Spectral Domain Green's Functions Research Articles

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.

Two techniques for the efficient numerical calculation of the Green's functions for planar shielded circuits and antennas

In this paper we present new contributions to the computation of the Green's functions arising in the analysis of multilayered shielded printed circuits and antennas. First the quasistatic term of the spectral domain Green's functions is extracted so that the convergence of the reminder dynamic modal series is enhanced. Moreover, it is shown that by extracting a second-order quasi-static term the convergence is further improved. In regard to the quasi-static terms, they are computed in the spatial domain by numerically evaluating the associated spatial images series. Then a new and efficient technique is developed for the summation of the slowly convergent modal series. The technique can be viewed as the application of the integration by parts technique to discrete sequences and greatly accelerates the convergence rate of the series involved. It is shown that the new algorithm is numerically very robust and leads to a drastic reduction in the computational effort and time usually required for the numerical evaluation of the shielded Green's functions.

Resonant Behaviours of Microstrip Antenna in Multilayered Media: an Efficient Full-Wave Analysis - Abstract

This paper presents an efficient analysis of a microstrip antenna in multilayered media using the method of moments (MoM). The general forms of spectral-domain Green's functions for multilayered media are converted into the spatial-domain Green's functions using the discrete complex image method (DCIM). With the spatial-domain Green's functions, the mixed potential integral equation (MPIE) is discretized in spatial domain, and the resultant system of equations is then solved using the biconjugate gradient (BCG) method. As applications, resonant frequencies of microstrip antennas in multilayered media are analysed. The numerical results show that the present method is an efficient and accurate scheme for analysing microstrip antennas in multilayered media.

Closed-form Green's functions for cylindrically stratified media

A numerically efficient technique is developed to obtain the spatial-domain closed-form Green's functions of the electric and magnetic fields due to z- and /spl phi/-oriented electric and magnetic sources embedded in an arbitrary layer of a cylindrical stratified medium. First, the electric- and magnetic-field components representing the coupled TM and TE modes are derived in the spectral domain for an arbitrary observation layer. The spectral-domain Green's functions are then obtained and approximated in terms of complex exponentials in two consecutive steps by using the generalized pencil of function method. For the Green's functions approximated in the first step, the large argument behavior of the zeroth-order Hankel functions is used for the transformation into the spatial domain with the use of the Sommerfeld identity. In the second step, the remaining part of the Green's functions are approximated on two complementary parts of a proposed deformed path and transformed into the spatial domain, analytically. The results obtained in the two consecutive steps are combined to yield the spatial-domain Green's functions in closed forms.

A model-based parameter estimation approach for numerical analysis of single-mode optical fibers

An efficient numerical method is proposed and implemented for the analysis of propagation characteristics of single-mode optical fibers with arbitrary refractive index profile. The method follows the concept of the so-called model-based parameter estimation, and the Pade algorithm is used to construct a low-order rational approximant of the spectral domain Green's function, obtained by solving a hierarchy of static problems. The sought eigenfrequency and field distribution are then estimated by computing, respectively, the dominant pole and the related residual of the rational approximant. A number of profiles are analyzed and experiments show that very accurate results can be cheaply obtained through this technique.

Spectral-domain Green's function of magnetic type for NRD guides and H-guides

Nonradiative dielectric guides and H-guides are widely used in millimeter-wave integrated circuits and antennas. To analyze the behavior of discontinuities, obstacles, and slots in such structures, an increasingly used mathematical formulation is the integral-equation approach, for which Green's function is required. Here, an efficient programmable full-wave Green's function, due to a magnetic-current element placed inside the dielectric layer, is derived in the spectral domain. In the derivation procedure, the field is divided into two parts: the incident and scattering fields. The contribution of the surface wave is included in the scattering part, while the singularity, when the field and source points are the same, is presented in the incident field part. By doing so, one can deal with the singularity caused by the source and surface-wave poles encountered in the integration separately and freely. The Green's function is then used to analyze the radiation characteristics of a single transverse slot in upper plate of the H-guide. The results obtained are in good agreement with experimental data available in literature.

Efficient electromagnetic modeling of microstrip structures in multilayer media

This paper presents an efficient method-of-moments solution of the mixed-potential integral equation for a general microstrip structure in multilayer media. In this method, the general forms of the spectral-domain Green's functions for multilayer media are derived first. The spatial-domain Green's functions are then obtained by the discrete complex-image method, which obviates the time-consuming numerical evaluation of the Sommerfeld integral. The Rao-Wilton-Glisson basis functions are employed to provide necessary flexibility to model arbitrary shapes. To expedite the computation of frequency response over a broad band, a reduced-order model is presented using asymptotic waveform evaluation. Numerical results of multilayer circuits and antennas are presented to show the efficiency and accuracy of this method.

Rectangular modes and dyadic Green's functions in a rectangular chirowaveguide. I. Theory

An analytic solution of electromagnetic-wave propagation in a rectangular chirowaveguide is represented in this paper in terms of spectral-domain dyadic Green's functions (DGF's) in a general form. The method used here is a combination of a wavefield decomposition method and DGF eigenfunction expansion technique. This DGF decomposition method avoids having to use the modified and normalized vector wave functions, which are found difficult to satisfy the boundary conditions of chirowaveguides in which the reconciliation of Dirichlet and Neumann conditions is impossible. On the other hand, this method can be generalized to a chirowaveguide of arbitrary cross section and is found reducible to a nonchiral case. It is observed that in a similar fashion to the conventional rectangular waveguide, the duality between the electric and magnetic types of DGF's in the rectangular chirowaveguide does not exist. To show the reducibility of the generalized DGF's for bi-isotropic media, we summarized the procedure of utilizing the formulas and proved in detail that the form of the DGF's can be reduced to that for chiral media and achiral (isotropic) media. Exactly the same DGF's are obtainable for the isotropic media by reducing the general formulas. The electric and magnetic fields in the rectangular chirowaveguide due to a point dipole excitation oriented in the y-direction are derived. The detailed numerical analysis includes the novel features of the dispersion relations, the effects of chirality on the novel features of the rectangular chirowaveguides, some newly discovered features, and vector field plots and contour plots of higher order modes of electric and magnetic fields.

Comments on "On the use of /spl rho/-algorithm in series acceleration"

For original paper by Singh and Singh see IEEE Trans Antennas Propag., vol.39, p.1514-17, 1991 October. Tan comments that Singh and Singh have correctly stated that the /spl epsiv/ algorithm is effective for accelerating the convergence of alternating series whereas the /spl rho/ algorithm is suitable for monotonic series; Tan comments that they have failed to recognize that sequences containing the spatial- or spectral-domain Green's function series partial sums are not monotonic, but oscillatory about certain limiting values. In fact, this suggests that the /spl epsiv/ algorithm should be a more suitable accelerator for the spatial- or spectral-domain Green's function series. The use of an example of the monotonic series Sn=/spl Sigma//sub 1//sup n/1/(m/sup 2/) to illustrate the effectiveness of the /spl rho/ algorithm over the /spl epsiv/ algorithm is, therefore, not relevant in a paper whose objective concerns the study of effective accelerators for convergence of the spatial- or spectral-domain Green's function series.

Microstripline-fed cylindrical slot antennas

The characteristics of a microstripline-fed cylindrical slot antenna are presented. The integral equation, which involves spectral domain Green's functions and unknown slot electric field, is numerically solved using the method of moments. Computed results are compared with a slot antenna on a planar surface to demonstrate the validity and accuracy of the method. The effects of the size of the cylinder on the input impedance and far-field pattern are investigated.

Single-mode optical fibers using Pade approximants

We propose a new, fast, and accurate numerical technique for analyzing single-mode optical fibers with arbitrary (transverse) refractive index profile. The method is based upon a Pade (rational) approximation of the spectral domain Green's function of the fiber, obtained by solving a hierarchy of static problems. The sought eigenfrequency and modal field are accordingly estimated by computing, respectively, the dominant pole and the related residual of the rational approximant. Numerical simulations and comparison with known analytical results indicate that the proposed method is highly accurate, reliable, and computationally affordable.

Microstripline- and stripline-fed aperture-coupled cylindrical rectangular microstrip antennas

Stripline-fed and microstripline-fed aperture-coupled cylindrical rectangular microstrip antennas are investigated. The equivalence principle is invoked to separate the feedline and the antenna patch with equivalent magnetic currents distribution on the aperture region. The Lorentz reciprocity theorem is applied to find the interactions between the aperture and the feedline. The unknown patch current and aperture field are determined by solving coupled integral equations, which involve spectral-domain Green's functions, using Galerkin procedure. Numerical results of input-impedance and far-field patterns are compared with those for antennas on a planar surface.

Continuous wavelet representation of Green functions in layered media

A continuous wavelet analysis technique is applied in the spectral domain to efficiently represent the multiscale features of the spectral-domain Green functions in layered media. Numerical examples for a microstrip and a shielded microstrip are presented.

A Full Wave Analysis Method for Frequency Selective Surfaces On Ferrite Substrates

Frequency selective surfaces (FSS) have numerous applications in microwave and optical systems. In this work, instead of traditional dielectric substrates, ferrite substrates are used. By using ferrite materials, one can change the spectral properties of these structures without physically altering them. The transmission matrices for the ferrite substrate and the air, above and below the ferrite substrate, are derived here. By combining these transmission matrices along with the boundary conditions, the spectral domain Green's function is obtained. This process can be carried out for both the in-plane and perpendicular bias of the ferrite. Several results are presented to show the tunability of frequency selective surfaces with ferrite substrates as a function of the applied dc bias. Some special treatment is used in the transmission matrix to avoid its singularity for some evanescent modes.

Analysis of finite-phased arrays of aperture-coupled stacked microstrip antennas

Analytical results for finite-phased arrays of aperture-coupled stacked microstrip antennas are presented. In order to evaluate the characteristics of aperture-coupled microstrip antennas in a finite array and derive the moment-method solutions for the unknown current distributions on the patches and slots, the reciprocity theorem and the spectral domain Green's functions for a dielectric slab are used. Various sized arrays are considered and compared with solutions for an infinite array. Numerical results are presented to illustrate the input impedance, mutual coupling, active reflection coefficient versus scan angle, radiation efficiency, and active-element gain patterns.

Dyadic Green's Functions for the Inhomogeneous Cylindrical Waveguide and Cavity and Their Applications

The general expressions of the spectral-domain dyadic Green's functions for an inhomogeneous cylindrical waveguide and an inhomogeneous cylindrical cavity are formulated by the method of eigenfunction expansion and scattering superposition. The excitation current source can be in an arbitrary region. The dyadic Green's functions are used to calculate the phase constants and the cut-off characteristics of a dielectric-loaded cylindrical waveguide and the resonant frequencies of a dielectric-loaded cylindrical cavity. Complete agreement with published data is obtained.

Characteristics of aperture-coupled coplanar microstrip subarrays

The characteristics of aperture-coupled microstrip antennas with parasitic elements are studied. Four configurations for increasing the bandwidth of aperture-coupled microstrip antennas are described. Additional patches are gap-coupled to the nonradiating edges of the rectangular fed patch. The spectral domain Green function approach and the reciprocity method are used for the analysis. The SWR bandwidth and the E- and H-plane beamwidths can be improved by changing the sizes and the locations of the parasitic patches. Low backlobe radiation can be achieved by locating a plane reflector slightly below the microstrip feedline. The bandwidth of the microstrip subarray can also be enhanced with the addition of the plane reflector. The theory is confirmed by experimental data.

A fast moment method algorithm using spectral domain wavelet concepts

A multiresolution wavelet algorithm is developed for the fast solution of electromagnetic scattering problems. A multiscale feature of the spectral domain Green's function is observed in the joint spectral‐spatial representation. Owing to the multiscale nature of the electrodynamic Green's function in the spectral domain, wavelet application in the spectral domain (KDWT) is more appropriate in representing the Green's function than the wavelet transform applied in the space domain (SDWT). Using the KDWT, a sparse moment impedance matrix, which is a discretized form of the Green's function, is obtained and a fast multiresolution moment method algorithm is developed in conjunction with the conjugate gradient solver. For a square cylinder the sparsity of the moment method matrix and the resulting time performance are compared with those from the conventional moment method. It is found that the KDWT algorithm leads to a matrix‐vector multiplication which scales with an order less than N2.

The characteristic impedance of a cylindrical strip line and a microstrip line

A full-wave approach based on the spectral-domain method is applied to a cylindrical strip line and a microstrip line. The effects of the dielectric substrates and the size of the cylinder are taken into account by the spectral-domain Green's functions. Numerical results showing the characteristic impedance of the lines at high frequency are presented. These results are compared with some available limiting cases. © 1996 John Wiley & Sons, Inc.

Input impedance of microstrip‐slot‐coupled dielectric resonator antennas mounted on thin dielectric layers

An efficient numerical technique based upon a surface integral equation formulation for the coupling of bodies of revolution (BORs) to non-BOR geometries for the design of practical microstrip-slot-aperture-coupled dielectric resonator antennas is presented. The moment method matrix fill time and memory requirements are significantly reduced by utilizing Fourier mode basis functions on the BOR together with the spectral domain Green's function for the printed circuit board. Two practical antennas are designed and fabricated. Antenna input impedances predicted by this technique are in good agreement with those of the actual devices. © 1996 John Wiley & Sons, Inc.