Electric-Type Dyadic Green's Functions for a Corrugated Rectangular Metaguide Based on Asymptotic Boundary Conditions

The Green's functions for the mixed potential electric field integral equation are derived for a rectangular waveguide with dielectric-filled corrugations supporting left- as well as right-hand propagation. Under the asymptotic boundary conditions assumption, the expressions of the Green's dyadic components can be decomposed into terms that represent conventional waveguide modes and others that represent hybrid metaguide modes. A simple approach is used to find the poles of the spectral domain expressions before obtaining the spatial domain expressions using the inverse Fourier transform. The dispersion diagram reflects very interesting characteristics for the structure and the deviation from the conventional case. The derived Green's function is verified by considering the problem of a probe excitation and comparing the input impedance obtained using a moment method procedure based on the present theory and the finite-difference time-domain method     

Flexibility in the choice of Green's function for the boundaryelement method

Several useful Green's functions are derived for the quasi-static analysis of shielded planar transmission lines by the boundary element method. These newly employed Green's functions satisfy forced boundary conditions in a rectangular region. The integral equation does not have a singular point and the integrand contains only the normal derivative of the electric potential. The present method is proposed to characterize multilayered and multi-conductor structures. Numerical results are presented for a microstrip, a suspended line, and a coplanar waveguide. For the coplanar waveguide, a combined Green's function is also studied. This combined Green's function further reduces the memory size in computation. All of these Green's functions are represented in infinite series. The resulting matrix equation has slowly convergent matrix elements. To reduce the computation time of matrix elements, we split the original series in two parts. The geometric series method is employed to convert one part into a fast convergent form (4 terms). For the other part, only a few terms (less than 20) require computation     

A Multifilament Method-of-Moments Solution for the Input Impedance of a Probe-Excited Semi-Infinite Waveguide

The input impedance and surface currents of a probe-excited, short-circuited semi-infinite waveguide are determined by the method of moments. Expressions are given for the impressed electric field used to excite the probe from the coaxial source input using a semi-infinite-waveguide Green's function, and expressions are given for a free-space approximate impressed electric field which arises from the coaxial source input. The method-of-moments formulation used is based on a multifilament current approximation and solves for the surface currents of the probe as a function of probe angle around the probe. Comparison of theory and experiment is made.     

Discontinuities in a Rectangular Waveguide Partially Filled with Dielectric

The modal spectrum for a rectangular waveguide with a dielectric slab at the bottom of the guide is obtained following the Characteristic Green's Function method developed by Marcuvitz. Then a four-terminal network is found as equivalent to the junction of the partially filled waveguide and an empty rectangular waveguide. An integral equation is written for the electric field at the plane of the junction and variational expressions are derived for the parameters of the four-terminal network connecting the transmission line equivalent to the partially filled waveguide to the transmission line equivalent to the empty guide. A reasonable guess for the electric field at the discontinuity gives approximate values for the parameters of the four-terminal network. These values agree with experiment. The parameters of the network are plotted vs frequency and thickness of the slab.     

Electromagnetic field plot of an inductive window by the momentmethod

A moment method is used to plot the electromagnetic field of an inductive window in a TE₁₀-mode rectangular waveguide. Green's dyadic functions are derived based on Tai's approach, which is a modified form of Hansen's vector wave functions. Based on the computed electric fields, the S matrix and the equivalent aperture reactance of the waveguide window are calculated. This calculation agrees with the previously published closed-form results of N. Marcuvitz (1964)     

Input impedance of a probe-excited semi-infinite rectangularwaveguide with arbitrary multilayered loads: part II-a full-waveanalysis

For pt.I see ibid., vol.43, pt.A, pp.1559-66 (July 1995). Utilizing the dyadic Green's functions (DGF's) derived in Part I of this paper, the input impedance of a coaxial probe located inside a semi-infinite rectangular waveguide has been generally formulated. The electromagnetic DGF's for a rectangular cavity with a dielectric load are also obtained from the general expressions given in Part I. Using the full-wave analysis, a dielectric-loaded rectangular cavity is further considered and the input impedance is specified. To improve the computational accuracy, an alternative form of electric DGF's of the second kind is developed and expressed in terms of the guided-wave eigenvalues for the rectangular loaded cavity. The probe-input reactance and the phase of the reflection coefficients are computed using the conventional form of electric DGF and the alternative form of magnetic DGF. Data are obtained from experiments performed on a dielectric-loaded cavity and compared with the numerical results. Agreement of the theoretical and experimental results confirms the applicability of the theoretical analysis given in this paper     

EM analysis of a conducting scatterer in optic dielectric waveguide

A method to compute the scattered field of curved mirrors and gratings in a dielectric slab waveguide is proposed. In contrast to the beam propagation method (BPM) for this kind of problems, the method of moment is adopted. By introducing the dyadic Green's function in a slab waveguide, the electric field integral equations for induced current distribution on the conducting obstacles are derived. To improve the computational efficiency, the modified Green's function is incorporated into the computation program. With this study, the effects of grooves of gratings and the finite extent of the mirrors in dielectric waveguides can be investigated in more detail     

无辐射介质波导中的并矢格林函数

本文利用本征函数展开法推导了无辐射介质(NRD)波导中的并矢格林函数,给出了其中电型并矢格林函数的完备形式。     

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.     

Input impedance of a coaxial-line fed probe in a thick coaxial-linewaveguide

The Green's functions for determining the electromagnetic fields inside a semiinfinite coaxial line due to a radially directed, infinitesimally thin, and short-current element have been derived. In addition to the TEM mode, TE and TM modes are also considered. Based on the Green's functions, a closed-form formula for determining the input impedance of a probe in a coaxial line terminated at an arbitrary load has been derived. Good agreement is observed between the theoretical results and experimental measurements over a wide frequency band for several configurations of interest. At low frequencies where the TEM mode is dominating, there is practically no difference between the results obtained by the rigorous analysis and those by a simple formula derived from the transmission-line theory. However, at frequencies where TE and TM modes are no longer insignificant, there is a noticeable discrepancy between the results obtained by the rigorous and not-so-rigorous methods     

Domain integral equation analysis of integrated optical channel andridge waveguides in stratified media

A domain integral equation approach to computing both the propagation constants and the corresponding electromagnetic field distributions of guided waves in an integrated optical waveguide is discussed. The waveguide is embedded in a stratified medium. The refractive index of the waveguide may be graded, but the refractive indices of the layers of the stratified medium are assumed to be piecewise homogeneous. The waveguide is regarded as a perturbation of its embedding, so the electric field strength can be expressed in terms of domain integral representation. The kernel of this integral consists of a dyadic Green's function, which is constructed using an operator approach. By investigating the electric field strength within the waveguide, it is possible to derive an integral equation that represents an eigenvalue problem that is solved numerically by applying the method of moments. The application of the domain integral equation approach in combination with a numerically stable evaluation of the Green's kernel functions provides a new and valuable tool for the characterization of integrated optical waveguides embedded in stratified media. Numerical results for various channel and ridge waveguides are presented and are compared with those of other methods where possible     

Analysis of longitudinal slots in ridged waveguides using a hybridfinite element-Galerkin technique

A hybrid approach, combining the finite element method (FEM) with an integral equation formulation of the tangential electric field, is developed for the solution of longitudinal slots cut in the broad wall of finite thickness of a ridged waveguide. The system of integral equations formulated at both interfaces of the slot, is solved using the Galerkin approach with sinusoidal basis and testing functions. The Green's function for the internal waveguide region, as called for in the integral equation formulation, is generated numerically, utilizing the eigenvalues and eigenfunctions of the waveguide as computed by the FEM with Lagrangian fourth order polynomials. This approach is quite general, allowing for arbitrary waveguide cross sections and compositions. Computations of the dot characteristics performed in this way agree very well with previously documented as well as our own experimental results     

A full-wave analysis of an arbitrarily shaped dielectric waveguideusing Green's scalar identity

An integral equation analysis is proposed to determine the phase constant of an arbitrarily shaped dielectric waveguide. The main feature of this approach is the use of Green's scalar identity in which only simple contour integrals have to be evaluated. Different scalar Green's functions are considered to satisfy the boundary conditions for the electric and magnetic fields in each region. This approach is combined with the boundary element technique with linear elements for the computation. The case of the rectangular dielectric image waveguide is discussed. and numerical results are shown to be consistent with other theories and experiments. The cases of hollow rectangular and semicircular image waveguides are analyzed, and numerical results are presented     

Dyadic Green's Functions for Integrated Electronic and Optical Circuits

Layered structures play an important role in both integrated microwave circuits and optical integrated circuits. Accurate prediction of device behavior requires evaluation of fields in the system. An increasingly used mathematical formulation refies on integral equations the electric field in the device is expressed in terms of the device current integrated into an electric Green's function. Details of the development of the specialized Green's functions used by various researchers have not appeared in the literature. We present the development of general dyadic electric Green's functions for layered structures; this dyadic formulation allows extension of previous analyses to cases where currents are arbitrarily directed. The electric-field Green's dyads are found in terms of associated Hertzian potential Green's dyads, developed via Sommerfeld's classic method. Incidently, boundary conditions for electric Hertzian potential are utiltzed; these boundary conditions, which have been a source of confusion in the research community, are developed in full generality. The dyadic forms derived herein are reducible in special cases to the Green's functions used by other workers.     

Different Representations of Dyadic Green's Functions for a Rectangular Cavity

Several different but equivalent expressions of the dyadic Green's functions for a rectangular cavity have been derived. The mathematical relations between the dyadic Green's function of the vector potential type and that of the electric type are shown in detail. This work supplements the one by Morse and Feshbach.     

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     

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 φ-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     

Electric dyadic Green's functions in the source region

A straightforward approach that does not involve delta-function techniques is used to rigorously derive a generalized electric dyadic Green's function which defines uniquely the electric field inside as well as outside the source region. The electric dyadic Green's function, unlike the magnetic Green's function and the impulse functions of linear circuit theory, requires the specification of two dyadics: the conventional dyadic G^-eoutside its singularity and a source dyadic L^-which is determined solely from the geometry of the "principal volume" chosen to exclude the singularity of G^-e. The source dyadic L^-is characterized mathematically, interpreted physically as a generalized depolarizing dyadic, and evaluated for a number of principal volumes (self-cells) which are commonly used in numerical integration or solution schemes. Discrepancies at the source point among electric dyadic Green's functions derived by a number of authors are shown to be explainable and reconcilable merely through the proper choice of the principal volume. Moreover, the ordinary delta-function method, which by itself is shown to be inadequate to extract uniquely the proper electric dyadic Green's function in the source region, can be supplemented by a simple procedure to yield unambiguously the correct Green's function representation and associated fields.     

Mixed-potential integral expression formulation of the electricfield in a stratified dielectric medium-application to the case of aprobe current source

The well-known procedure for determining the electric field in a structure consisting of an arbitrary number of planar dielectric layers is modified in order to obtain a form specially suited for the analysis of multiprobe multipath configurations. In general, the field is generated by arbitrary currents in the layers and arbitrary sheet currents in the transitions between the layers. The currents may be electric as well as magnetic, and the dielectric layers are isotropic, homogeneous, and lossy. The procedure results in Green's functions especially suited for the analysis of multiprobe multipatch configurations. They can be used in an efficient mixed-potential integral expression formulation. The theoretical procedure is applied in the case of a probe current source situated in one of the dielectric layers of the structure. For this probe current a highly efficient attachment current distribution is derived. Comparison of measured and calculated results for example structures proves the accuracy of both the approach and the attachment mode     

完全导电圆锥并矢Green函数

本文运用算子法和并矢运算的分布理论法,求解了完全导电圆锥并矢Green函数,且证明解是满足电磁基本方程的。