Perturbation Analysis of Rectangular Waveguide Containing Transversely Magnetized Semiconductor

The boundary value problem of rectangular waveguide, filled with transversely magnetized semiconductor or plasma, is solved by a perturbation method reported earlier. The solution by first-order theory is compared to the results of an experiment in which surface currents in the guide wall due to perturbed and unperturbed TE/sub 1,0/ wave in N-type Silicon are sampled and segregated. Theoretical and experimental results are in excellent agreement.     

Computation of TM and TE modes in waveguides based on a surfaceintegral formulation

The surface integral formulation is used for the computation of TM and TE modes propagating in dielectric loaded waveguides. This formulation makes use of the surface equivalence principle whereby the field at any point internal or external to the waveguide can be expressed in terms of equivalent surface currents. This procedure reduces the original problem into a set of integro-differential equations which is then reduced to a matrix equation using the method of moments. The solution of this matrix equation provides the propagation characteristics of the waveguide and the equivalent surface currents existing on the waveguide walls. The equivalent surface currents can be used to compute the fields at all points, both inside and outside the waveguide. The surface integral method has been used to compute the propagation characteristics of waves propagating in dielectric loaded waveguides. The computed results agree very well with analytical and published data. A method that can be used to remove spurious modes is illustrated     

A TE/TM modal solution for rectangular hard waveguides

A TE/TM modal solution for a longitudinally corrugated rectangular waveguide is developed. These longitudinal corrugations can be used to excite a quasi-TEM wave and form a hard waveguide by correctly choosing the impedance at the guide wall. The correctly chosen impedance is referred to as the hard boundary condition. The modal solution developed here solves the problem of longitudinal corrugations filled with a dielectric material by first finding and solving the characteristic equation for a complete TE/TM modal set. It is shown that this TE/TM mode solution can be used to achieve the hard boundary condition resulting in the quasi-TEM wave in a hard waveguide for discrete values of corrugation depth. Beyond each of these depths, a mode becomes a surface wave. The theoretical mode set is amenable to the solution of problems using the mode-matching method. A combination of the mode-matching method and the TE/TM modal solution will allow the solution of larger problems.     

Radiation and scattering from infinite periodic printed antennaswith inhomogeneous media

The hybrid method of moments (MoM)/Green's function method technique is applied to infinite periodic printed antenna arrays containing dielectric inhomogeneities. The solution uses an integral equation for an infinite periodic printed array on or over a homogeneous dielectric substrate, coupled with equivalent volume polarization currents for dielectric inhomogeneities on top of the homogeneous substrate. Volume pulse-basis functions were used to expand the volume polarization currents. A hybrid MoM/Green's function method solution was then obtained through the matrix form of the problem. The two-dimensional (2-D) solution of plane wave scattering from a grounded dielectric slab was used to validate the reaction impedance of the dielectric inhomogeneity. Several infinite periodic printed dipole arrays with dielectric supports and overlays were studied with this solution and good agreement was observed between the hybrid MoM/Green's function method and waveguide simulator experiments     

Multifrequency formulation for electromagnetic scattering usingshifted-frequency internal equivalence

A new formulation for multifrequency electromagnetic scattering problems involving homogeneous or inhomogeneous bodies is introduced and discussed. The formulation is developed using the shifted-frequency internal equivalence in the construction of the internal equivalence in the scattering problem. With this approach, the equivalent currents for the internally equivalent problem radiate a chosen fixed frequency which is different from the frequency of the incident wave. These equivalent currents are functions of the incident and shifted frequencies, material parameters, and the total field inside the body and on its boundary. A combination of this internally equivalent problem with an externally equivalent one, so as to match the tangential fields at the boundary of the body, results in the new formulation. The formulation and its application to generate multifrequency data using internal data generated at a single frequency in a volume-surface integral-equation approach utilizing the method of moments in the solution are explained and exemplified using a simple inhomogeneous slab problem     

Scattering from multiple conducting and dielectric bodies ofarbitrary shape

A simple moment-method solution is presented for the problem of electromagnetic scattering from structures consisting of multiple perfectly conducting and dielectric bodies of arbitrary shape. The system is excited by a plane wave. The surface equivalence principle is used to replace the bodies by equivalent electric and magnetic surface currents, radiating into an unbounded medium. A set of coupled integral equations, involving the surface currents, is obtained by enforcing the boundary conditions on the tangential components of the total electric and magnetic fields. The method of moments is used to solve the integral equations. The surfaces of the bodies are approximated by planar triangular patches, and linearly varying vector functions are used for both expansion and testing functions. Some of the limitations of the method are briefly discussed. Results for the scattering cross sections are presented. The computed results are in very good agreement with the exact solutions and with published data     

A versatile impedance boundary method of moments computationaltechnique for solving the one-dimensional Schrodinger equation withapplication to quantum well and quantum wire problems

A versatile and efficient computational technique for use in the analysis of quantum wells (QWs) and a class of quantum wires with arbitrary potential profiles is presented. This expansion technique is an extension of the impedance boundary method of moments (IBMOM), which was first developed for analysis of planar optical waveguide structures. The similarity in formulation of the electromagnetic problem and the QW problem is exploited, Eigenenergies or quasi-eigenenergies, wave functions and, for quantum wires with separable wave functions, conductance are determined. No discretization or step approximation is required of potential profiles which can be described in functional form. Computational results are presented to demonstrate the accuracy and efficiency of the technique     

Diffraction of guided waves by the end face of a dielectric slab waveguide terminated with a finite conductive strip

The diffraction of guided waves by the end face of a dielectric slab waveguide short circuited with a finite conductive strip is analyzed. An integral equation technique is employed to formulate the corresponding boundary problem. The unknown term in this integral equations is the electric field E(x) on the terminal plane of the waveguide. The homogeneous term is determined from the incident guided wave. A method of moments technique is employed to compute approximately the electric field E(x) by using Laguerre functions as describing and testing functions. The reflection coefficients of the guided waves are computed by using the approximate expression of the E(x) field. Numerical results are given for several guide and conductor plate dimensions.     

Unequal-Arm Finite-Difference Operators in the Positive-Definite Successive Overrelaxation (PDSOR) Algorithm

In an earlier publication, a procedure was described that permitted the application of successive overrelaxation (SOR) to the solution of higher modes of any uniform waveguide of arbitrary cross section, filled with an isotropic and homogeneous medium. An algorithm was described that employed a thirteen-point finite-difference operator formed from five constituent five-point operators, such that the resulting matrix was positive semidefinite at the correct eigenvalue and was positive definite otherwise. For compactness the method is called positive definite successive overrelaxation (PDSOR). For simplicity boundary fitting was accomplished by causing horizontal waveguide deformations at each horizontal mesh line to the nearest node point. This paper describes an improvement of the PDSOR algorithm to cater for unequal-armed operators so that the waveguide wall need not be distorted from its actual shape. Improved accuracy is obtained for fields in the vicinity of the boundary and for eigenvalues. A finite-difference first-order perturbation method (that makes use of the accurately determined wall currents) for attenuation in arbitrarily shaped waveguides is described. Normalized curves are presented giving attenuation of sets of TE and TM modes in circular, lunar, T-septate lunar, single-ridge, and T-septate rectangular waveguides.     

Computation of cutoff wavenumbers of TE and TM modes in waveguidesof arbitrary cross sections using a surface integral formulation

A procedure is described for obtaining the cutoff wave numbers of transverse electric (TE) and transverse magnetic (TM) modes in waveguides of arbitrary cross section. A surface integral equation approach is used in which the E-field equation has been transformed into a matrix equation using the method of moments. An iterative technique is used to pick the eigenvalues of the solution matrix which corresponds to the waveguide cutoff wave numbers. The salient features of this technique are its speed, its simplicity, and the absence of any spurious modes when waveguides of arbitrary cross section are treated. The first four modes are tabulated for various waveguides, and the results are in very good agreement with published data     

Solutions for Some Waveguide Discontinuities by the Method of Moments (Short Papers)

The electromagnetic boundary value problem of two waveguides coupled by an aperture or an aperture in a waveguide radiating into free space may be described by an integral equation. An analytical solution to this integral equation cannot be readily found due to the complexity of the kernel. However, extremely useful results may be obtained if the method of moments is employed to reduce the integral equation to a matrix equation which can be solved by known methods. In this short paper, series and shunt slots in a rectangular waveguide are analyzed using this technique.     

Excitation of dielectric resonator antennas by a waveguide probe: modeling technique and wide-band design

Analysis of a dielectric resonator antenna (DRA) fed by a waveguide probe is presented. The probe is excited by the dominant mode of a waveguide and extends into the DRA through an aperture in the waveguide wall. The DRA has, in general, an arbitrary shape and resides on an infinite ground plane, which coincides with the exterior of the waveguide broad wall. A simple and efficient analysis procedure is implemented where the problem is divided into two parts. In the upper part, the input impedance of the DRA excited by a coaxial probe is obtained with respect to the feeding position on the ground plane independent of the waveguide part. Then the input impedance is transformed to the waveguide part as a concentrated load at the end of the probe connected to the waveguide wall. The effect of the wall thickness is taken into account by modeling the section of the probe passing through the waveguide wall as a coaxial cable transmission line supporting the transverse electromagnetic mode. Thus the DRA input impedance is transferred from the ground plane reference to the waveguide inner wall reference. Results obtained using the method of moments are compared with those obtained using the finite-difference time-domain method and exhibit very good agreement. The procedure is used to achieve a bandwidth of 50% for a stacked DRA excited by a waveguide probe.     

Rayonnement d’une grille plane de fils continus et discontinus

This paper relates the scattering of a electromagnetic plane wave by a plane grating of conducting wires. The wires are parallel, equidistant and alternatively continuous and discontinuous. The discontinuous wires may be considered as dipole lines. The problem is numerically resolved. The conductor currents are determined by means of a system of first kind integral equations which is converted in a linear equations system by the moments method. The knowledge of currents permits the calculation of the reflection and transmission factors of the grating. Thus a matched state and a resonant state appear for discrete frequencies, where the transmission factor modulus is respectively 1 and 0. Experimentation on waveguide simulators gives a good agreement with numerical results.     

Domain-integral analysis of channel waveguides in anisotropicmultilayered media

A domain-integral equation method is presented to determine both propagation constants and the electromagnetic field distributions of guided surface wave modes in integrated optical waveguides. Both the waveguide and its multilayered embedding are anisotropic. The permittivity tensor of the embedding is assumed to be piecewise homogeneous. The kernels of the domain-integral equations consist of Green's tensors. The integral equations form an eigenvalue problem where the electric field strength represents the eigenvector. This problem is solved numerically by applying the method of moments. Numerical results are presented for an anisotropic ridge waveguide, embedded in an anisotropic multilayered medium     

Investigation of diffraction of an electromagnetic wave arbitrarily incident on a locally inhomogeneous medium interface

The 3D problem of reflection of a plane electromagnetic wave by an irregular boundary containing a locally inhomogeneous well conducting section is considered. The boundary value problem for the system of Maxwell equations in an infinite section with an irregular boundary is reduced to the solution of systems of singular equations. A numerical algorithm for their solution is developed. Results of calculation of the currents induced on the irregularity and reflected field patterns are presented for the case of the E polarization.     

Finite length cylindrical scatterer near perfectly conducting ground--A transmission line mode approximation

A Pocklington type integro-differential equation, possessing an exact kernel, is formulated in terms of a complex frequency for the current induced on a thin finite-length cylindrical scatterer which is above, near, and parallel to a perfectly conducting ground plane. The circumferential variation of the axial current is assumed to be described by a transmission line mode approximation when the scatterer is near the ground plane. The integro-differential equation is reduced to a system of algebraic matrix equations through application of the method of moments. The singularity expansion method is utilized to determine the transient current response of the cylindrical scatterer to a unit step incident plane wave. Complex natural frequencies, natural mode vectors, normalization coefficients, and induced currents are compared to those found through a similar procedure with an approximate kernel, which assumes uniform circumferential variation of the axial current. The exact kernel with an assumed circumferential variation of the axial current is shown to be necessary when the thin cylindrical scatterer is near the ground plane.     

A Nonmodal Formulation for Electromagnetic Transmission through a Filled Slot of Arbitrary Cross Section in a Thick Conducting Screen

This paper considers the two-dimensional problem of electromagnetic transmission through a filled slot of arbitrary cross section in a thick perfectly conducting screen. The equivalence principle is used to divide the original problem into three isolated parts where postulated equivalent sources radiate into unbounded, homogeneous media. These equivalent electric and magnetic currents are chosen to ensure continuity of the tangential components of electric and magnetic fields at each aperture. An integral equation is written for each of the three parts with the equivalent currents as unknowns. The resulting set of coupled integral equations is solved by the method of moments. It is shown in the Appendix that this set of equations has a unique solution. The primary quantities computed are the equivalent magnetic and electric currents on each aperture and the electric current on the remaining portions of the slot cross section. These results are compared with those obtained from a modal solution, where the fields in the slot cross section are expressed in terms of parallel-plate waveguide modes.     

The invariance of the Maxwell equations which is used in the solution of problems of technical electromagnetics

The solution of a boundary electromagnetic problem with impedance boundary conditions is considered using the method based on the invariance of the Maxwell equations to the Lorentz transformations. The results of solution of problems about the wave propagation in a circular waveguide with imperfectly conducting bounding surfaces are compared.     

Analysis of Crossed Wires in a Plane-Wave Field

The currents and charges induced in a pair of electrically thin crossed wires by a normally incident plane electromagnetic wave are derived by analytical methods. The boundary conditions at the ends and at the junction are explained. The solution of a new integro-differential equation for the currents is obtained in terms of trigonometric and integral-trigonometric functions. Depending on the electrical lengths of the crossed elements and location of their junction a variety of quite different distributions of current and charge obtain. These determine the scattered near and far fields. Graphs of computed currents and charges per unit length on the four arms of several important cases are displayed. The accurate determination of the induced currents and charges on a mathematically tractable structure-the thin-wire cross-is an early step in a study that will proceed to electrically thick cylinders, wide strips, and their junctions in crossed configurations in an effort to gain a meaningful approximate understanding of the currents and charges induced on an aircraft by an electromagnetic pulse.     

Higher order impedance boundary conditions applied to scattering bycoated bodies of revolution

In this paper higher order impedance boundary conditions will be employed in the solution of scattering by coated conducting bodies of revolution. The higher order impedance solution reduces the total number of unknowns relative to the exact solution, and produces a system matrix which is less dense than that of the exact solution. The construction of the solution involves two distinct steps. In the first step the body of revolution is replaced by an equivalent set of electric and magnetic currents on its exterior surface which generate the true fields outside the body. An integral equation relating these currents through the free space Green's function is derived. Step two employs the higher order impedance boundary condition to relate the electric and magnetic currents on the surface of the body. This replaces the rigorous solution of the interior problem. The higher order impedance boundary conditions are derived by obtaining an exact impedance boundary condition in the spectral domain for the coated ground plane, approximating the impedances as ratios of polynomials in the transform variables, and employing the Fourier transform. The resulting spatial domain differential equations are solved in conjunction with the integral equation using the method of moments. Several examples of bistatic and monostatic radar cross section for coated bodies of revolution are used to illustrate the accuracy of the higher order impedance boundary condition solution relative to the standard impedance boundary condition solution and the exact solution. The effects of coating thickness, loss, and curvature on the accuracy of the solution are discussed