Anisotropic fibers studied by the Green's function method

The Green's function method is used to derive the fundamental mode fields of the anisotropic circularly symmetric step-profile fiber. The method is particularly simple for stress-induced birefringence. It also provides a single analytic expression for the loss of the leaky mode. generalizing the results we previously derived for some special cases using radiation modes [4], [5].     

A recursive Green's function method for boundary integral analysisof inhomogeneous domains

The recursive Green's function method (RGFM) for computation of fields scattered by two-dimensional (2-D) inhomogeneous dielectric bodies is presented. The algorithm efficiently constructs the Green's function for the inhomogeneous region by recursively combining known Green's functions from smaller subdomains. The fields on the scatterer surface are then computed using a boundary integral formulation. Proper implementation of the RGFM results in computational and storage complexities which scale as N^1.5 and N, respectively, where N is the total number of discrete cells in a domain. Comparisons of results obtained using the RGFM with those computed from moment method and exact solutions show the efficiency and accuracy of the technique     

An overview of the hybrid MM/Green's function method inelectromagnetics

An overview is presented of a hybrid technique for solving electromagnetic radiation and scattering problems by combining the method of moments (MM) with a special Green's function. The method, referred to as an MM/Green's function solution, combines the ability of MM solutions to treat geometrically complex bodies with the accuracy and computational efficiency of Green's function solutions. Compared to a standard MM solution, the MM/Green's function solution reduces the number of unknowns and thus the computer storage requirements. In most cases the CPU time for the MM/Green's function solution is considerably less than that for a standard MM solution. An example problem of TM scattering by a semicircular strip in the presence of a circular cylinder is solved by the MM, and by the MM/Green's function technique with a matrix, exact eigenfunction, and high-frequency Green's function     

Antenna modelling using discrete Green's function formulation ofFDTD method

In a recent paper by the authors (see ibid., vol. 35, no. 7, p. 554-5, 1999), the finite difference time domain (FDTD) method was re-formulated in terms of discrete convolution, using the analytical solution of the discrete Green's function (DGF), and applied to a 2D scattering example. This algorithm has now been fully implemented in 3D to solve scattering and antenna problems in the time domain while retaining full compatibility with Yee's FDTD algorithm     

A Correlation method for the determination of the dyadic Green's function of the electromagnetic field in diffraction problem

A correlation method is developed for the determination of the dyadic Green's function of the electromagnetic field in the presence of diffracting body. The dyadic Green's function G(r, t/rs, t') is determined by the temporal correlation function between a Gaussian and white random current source J(t') situated at rsand the electric field E(r, t) observed at a point r.     

Dielectric Green's function for parameters of microstrip

The program generates a data file of the dielectric Green's function in format suitable as input to the program which has been previously deposited in the IEE Program Library for computation of the parameters of microstrip. With the two programs, tables of microstrip parameters can be generated for any value of substrate permittivity. This program also provides the option of including the effect of an upper ground plane. The calculation embodies the quasistatic approximation.     

Application of successive approximation method to the computationof the Green's function in axisymmetric inhomogeneous media

The successive approximation method (SAM) is applied to the computation of the Green's function in axisymmetric inhomogeneous media, SAM is implemented by using an iterative procedure that produces a series, and the series is proven to be a Taylor series. The condition of the convergence is derived from the theory of functions of several complex variables. In each iteration, the Fourier-Hankel transform and its inverse are applied to the approximation of some order of the Green's function and the result is the approximation one order higher than the original. Fast Fourier-Hankel transform (FFHT) is employed to speed up the computation, and thereby, an algorithm SAM-FFHT is formulated     

Exterior moment method analysis of conducting scatterers by using the interior Green's function

A new method using a Green's function in the interior region of a conducting scatterer is proposed to obtain a mutual admittance matrix in an exterior moment method analysis. A numerical example of a two-dimensional magnetic strip source located on an exterior surface of a perfectly conducting rectangular cylinder shows the validity of the method.<>     

The dyadic Green's function for the cylindrical chirostrip antenna

Using the eigenfunction expansion of dyadic Green's function in unbounded chiral medium, and the method of scattering superposition, the expressions of dyadic Green's function for the one and two—layer cylindrical chirostrip antennas are derived, when the field sources are placed in any layer of cylindrical chirostrip antenna. Also, using the method of saddle point integration, the asymptotic expression of dyadic Green's function for the wraparound chirostrip antenna is obtained. The results can be directly used to analyse the radiation characteristics of cylindrical chirostrip dipolc antenna, et al.     

Efficient computation of the 2-D Green's function for 1-D periodic structures using the Ewald method

The Ewald method is applied to accelerate the evaluation of the Green's function of an infinite periodic phased array of line sources. The Ewald representation for a cylindrical wave is obtained from the known representation for the spherical wave, and a systematic general procedure is applied to extend previous results. Only a few terms are needed to evaluate Ewald sums, which are cast in terms of error functions and exponential integrals, to high accuracy. Singularities and convergence rates are analyzed, and a recipe for selecting the Ewald splitting parameter /spl epsiv/ is given to handle both low and high frequency ranges. Indeed, it is shown analytically that the choice of the standard optimal splitting parameter /spl epsiv//sub 0/ will cause overflow errors at high frequencies. Numerical examples illustrate the results and the sensitivity of the Ewald representation to the splitting parameter /spl epsiv/.     

Image buildup for the rectangular waveguide tensor Green's function

Tensor Green's functions, of both electric and magnetic type, are produced for the rectangular waveguide through summation of a doubly infinite series of free-space contributions obtained from endless imaging across (perfectly conducting) guide walls. The requisite summation is facilitated by resorting to a Fourier integral representation for the basic free-space kernel, followed by appeal to the Poisson summation formula. That latter, in particular, engenders, through Dirac delta function appearance, an automatic decomposition into waveguide modes. Indication is further made as to how the imaging method may naturally be extended to assemble mode-decomposed Green's functions in an axially bounded, rectangular cavity.     

Properties of the dyadic Green's function for an unboundedanisotropic medium

Radiation in an unbounded anisotropic medium is treated analytically by studying the dyadic Green's function of the problem, initially expressed as a triple Fourier integral which is next reduced to a double one. Under certain conditions, the existence of incoming waves is verified. It is also found that exponentially decaying waves are possible in such media. Finally, the existence of branch points in the remaining integrand function is investigated, and appropriate branch cuts are proposed     

Efficient calculation of the Green's function for multilayeredplanar periodic structures

An efficient calculation scheme is presented for the periodic Green's function in planar multilayered structures. The proposed method is based on the static complex image conversion, and the Ewald sum technique and it converts the slowly convergent Green's function into the sum of two rapidly convergent series     

Parameter extraction for on-chip interconnects by double-image Green's function method combined with hierarchical algorithm

A novel double-image Green's function approach combined with the hierarchical algorithm is proposed to compute the frequency-dependent capacitance and conductance for the on-chip transmission lines and interconnects embedded in multiple SiO/sub 2/ layers of the general CMOS process. The effect of a protective layer and lossy silicon substrate layer of the CMOS process are considered in the four-layer structure deduced by the equivalent dielectric-constant approach whose adaptability is further proven in this paper. This double-image Green's function approach is fast convergent with the increasing order of reflections and transmissions, which is further accelerated by the hierarchical algorithm for computation of the Green's function rapidly. Moreover, the proposed method avoids the computation of bound charges on the dielectric interfaces. The frequency-dependent capacitance and conductance gained from the proposed method are shown to be in good agreement with the data obtained by other relevant methods.     

Speedy computation of time-domain Green's function for microstripstructures

A speedy computation of the time-domain Green's function for microstrip structures is performed. The spatial Green's function in the frequency domain is written as the sum of real- and complex-image terms, which are respectively converted into the time domain analytically and numerically via fast Fourier transforms. The coefficients of the complex-image terms are both space and frequency independent and are computed only once, which results in a speedy algorithm     

A comparison of acceleration procedures for the two-dimensionalperiodic Green's function

Alternate acceleration procedures are evaluated for the two-dimensional free-space periodic Green's function. Two of these techniques yield exponential convergence rates and are preferable if high accuracies are required. Numerical aspects of these procedures are described     

Dyadic Green's function in bounded media

A new theory for the evaluation of the dyadic Green's functions in a homogeneous medium bounded by perfectly conducting walls is presented. The peculiarities of this theory are 1) the Green's functions are systematically and explicitly decomposed in a singular and an analytical part, and 2) these two parts are formulated in a general manner, i.e., independent on the boundaries. As an application, the Green's functions in a conical guide are evaluated.     

Double-image Green's function method for 3-D capacitance and conductance extraction of on-chip transmission lines

A new double-image Green's function approach is developed to compute the frequency-dependent capacitance and conductance for three-dimensional multilayered on-chip transmission lines on silicon substrate. The ε-algorithm of the Pade approximation is adopted to reduce the time for establishing the coefficient matrix. The parameters gained from this new approach are shown to be in good agreement with the data obtained by the total charge Green's function method.     

Ray-optical solution for the dyadic Green's function in a rectangular cavity

The ray-optical method, which has been successfully employed for the analysis of diffraction and scattering problems, is used to derive the Green's function in a rectangular cavity. Despite the asymptotic approximations inherent in the method, it is shown that it gives a physical or geometrical insight into the mechanisms of propagation in guiding structures leading to exact or rigorous solutions not always provided by other methods.