper we fit the tail by a sum of finite usually 10 to 20 complex exponentials using the matrix pencil method mpm the integral of the tail of the si is then simply calculated by summing some complex numbers no numerical integration is needed in this process as the integrals can be done analytically good accuracy is achieved with a small number of evaluations for the integral kernel 60 points for the mpm as compared with hundreds or thousands of functional evaluations using the traditional extrapolation methods along the tails of the si simulation results show that to obtain the similar accuracy in the evaluation of the si the mpm is approximately 10 times faster than the traditional extrapolation methods moreover since the mpm is robust to the effects of noise this method is more stable especially for large values of the horizontal distances the method proposed in this paper is thus a new and better technique to obtain accurate results for the computation of the green s function for a layered media in the spatial domain

a novel efficient technique for the calculation of the green s functions in rectangular waveguides based on accelerated series decomposition a new efficient technique for computing the green s functions inside rectangular waveguides is presented after a summary of the classical approaches and their difficulties a new strategy is proposed based on the decomposition of the main spectral series into simpler terms although the resulting series present better convergence rate several acceleration techniques are combined to further improve the efficiency several results are presented to demonstrate the improvements in convergence rates obtained using the new decomposition

a newly developed formulation suitable for matrix manipulation of layered medium green s functions based on a recently developed formulation of the dyadic green s function for layered media dglm this work gives the matrix element representation of the dglm for general rwg basis functions including basis functions straddling across different layers and half rwg basis function attached to an infinite ground plane it has been rigorously proved that this representation is absent of any undesired line integrals the same as the popular michalski zheng s formulation of type c this work also gives the analytical solution for some typical cylindrically symmetric problems which can be used to validate any formulation for layered medium problems

a numerical methodology for efficient evaluation of 2d sommerfeld integrals in the dielectric half space problem the analysis of 2d scattering in the presence of a dielectric half space by integral equation formulations involves repeated evaluation of sommerfeld integrals deformation of the contour to the steepest descent path results in a well behaved integrand that can be readily integrated a well known drawback of this method is that an analytical expression for the path is available only for evaluation of the reflected fields but not for the evaluation of the transmitted fields a simple scheme for numerical determination of the steepest descent path valid for both cases is presented the computational cost of the numerical determination is comparable to that of evaluating the analytical expression for the steepest descent path for reflected fields when necessary contributions from branch cut integrals and a second saddle point are taken into account certain ranges of the input parameters which result in integrands that vary rapidly in the neighborhood of the saddle point require special treatment alternative paths and specialized gaussian quadrature rules for these cases are also proposed an implementation of the proposed numerically determined steepest descent path nd sdp method is freely available for download

clarification of issues on the closed form green s functions in stratified media the closed form green s functions cfgf derived for the vector and scalar potentials in planar multilayer media have been revisited to clarify some issues and misunderstandings on the derivation of these green s functions in addition the range of validity of these green s functions is assessed with and without explicit evaluation of the surface wave contributions as it is well known the derivation of the cfgf begins with the approximation of the spectral domain green s functions by complex exponentials and continues with applying the sommerfeld identity to cast these approximated spectral domain green s functions into the space domain in closed forms questions and misunderstandings of this derivation which have mainly originated from the approximation process of the spectral domain green s functions in terms of complex exponentials can be categorized and discussed under the topics of 1 branch point contributions 2 surface wave pole contributions and 3 the accuracy of the obtained cfgf when these issues are clarified the region of validity of the cfgf so obtained may be defined better therefore in this paper these issues will be addressed first and then their origins and possible remedies will be provided with solid analysis and numerical demonstrations

quasi 3 d mixed potential integral equation formulation for periodic structures this paper introduces the use of the quasi 3 d mixed potential integral equation formulation for structures with a periodicity in two dimensions the quasi 3 d formulation allows to use both horizontal and vertical conductors and dielectric inclusions the key innovation is the use of an effective algorithm to calculate periodic green s functions pgfs for vertical currents in the planar multilayered background medium this algorithm retains the same scheme as for a single source green s function gf in both cases the gfs are calculated via an inverse fourier transform of the gfs in the spectral domain which are known in closed form in order to remedy the poor convergence for small source observation distances an asymptotic extraction is used yielding a very compact algorithm and acceleration techniques are applied simple guidelines are proposed to construct asymptotes having the required leading terms and a good convergence it is shown that many acceleration algorithms widely used in literature are actually able to perform well only in specific circumstances as far as the authors can see there is still no general and robust technique yielding highly accurate results under all circumstances several examples illustrate the efficiency of the technique

multilayered media green s functions in integral equation formulations a compact representation is given of the electric and magnetic type dyadic green s functions for plane stratified multilayered uniaxial media based on the transmission line network analog along the aids normal to the stratification furthermore mixed potential integral equations are derived within the framework of this transmission line formalism for arbitrarily shaped conducting or penetrable objects embedded in the multilayered medium the development emphasizes laterally unbounded environments but an extension to the case of a medium enclosed by a rectangular shield is also included

fast and accurate mom analysis of periodic arrays of multilayered stacked rectangular patches with application to the design of reflectarray antennas the scattering of plane waves by periodic arrays of stacked rectangular patches in multilayered substrates is a problem that has to be solved many times when designing reflectarray antennas made of those patches under the local periodicity assumption the solution to the periodic multilayered problem has been traditionally carried out by means of the galerkin s version of the method of moments mom in the spectral domain this approach involves the computation of double infinite summations and whereas some of these summations converge very fast some other converge very slowly in this paper the slowly convergent summations are computed by making use of an enhanced mixed potential integral equation mpie formulation of the mom in the spatial domain this enhanced formulation is based on the interpolation of the multilayered periodic green s functions and on the efficient computation of the four dimensional 4 d integrals leading to the mom matrix entries both the novel hybrid spectral spatial mom code and the standard spectral domain mom code have been used for the design of a contoured beam reflectarray antenna it has been verified that the spectral spatial mom code requires cpu times that are typically 30 times smaller than those required by the pure spectral domain mom code

accurate and efficient computation of layered medium doubly periodic green s function in matrix friendly formulation this communication proposes a novel approach to evaluate the doubly periodic green s function for layered medium in matrix friendly formulation several techniques including factorization of the green s function generalized pencil of function method and high order taylor expansion are employed in a delicate manner to derive the high order asymptotic expressions which are then evaluated by new fast convergent series derived from ewald transformation this approach delivers fast and highly accurate results as well as high order convergence and also allows fast frequency sweep for calculating brillouin diagram in eigenvalue problem and for normal incidence in scattering problem

enhanced mom analysis of the scattering by periodic strip gratings in multilayered substrates the method of moments mom is applied to the analysis of the scattering of a multilayered periodic strip grating by a plane wave with oblique incidence and arbitrary polarization although this problem has been traditionally solved by means of the mom in the spectral domain this is an approach which leads to the computation of slowly convergent infinite summations in this paper the problem is solved by means of the mixed potential integral equation mpie formulation of the mom in the spatial domain while applying the mom in the spatial domain two improvements are introduced which lead to important cpu time savings first the multilayered periodic green s functions are accurately interpolated in terms of chebyshev polynomials second half the integrals involved in the computation of the mom matrix entries are obtained in closed form as a consequence of these two improvements the spatial domain version of the mom presented in this paper turns out to be between one and two orders of magnitude faster than the conventional spectral domain version when basis functions that account for edge singularities are used in the modeling of the current density on the metallizations

efficient formulation of closed form green s functions for general electric and magnetic sources in multilayered media a complete set of closed form multilayered media green s functions with general electric and magnetic sources is presented the green s functions are written in the mixed potential integral equation formulation which is consistent with the michalski zheng 1990 c formulation in addition the differentiations of the curl operator are taken in the spectral domain this leads to calculation of the first and second order sommerfeld integrals and differentiation with respect to z traditionally only the zeroth order sommerfeld integrals are expressed in the closed form by the discrete complex image method with sommerfeld identity here we present a generalized sommerfeld identity by which also the higher order sommerfeld integrals can be expressed in closed form the closed form expressions are derived so that all required differentiations are obtained in closed form and numerical differentiation can be avoided in addition the number of required closed form green s functions is minimized in the source layer only three and in other layers four spectral domain functions have to be considered in writing the mixed potential green s functions with general electric and magnetic source in closed form in the source layer the derived closed form green s expressions are valid for all field and source points and in the other layers they are valid for a fixed z coordinate of a field point the power of the formulation becomes evident when both the electric and magnetic sources are present e g in the electromagnetic scattering by dielectric buried objects

the implementation of multilevel green s function interpolation method for full wave electromagnetic problems we extend the multilevel green s function interpolation method mlgfim developed for quasi electrostatic problems to full wave simulations the difficulty in applying the interpolation approach lies in the additional rapidly changing phase term associated with the full wave green s functions to enhance the efficiency and accuracy of the full wave green s function interpolation a scattered point set consisting of two staggered tartan grids in conjunction with radial basis function interpolation is employed to further reduce the computational complexity the qr factorization technique is applied to compress the low rank green s function matrices for electromagnetic scattering from pec spheres up to a diameter of eight wavelengths the proposed method compares well with mie s scattering in accuracy and shows the o nlogn efficiency as the method is kernel independent its extension to structures in layered medium is straightforward in the numerical simulations of finite microstrip patch arrays up to 11 by 11 elements the proposed method demonstrates very favorable dependencies of cpu time and memory storage requirement versus the number of unknowns

a hybrid three dimensional electromagnetic modeling scheme we present an efficient numerical method for computing electromagnetic em scattering of arbitrary three dimensional 3 d local inhomogeneities buried in a uniform or two layered earth in this scheme the inhomogeneity is enclosed by a volume whose conductivity is discretized by a finite element mesh and whose boundary is only a slight distance away from the inhomogeneity the scheme uses two sets of independent equations the first is a set of finite element equations derived from a variational integral and the second is a mathematical expression for the fields at the boundany in terms of electric fields inside the boundary the green s function is used to derive the second set of equations an iterative algorithm has been developed to solve these two sets of equations the solutions are the electric fields at nodes inside the finite element mesh the scattered fields anywhere may then be obtained by performing volume integrations over the inhomogeneous region the scheme is used for modeling 3 d inho

two dimensional discrete complex image method dcim for closed form green s function of arbitrary 3d structures in general multilayered media the traditional discrete complex image method dcim is not efficient when the source and field points are in different layers because all the spatial coordinates can not be analytically included in the image terms in spatial domain a two dimensional method 2d dcim is introduced in this paper in the new methodology we reorganize the spectral kernel as a 2d function we use the 2d matrix pencil method 2d mpm to fit this 2d function and to generate a set of complex images independent of any spatial coordinates the closed form spatial domain green s function can be obtained for arbitrary locations of source and field points in general multilayered media compared with traditional 1d dcim we do not have to run mpm for each vertical combination of source and field points the efficiency of the matrix filling kernel of method of moments mom is significantly improved

fast calculations of dyadic green s functions for electromagnetic scattering in a multilayered medium abstract in this paper we introduce a novel acceleration method for the calculation of dyadic green s functions for the mixed potential integral equation formulation of electromagnetic scattering of scatterers embedded in a multilayered medium numerical results are provided to demonstrate the efficiency and accuracy of the proposed method

higher order frequency domain computational electromagnetics a review of the higher order computational electromagnetics cem for antenna wireless and microwave engineering applications is presented higher order cem techniques use current field basis functions of higher orders defined on large e g on the order of a wavelength in each dimension curvilinear geometrical elements which greatly reduces the number of unknowns for a given problem the paper reviews all major surface volume integral and differential equation electromagnetic formulations within a higher order computational framework focusing on frequency domain solutions with a systematic and unified review of generalized curved parametric quadrilateral triangular hexahedral and tetrahedral elements and various types of higher order hierarchical and interpolatory vector basis functions in both divergence and curl conforming arrangements a large number of actual higher order techniques representing various combinations of formulations elements bases and solution procedures are identified and discussed the examples demonstrate the accuracy efficiency and versatility of higher order techniques and their advantages over low order discretizations the most important one being a much faster higher order convergence of the solution it is demonstrated that both components of the higher order modeling namely higher order geometrical modeling and higher order current field modeling are essential for accurate and efficient cem analysis of general antenna scattering and microwave structures

analytical expressions for spatial domain green s functions in layered media accurate and efficient formulas for computing spatial domain green s functions are presented in this paper to apply the formulas we only require a set of sample points of the spectral domain green s function sdgf on an integration path avoiding its singularities and an infinite domain tail path since the sampling is carried out for the integrand excluding the bessel function the number of sample points required is much smaller than the numerical integration method this aspect of the proposed method proves to be very advantageous for evaluating closed form green s functions at large source observer distances it is shown that the proposed formulas provide accurate results for both the near and far field regions as well as a wide range of material parameters such as lossless lossy left handed materials as well as multilayered substrates

efficient computation of the off diagonal elements of the vector potential multilayered periodic dyadic green s function the authors focus on the efficient computation of the slowly convergent infinite series that lead to the off diagonal elements of the vector potential multilayered periodic dyadic green s function two different approaches based on kummer s transformation are applied to the evaluation of these series the well known approach that makes use of the generalized pencil of functions gpof and ewald s method is the fastest approach but it does not provide accurate results when the distance between the field point and any of the source points is close to zero to avoid this problem we present a novel approach based on the gpof and the spectral kummer poisson s method with higher order asymptotic extraction this latter approach is slightly slower than the former one but it is accurate in the whole range of distances between the field point and the sources

a high performance upgrade of the perfectly matched layer multilevel fast multipole algorithm for large planar microwave structures an improvement of the perfectly matched layer multilevel fast multipole algorithm pml mlfma for simulating large planar microwave structures is presented by exploiting the low rank property of the pml mlfma multimodal aggregation and disaggregation matrices considerable reductions in memory usage and computation time are obtained the method has been extensively validated demonstrating complete error controllability when simulating large planar microwave structures reductions in memory requirements and cpu time of more than 60 and 40 have been achieved

regularization of mixed potential layered media green s functions for efficient interpolation procedures in planar periodic structures the problem of improving the computational efficiency in the numerical analysis of planar periodic structures is investigated here using the mixed potential integral equation mpie approach a new regularization of the periodic green s functions pgfs that are involved in the analysis of multilayered structures is introduced based on the effective medium concept this regularization involves extracting the singularities of the pgfs up to second order terms the resulting regularized pgf is very smooth and amenable to interpolation thus optimized interpolation procedures for the pgfs can be applied resulting in a considerable reduction of computation time without any significant effect on the accuracy another benefit of the regularization is that it significantly enhances the convergence of the series for both the vector and scalar potential pgfs the theoretical formulation is fully validated with various numerical results for both two dimensional 2 d and one dimensional 1 d layered media periodic structures

a novel analysis of microstrip structures using the gaussian green s function method a novel closed form expression is derived for spatial green s functions of microstrip structures by expanding the spectral green s function into a gaussian series this innovative method is called the gaussian green s function ggf method due to the gaussian form in the closed form green s function representation the main advantage of the ggf method lies in its precision as well as rapid convergence to demonstrate the versatility of this method the current distribution of a microstrip antenna is achieved via the combination of the method of moments mom and ggf method it is shown that this method can be computationally very efficient with less than 1 error compared to the numerical integration of the spectral integral also the results of the ggf method have been compared to the results of the commercial full wave software of agilent ads

spectral domain iterative analysis of single and double layered microstrip antennas using the conjugate gradient algorithm an analysis for single and double layered microstrip antennas is described the planarity of these structures makes it possible to construct a general spectral representation for any number of layers and to derive the spectral green s dyad in a compact fashion using a transmission line analogy a formulation of the antenna problem in the spectral domain incorporating this dyad is coupled with the conjugate gradient algorithm whose applicability as an efficient way of analyzing a number of microstrip antennas is studied results are quite accurate conclusions pertaining to the applicability of the method including effects of problem parameters on convergence rates are drawn

surface electric fields and impedance matrix elements of stratified media for the various geometrical configurations of waves in stratified media we consider the important case when both source and field points are located on the same interface separating two different dielectric media we denote this configuration as surface electric field case in this paper the electric fields are calculated numerically without using potentials for the surface electric field case the integrand of the electric field grows with k sub spl rho sup 3 2 for large spl kappa sub spl rho making the sommerfeld integral singular to calculate the surface electric fields in the spatial domain we previously applied a technique of higher order asymptotic extraction in the higher order asymptotic extraction the higher order asymptotic parts were calculated analytically the remainder which has an integrand decays as spl kappa sub spl rho sup 3 2 was calculated numerically along the sommerfeld contour path of integration in this paper we use a different extraction technique the half space extraction after the half space extraction the integrand of the sommerfeld integral of stratified media decays exponentially and the integral is calculated along the sommerfeld integration path the half space extraction part is calculated by numerical integration along the vertical branch cuts the surface electric fields for stratified media using half space extraction and higher order asymptotic extraction are in good agreement to validate the accuracy of the solution we also compute the impedance matrix elements using surface electric fields testing and basis functions all in the spatial domain the results are then compared with the results of the spectral domain method the comparisons of the complex impedance matrix elements are tabulated and show that the difference is less than 2

evaluation of the green s function for the mixed potential integral equation mpie method in the time domain for layered media in the use of the time domain integral equation tdie method for the analysis of layered media it is important to have the time domain layered medium green s function computed for many source to field distances spl rho and time instants t in this paper a numerical method is used that computes the mixed potential green s functions g sub v spl rho t and g sub a spl rho t for a multilayered medium for many spl rho s and t s simultaneously the method is applicable to multilayered media and for lossless or lossy dispersive media salient features of the method are 1 the use of complex spl omega so that the surface wave poles are lifted off the real k sub spl rho axis such that pole extractions are not required 2 the use of half space extraction so that the integrand for the sommerfeld integral decays exponentially along the k sub spl rho axis to obtain fast convergence of the integral and 3 the use of the fast hankel transform so that the green s function is calculated for many values of spl rho simultaneously for a four layer medium we illustrate the numerical results by a three dimensional plot of spl rho g sub v spl rho t versus spl rho and t and demonstrate the space time evolution of these green s functions for a maximum frequency range of 8 ghz the method requires only a few cpu minutes to compute a table of 100 points in spl rho spl times 168 points in t uniformly spaced values of g sub v spl rho t on an 867 mhz pentium pc

pattern selectivity in neural networks as a means of understanding basin structures the authors study the problem of learning and retrieving for a pair of correlated patterns within an extensive number of uncorrelated patterns for networks where learning may be treated as an optimization process with respect to an arbitrary cost function this formulation is then applied to several specific examples where they study the pattern selectivity of these systems i e their ability to differentiate correlated patterns and investigate the process of basin shrinking with increasing loading levels they define and discuss several different retrieval phases whose existence depends on the competitive interplay of the loading level and the pattern correlation discussion of asymptotic retrieval is restricted to dilute asymmetric networks

analysis of stacked microstrip patches with a mixed potential integral equation a method based on the mixed potential integral equation for the analysis of flat microstrip antennas in a double layer substrate is presented the method is used to compute the input impedance of a stacked patch configuration this structure permits a larger bandwidth and may also provide dual frequency operation the green s functions are discussed in detail and numerical results are obtained for the propagation constant of the dominant surface wave theoretical and experimental results are compared for a dual frequency and a broadband stacked patch antenna theoretical results for the input impedance are in good agreement with measurements the difference between theoretical and experimental results for the resonant frequency is less than 4 5 in all cases

a hybrid mom solution of scattering from finite arrays of cylindrical cavities in a ground plane in this paper we propose a novel hybrid space spectral domain method of moments mom calculation of canonical plane wave scattering from finite periodic structures comprised of dissimilar cylindrical cavities in an infinite ground plane covered by a dielectric superstrate we take full advantage of analyzing this particular type of problem comprised of a canonical geometry by employing a set of entire domain basis functions waveguide modes which truly span the hilbert space in which the desired solution resides the convergence behavior of a solution using said functions is quite robust results show that typically only a few basis functions are required to adequately represent the aperture fields with fidelity we have also reformulated the conventional magnetic field integral equation in a hybrid fashion whereby the exterior unbounded half space mom interaction terms have been cast in the spectral domain and the interior cavity interactions cast in the space domain directly the spectral representation allows us to trivially include a superstrate layer in the geometry and additionally leads to an efficient evaluation of the interaction integrals due to an overall reduction in the spatial dimensionality the interior interactions are readily handled in the space domain where we take advantage of the orthogonality property of waveguide modes most importantly the technique is significantly more accurate than purely numerical methods i e those in which a discretization of the geometry is necessary

spectral dyadic green s function formulation for planar integrated structures the problem of the complete determination of the dyadic spectral green s function for an integrated planar structure with a grounded dielectric slab has been considered and solved in a rigorous way by using the spectral theory of the electromagnetic field the reciprocity theorem and the geometrical symmetry of the structure have demonstrated the different roles played by the independent terms of the spectral green s function in the evaluation of the electromagnetic characteristics of the grounded slab excited with a general source furthermore an equivalent circuit representation of the structure allowing a noteworthy simplification in the determination of the total power has been obtained these equivalent circuits and the derived spectral green s function presented here can be used to analyze and design microstrip antennas of arbitrary shape with a general type of loading such as matched or unmatched loads parasitic and shorting pins

extrapolation methods for sommerfeld integral tails a review is presented of the extrapolation methods for accelerating the convergence of sommerfeld type integrals i e semi infinite range integrals with bessel function kernels which arise in problems involving antennas or scatterers embedded in planar multilayered media attention is limited to partition extrapolation procedures in which the sommerfeld integral is evaluated as a sum of a series of partial integrals over finite subintervals and is accelerated by an extrapolation method applied over the real axis tail segment spl alpha spl infin of the integration path where spl alpha 0 is selected to ensure that the integrand is well behaved an analytical form of the asymptotic truncation error or the remainder which characterizes the convergence properties of the sequence of partial sums and serves as a basis for some of the most efficient extrapolation methods is derived several extrapolation algorithms deemed to be the most suitable for the sommerfeld integrals are described and their performance is compared it is demonstrated that the performance of these methods is strongly affected by the horizontal displacement of the source and field points spl rho and by the choice of the subinterval break points furthermore it is found that some well known extrapolation techniques may fail for a number of values of spl rho and ways to remedy this are suggested finally the most effective extrapolation methods for accelerating sommerfeld integral tails are recommended

a frequency domain near field to far field transform for planar layered media we report a frequency domain near field to far field transform nffft for the numerical modeling of radiation and scattering in planar multilayered spaces although the results are equivalent to those of demarest 1996 the formulation is more compact more stable and applicable to observation angles in the lower half space furthermore the results are presented in a vector potential formalism that is more easily adaptable to existing free space implementations the nffft algorithm can be used in any differential equation based finite numerical method including but not limited to the finite difference time domain fdtd method and the finite element method fem

level set methods for the displacement of layered materials previous multi layered folding models have struggled to describe the geometry of the interfaces between layers in the level set method lsm a single function x y t can be used to encode all the information of a multi layer material in which all layers are in contact and thus is a very natural way of dealing with the geometry this paper shows the potential for the lsm in multi layer problems by demonstrating that it can describe the geometry of multi layer folding patterns including those with singularities the method is then applied to describe the mechanics of the modelling of parallel folding in multi layered structures

accurate model of arbitrary wire antennas in free space above or inside ground an accurate model of wire antennas in free space above or inside lossy ground is presented in which the current is assumed to flow on the surface of the wire and the testing is also performed on the surface to replace the traditional delta gap source a more accurate source model is developed by using the huygens principle from this principle and reciprocity theorem a variational formulation of the input admittance is derived when the triangle function is chosen as both basis and weighting functions all the elements of impedance matrix and source vector are formulated in closed forms which can be rapidly computed several numerical results are given comparing with measured data both the current distribution and input impedance by this model are more accurate than those of delta gap model

resonance frequency of a rectangular microstrip patch the microstrip patch resonant frequency problem is formulated in terms of an integral equation using vector fourier transforms using galerkins s method in solving the integral equation the resonant frequency of the microstrip patch is studied with both chebyshev polynomials and sinusoidal functions as basis functions in the case of the chebyshev polynomials the edge singularity is included but it is not important for convergence furthermore the resonant frequency of the microstrip patch is ascertained with a perturbation calculation the results for galerkin s method and experiments are in good agreement the perturbation calculation agrees asymptotically with galerkin s method with the aim of developing a computer aided design formula the solutions obtained by galerkin s method are interpolated with a three variable polynomial

an efficient approach for extracting poles of green s functions in general multilayered media a fast approach of closed form green s functions for mixed potential integral equation analysis of both near field and far field in planar multilayered media is presented in this paper since all components of the green s functions in spectral domain are restructured concisely by four elementary functions the surface wave pole extraction is very effective in terms of a function related to the generalized reflection coefficients meanwhile the number of required two level discrete complex image method dcim with high order sommerfeld identities is also minimized under this scheme the numerical results show that this approach is more efficient and accurate for the electromagnetic scattering by and radiation in the presence of electrically large three dimensional 3 d objects in multilayered media although lossless examples are considered in the numerical examples the method presented here works also for the lossy materials where the poles move away from the real axis in the complex plane

locating all the modes of green s function for a three layered medium based on the path tracking algorithm through a mathematical analysis on the relationship between the characteristic equations of the microstrip geometry and a configuration with a three layered medium a method based on the path tracking algorithm is proposed for precisely locating all the modes for a three layered medium with moderate thickness including surface wave modes leaky wave modes and improper real modes with this method the difficulty caused by branch points and cuts in the contour integral method could be avoided this method can be applied not only in the discrete complex image method dcim but also in the steepest descent path sdp method the proposed method can be extended to more complicated configurations

a new green s function formulation for modeling homogeneous objects in layered medium a new green s function formulation is developed systematically for modeling general homogeneous dielectric or magnetic objects in a layered medium the dyadic form of the green s function is first derived based on the pilot vector potential approach the matrix representation in the moment method implementation is then derived by applying integration by parts and vector identities the line integral issue in the matrix representation is investigated based on the continuity property of the propagation factor and the consistency of the primary term and the secondary term the extinction theorem is then revisited in the inhomogeneous background and a surface integral equation for general homogeneous objects is set up different from the popular mixed potential integral equation formulation this method avoids the artificial definition of scalar potential the singularity of the matrix representation of the green s function can be made as weak as possible several numerical results are demonstrated to validate the formulation developed in this paper finally the duality principle of the layered medium green s function is discussed in the appendix to make the formulation succinct