Integral equation solution for analyzing scattering fromone-dimensional periodic coated strips

A set of integral equations based on the surface/surface formulation are developed for analyzing electromagnetic scattering by one-dimensional periodic structures. To compare the accuracy, efficiency, and robustness of the formulation, the electric field integral equation (EFIE), magnetic field integral equation (MFIE), and combined field integral equation (CFIE) are developed for analyzing the same structure for different excitations. Due to the periodicity of the structure, the integral equations are formulated in the spectral domain using the Fourier transform of the integrodifferential operators. The generalized-biconjugate-gradient-fast Fourier transform method with subdomain basis functions is used to solve the matrix equation     

Mixed-field hybrid FEM/BEM formulation for two-dimensional TEradiation and scattering by resistive strips

A new mixed-field, hybrid finite-element method (FEM) (E-field)/BEM (H-field) formulation is presented for modeling the two-dimensional (2-D) radiation and scattering from scatterers comprised with inhomogeneous materials including resistive cards and perfectly electrically conducting (PEC) strips for the TE polarization. Using the usual H-field formulation leads to the requirement for the use of a special gap element. The E-field formulation will result in a much more cumbersome BEM integral. The new mixed-field formulation retains the simplicity of the scalar formulation and is useful for problems which cannot be treated elegantly with the existing approach. The new formulation has been implemented into a 2-D FEM/BEM computer code. Numerical results obtained compare well to previously published results     

Electromagnetic radiation and scattering from finite conducting anddielectric structures: surface/surface formulation

An efficient and accurate numerical procedure for the analysis of the electromagnetic scattering and radiation from arbitrarily shaped, composite finite conducting and dielectric bodies is proposed. A set of coupled electric field integral equations involving surface equivalent electric and magnetic currents is used. The coupled integral equations are solved through planar triangular patch modeling and the method of moments. Two separate, mutually orthogonal vector functions for each edge connecting a pair of triangular patches have been developed. Numerical results for disk/cone and cylinder/cone structures are compared with other available data. Limited comparison with experimental data has also been made     

Electromagnetic scattering from electrically large coated flat and curved strips: Entire domain Galerkin formulation

Efficient numerical solutions are presented for electromagnetic scattering for classes of electrically large, coated, perfectly conducting strips which are flat or curved. The formulation is based on the solution of a coupled system of electric- and magnetic-field integral equations using the method of moments (MM). Entire domain Galerkin representations for the currents are used on the surface of the coating and at the coating-conductor interface. The resulting symmetric matrix equation is well conditioned and admits rapid, accurate solutions. Numerical results are presented for various coating thicknesses, strip widths, and curvatures for the transverse electric (TE) and transverse magnetic (TM) cases. The convergence of the Galerkin solution is examined as a function of these parameters. The effect of the edge approximation on the choice of expansion functions is discussed. The numerical results are compared with experimental measurements.     

A UGO/EUTD solution for the scattering and diffraction from cubicpolynomial strips

A combined uniform geometrical optics (UGO) and extended uniform geometrical theory of diffraction (EUTD) solution is developed for scattering and diffraction by perfectly conducting cubic polynomial strips. The new solution overcomes the difficulties of the classic GO/UTD solution near caustics and composite shadow boundaries. The approach for constructing the UGO/EUTD solution is based on a spatial domain physical optics (PO) radiation integral representation for the scattered field, which is then reduced using a uniform asymptotic procedure. New uniform reflection, zero-curvature diffraction, and edge diffraction coefficients are derived and involve the ordinary and incomplete Airy integrals as canonical functions. The UGO/EUTD solution is very efficient and provides useful physical insight into the various scattering and diffraction processes. It is also universal in nature and can be used to effectively describe the scattered fields from flat, strictly concave or convex, and concave-convex boundaries containing edges. Its accuracy is confirmed via comparison with some reference moment method (MM) results     

An open surface integral formulation for electromagnetic scattering by material plates

Using the surface equivalence theorem, four coupled integral equations are developed for electromagnetic scattering by a thin material plate. Using symmetry properties, it is shown that these equations can be written as open surface integral equations. Surface impedance relationships are obtained and used to eliminate two of the four integral equations. The remaining two equations are solved using the method of moments (MM). Numerical results for penetrable and impenetrable material plates are in reasonable agreement with measurements.     

A spectral-iteration approach for analyzing scattering from frequency selective surfaces

A novel technique, called the spectral-iteration approach, for analyzing the problem of scattering from periodically perforated screens which find useful applications as radomes, optical filters, artificial dielectrics, and so on is applied. The formulation is carried out in the spectral domain where a set of algebraic equations is obtained directly for the spectral coefficients of the aperture field distribution (or the induced current density) rather than via an integral equation formulation. These equations are then solved simultaneously using an iterative procedure developed in this paper that circumvents the need for matrix inversion. Because the matrix solution is avoided in the spectral approach, it is capable of handling large aperture sizes in a computationally efficient manner. The efficiency of computation results from the use of the fast Fourier transform (FFT) algorithm which is employed in the derivation of the algebraic equations and in the iteration procedure. A unique feature of the spectral-iteration approach is that it has a built-in boundary-condition check which provides a reliable indication of the accuracy of the solution. It is also shown that the spectral domain technique can be applied to even a wider class of geometries, e.g., the step discontinuity in a waveguide.     

Sinusoidal reaction formulation for radiation and scattering from conducting surfaces

A piecewise-sinusoidal reaction technique is developed for scattering and radiation from perfectly conducting bodies of arbitrary shape. This paper presents the theory and numerical results for scattering patterns of rectangular plates and radiation patterns of corner-reflector antennas. In all cases, experimental measurements are included for comparison with the calculated data.     

A canonical formulation for analyzing multielement unstable resonators

A simple but general formulation for the unified analysis of many different varieties of unstable optical resonators is obtained by expressing the round-trip Huygens' integral for the resonator in terms of the round-trip paraxial ray matrix. Complicated multielement resonators, ring resonators, and unstable resonators with variable-reflectivity output mirrors are thereby all reduced to a single equivalent collimated-beam diffraction problem. Essential assumptions in the analysis are that all elements in the resonator obey paraxial ray theory and that there is only one significant output coupler or limiting aperture per round trip inside the resonator. The only parameters needed to describe an arbitrary unstable resonator in this formulation are the round-trip magnificationMand either the equivalent Fresnel number Neqor else an equivalent collimated Fresnel numberN_{c} = [2M^{2}/(M^{2} - 1)] N_{eq}, plus for variable-reflectivity mirrors a specification of the mirror reflectivity profile.     

Numerical evaluation of Rayleigh hypothesis for analyzing scattering from corrugated gratings--TE polarization

Diffraction of parallel polarized electromagnetic waves from corrugated periodic perfectly conducting surfaces is analyzed by both a rigorous method and a method based on the Rayleigh hypothesis. The accuracy of the rigorous technique is established by comparing results against other theoretical and experimental results. Further results are then obtained and used as standards against which results based on the Rayleigh method are compared for accuracy. These comparisons indicate that the Rayleigh method gives reasonably accurate results for gratings with surface height to period ratios of up to0.88/(2pi). This confirms that the Rayleigh method is also applicable to these nonanalytic surfaces and leads to accuracies that are higher than those normally assumed in the literature.     

A new solution for TE plane-wave scattering from a symmetricdouble-strip grating composed of equal strips

The paper presents a new rigorous solution for the problem of TE plane-wave scattering from a periodic planar symmetric double-strip grating, i.e., the grating which has two equal strips per unit cell. The grating is placed at a dielectric interface and is assumed to be perfectly conductive and infinite in length and width. The formulation is based on a multimode equivalent network representation and the relevant integral equation defined on two separate intervals is rigorously solved by reducing to two simpler equations with known solutions. From this a new simple analytic expression is obtained for the coupling matrix elements which involves no integration. Some computations based on this new expression are carried out and the results are compared to those obtained by the Riemann-Hilbert method and also to some of the previously obtained single-strip results in the limiting case     

A general method for analyzing em wave scattering from arbitrarily shaped two-dimensional periodic surfaces

In this paper the Method of Lines (MoL) is successfully extended to solve the EM wave scattering problems of periodic surfaces with arbitrary profile. As examples, the scattering coefficients of space harmonics of corrugated and sinusoidal surfaces are calculated. The results are in good agreement with available data from Wirgin and from A.K.Jordan et al. In addition, the results of comb structure are also calculated. The flexibility and less computation of this method make it eligible for analyzing various two-dimensional periodic structures.     

The scattering matrix formulation for overmoded coaxial cavities

The scattering matrix formulation for complex right-circular activities is extended to coaxial circuits with variable inner radii. The modified eigenvectors, which include the TEM wave, and the modified boundary conditions are presented. The properties of several configurations are examined and transmission measurements are shown to be in good agreement with theory     

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     

The field feedback formulation for electromagnetic scattering computations

A new procedure is described for the solution of electromagnetic scattering problems in unbounded regions. Using this technique a spatial region enclosing the scatterer is initially decoupled from the exterior region and the fields therein are considered as the solution of an interior Dirichlet boundary value problem. The interior region solution is then recoupled to the unbounded exterior region by use of the equivalence principle. Such a process can be symbolically represented as a simple feedback system. The formulation is demonstrated for the case of plane wave scattering by finite metallic circular cylinders. A finite element solution of the interior problem is utilized in this example in conjunction with a field representation using a special case of coupled azimuthal potentials.     

An improved MFIE formulation for TE-wave scattering from lossy,inhomogeneous dielectric cylinders

A method-of-moments formulation involving the magnetic-field integral equation (MFIE) is presented for the analysis of nonhomogeneous electric (TE) source. The approach involves the use of triangular subdomain cells, a piecewise linear expansion for the total magnetic field, and point matching at the nodal points of the triangular-cell model. Results for internal fields and radar cross section are presented and shown to be stable and convergent, even for dielectrics characterized by a large-magnitude complex relative permittivity. It is noted that the complementary problem of TM-wave scattering from ferrite cylinders characterized by a permeability function can be treated using the dual to the approach presented     

Matrix formulation of electromagnetic scattering

A new method is proposed for the computation of the radar cross section and other associated field quantities arising when a smooth, perfectly conducting obstacle is illuminated by an incident electromagnetic wave. The scattered wave is first represented by a distribution of electric dipoles over the surface in question, with the response from any dipole proportional to the induced surface current density at that point. The surface current is then determined by the "boundary condition" that the scattered wave, through interference, precisely cancels the incident wave inside the obstacle. One obtains in this mariner a pair of coupled (infinite) matrix equations for the surface current. Green's identity permits decoupling of the equations, reducing the problem to roughly the equivalent of two independent scalar problems. The equations have been specialized to axially symmetric obstacles and then solved numerically on the IBM 7094 for several examples of interest. Reciprocity and energy conservation are also examined and the resonant mode (interior) problem set up explicitly in matrix form.     

A frequency-domain differential equation formulation forelectromagnetic scattering from inhomogeneous cylinders

A procedure is described for calculating scattering cross-section data based on the numerical solution of differential equations in the frequency domain. The scatterers considered are two-dimensional and consist of lossy, inhomogeneous dielectric, magnetic, and perfectly conducting material. The appropriate wave equation is combined with an approximate local absorbing boundary condition and discretized with the finite-element method. Results for conducting and dielectric scatterers are presented to illustrate the accuracy and generality of the approach     

A method for computing scattering by large arrays of narrow strips

The electromagnetic scattering characteristics of an array of narrow, conducting strips can he developed readily by extending the work of Butler and Wilton who show that Chebyshev polynomials augmented with the edge condition can be used to solve the narrow-strip/narrow-slot integral equations. The strips reside in a homogeneous medium of infinite extent and are considered narrow relative to wavelength in the medium at the frequency of excitation. The unknown current distributions on the strips are represented as linear combinations of certain basis functions that are exact solutions to the approximate equation for an isolated narrow strip subject to a special excitation. The resulting power-series treatment allows easy calculation of the coupling terms among the strips in the array in a simple matrix equation by which the unknown coefficients in the current distribution expansions may be readily computed. With these coefficients, one can obtain the distribution of current on each strip and the total scattered field. The method is particularly well suited for handling large arrays with more strips than could be accommodated by the usual moment method. Numerical data-currents and scattered fields-are presented for various cases of interest.     

A spectral iteration technique for analyzing scattering fromcircuit analog absorbers

An iterative technique is described for solving for the current and field distributions in a structure composed of a periodic array of sheet conductors, deposited on a dielectric layered substrate, whether or not backed by a conductor. The incident field must be a plane wave but can be oblique. The periods array is taken into account by use of a Floquet mode field formalism, and an iterative method has been chosen that permits a numerical solution on personal computers by avoiding matrix inversions