PO near-field expression of a penetrable planar structure in terms of a line integral

An exact line integral representation of the physical optics (PO) field scattered in the near zone by a penetrable planar structure illuminated by a plane wave is discussed.     

Evaluation of reflected fields at caustic regions using a set of GO equivalent line currents

A set of equivalent electric and magnetic line currents is derived which supplements the geometrical optics (GO) solution in the far zone whenever one of the surface principal radii becomes very large. These hypothetical currents lie along the specular line of the surface and are shown to produce the same result as the stationary phase contribution of the physical optics integral. An example of a systematic application of such equivalent currents for the computation of the scattered field from a complex structure is also demonstrated.     

Fringe integral equation method for a truncated grounded dielectricslab

The problem of scattering by a semi-infinite grounded dielectric slab illuminated by an arbitrary incident TM_z polarized electric field is studied by solving a new set of “fringe” integral equations (F-IEs), whose functional unknowns are physically associated to the wave diffraction processes occurring at the truncation. The F-IEs are obtained by subtracting from the surface/surface integral equations pertinent to the truncated slab, an auxiliary set of equations obtained for the canonical problem of an infinite grounded slab illuminated by the same source. The F-IEs are solved by the method of moments by using a set of subdomain basis functions close to the truncation and semi-infinite domain basis functions far from it. These latter functions are properly shaped to reproduce the asymptotic behavior of the diffracted waves, which is obtained by physical inspection. The present solution is applied to the case of an electric line source located at the air-dielectric interface of the slab. Numerical results are compared with those calculated by a physical optics approach and by an alternative solution, in which the integral equation is constructed from the field continuity through an aperture orthogonal to the slab. The applications of the solution to an array of line currents are also presented and discussed     

Incremental length diffraction coefficients for an impedance wedge

An incremental length diffraction coefficient (ILDC) formulation is presented for the canonical problem of a locally tangent wedge with surface impedance boundary conditions on its faces. The resulting expressions are deduced in a rigorous fashion from a Sommerfeld spectral integral representation of the exact solution for the canonical wedge problem. The ILDC solution is cast into a convenient matrix form which is very simply related to the familiar geometrical theory of diffraction (GTD) expressions for the field on the Keller cone. The scattered field is decomposed into physical optics, surface wave, and fringe contributions. Most of the analysis is concerned with the fringe components; however, the particular features of the various contributions are discussed in detail     

High-frequency scattering from a wedge with impedance facesilluminated by a line source. II. Surface waves

For pt.I see ibid., vol.37, no.2, p.212-18 (1989). In Part I a rigorous integral representation for the field scattered at a finite distance from the edge of an impedance wedge when it is illuminated by a line source was derived. It was shown that the total field can be expressed as the sum of the geometrical optics (GO) field, the field diffracted by the edge, and terms related to the excitation of surface waves. The double spectral integral representation for the diffracted field was asymptotically evaluated there, in the case in which no surface wave can be supported by the two faces of the wedge. In particular, the high-frequency solution was expressed in the special format of the uniform geometrical theory of diffraction (UTD). Here, field contributions related to the surface wave excitation mechanism are examined. By a convenient asymptotic approximation of the integrals, a high-frequency solution which is uniform with respect to aspects of both incidence and observation is obtained. Moreover, this solution has useful symmetry properties so that it explicitly exhibits reciprocity. Numerical results are presented to show the relevance of the surface wave terms in the evaluation of the field     

Reduction of the number of unknowns in large stacked planarstructures by a fringe aperture formulation

For scattering problems comprising a combination of planar structures, the total number of unknowns may be significantly reduced if an aperture formulation is employed rather than a patch formulation. The rationale behind using the aperture formulation is based on the recognition that the decay rate of the scattered aperture field is independent of the size of the scatterer. Therefore, any scatterer may be surrounded by an aperture of fixed width over which an integral equation is formulated. The area of this aperture is proportional to the perimeter of the scatterer rather than its area, and it becomes much smaller compared with the entire scatterer area as the size of the scatterer increases, hence the reduction in the number of independent unknowns. A truncation criterion for the finite aperture is determined via a numerical study of the aperture field behavior for various angles of incidence. In addition, the a priori knowledge of the physical optics component is also taken into account, reducing the unknown function to an aperture field component that is the outcome of the remaining fringe current only. The total current distribution can be subsequently derived from this field by adding the known physical optics field and invoking the inverse of the Green's function in the spectral domain. This analysis of isolated planar scatterers results in a spectral scattering matrix representation that is subsequently used for cascading of stacked structures     

High frequency approximations to the physical optics scatteringintegral

Discusses two high frequency (HF) approximations to the physical optics (PO) scattering integral for the far field radar backscatter from a general curved edged reflecting surface viewed at arbitary aspect. The PO scattering integral is first approximated as the sum of a specular effect and an edge effect, where the latter is represented explicitly as a certain line integral evaluated over the boundary edge of the reflector. A closed form result is then obtained by applying the method of stationary phase to the line integral. With the exception of singularities that can occur at caustics, or when the specular point falls on the boundary edge, these HF approximations are found to work reasonably well for smooth surfaces whose Gaussian curvatures have constant sign (positive or negative, but never zero)     

Green's function for arbitrarily shaped dielectric bodies of revolution

In this paper, a solution is developed to calculate the electric field at one point in space due to an electric dipole exciting an arbitrarily shaped dielectric body of revolution (BOR). Specifically, the electric field is determined from the solution of coupled surface integral equations (SIE) for the induced surface electric and magnetic currents on the dielectric body excited by an elementary electric current dipole source. Both the interior and exterior fields to the dielectric BOR may be accurately evaluated via this approach. For a highly lossy dielectric body, the numerical Green's function is also obtainable from an approximate integral equation (AIE) based on a surface boundary condition. If this equation is solved by the method of moments, significant numerical efficiency over SIE is realized. Numerical results obtained by both SIE and AIE approaches agree with the exact solution for the special case of a dielectric sphere. With this numerical Green's function, the complicated radiation and scattering problems in the presence of an arbitrarily shaped dielectric BOR are readily solvable by the method of moments.     

Improvement of prompt response from impulse radiating antennas by aperture trimming

Reflector impulse radiating antennas (IRA) traditionally have been constructed by terminating a self-reciprocal, transverse electromagnetic (TEM) transmission-line feed structure into a paraboloidal reflector. The section of the paraboloid used is usually circular in cross-section, with the outer boundary coinciding with the circle of symmetry of the TEM feed. The reflector converts the spherical TEM mode on the feed line into an approximate plane wave in the near field by geometric optics. The prompt radiated electric field in the direction of focus is given in the physical optics approximation in terms of the integral of the electric field of the TEM mode over the aperture plane inside the reflector boundary. Balanced feed structures have TEM modes that provide both positive and negative contributions to this integral in the aperture plane. Determination of the contour where the principal component of the electric field in the TEM mode is zero identifies portions of the aperture that contribute destructively to the integral. These portions are removed, thereby increasing the prompt radiated field without altering the feed structure or the applied voltage waveform. Furthermore, decreasing the size of the TEM feed relative to the aperture size, followed by appropriate aperture trimming, allows an even greater increase in radiated field. Results are presented that predict an increase in prompt radiated fields for all electrode configurations. Improvements are largest for electrode angles that are large (with respect to the vertical). The trends predicted by the numerical results are verified by an experiment conducted on a time-domain antenna range.     

Comparison of various image induction (II) methods with physicaloptics (PO) for the far-field computation of flat-sectioned segmentedreflectors

Kottler's (1923) extension of Kirchhoff's diffraction integral to electromagnetic fields yields the copolarized and cross-polarized fields of segmented reflectors. For flat sections, the Maggi-Rubinowicz (1888, 1917) potential can be used to transform Kottler's surface integral into a line integral resulting in an expression composed entirely of line integrals. Computation is simplified by the use of the Asvestas (1985) potential which eliminates the need to compute a geometrical optics term required by the original Maggi-Rubinowicz potential. In computing the far fields, a further simplification is realized by considering the antenna in reception rather than in transmission as an involved dyadic potential is then replaced by a simple vector potential. This is an exact-analysis method in the context of the image-induction model which, in theory, provides results which are very close to the physical optics (PO) model for the transmitting antenna. An approximate closed-form method is obtained by applying the Gordon (1975) transform to Silver's (1949) vector far field equations     

Corner diffraction coefficients for the quarter plane

The current near a right-angled corner on a perfectly conducting flat scatterer illuminated by a plane wave is expressed as a sum of three currents. The first is the physical optics current, which describes the surface effect. The second is the fringe wave current, which is found from the half-plane solution and accounts for the distortion of the current caused by the edges. The third is the corner current, which is found from the numerical solution to the electric-field integral equation applied to the square plate, and accounts for the distortion of the current caused by the corner. It is found that the corner current for the right-angled corner, illuminated from a forward direction, consists mainly of two edge waves propagating along the edges forming the corner. Analytical expressions for these edge wave currents are constructed from the numerical results. A corner diffracted field is calculated by evaluating the asymptotic corner contributions to the radiation integral over the sum of the three currents. It is found that the corner contribution from the edge wave currents in some cases is of the same size as the corner contributions from the physical optics current and the fringe wave current     

Diffraction by an anisotropic dielectric half-plane: a uniformasymptotic PO solution

A uniform solution is proposed to, describe the diffraction by a penetrable anisotropic dielectric halfplane illuminated at normal incidence by an electromagnetic plane wave. Resorting to second-order boundary conditions on a sheet simulating a special type of anisotropic dielectric thin layer, a physical optics (PO) approximation for the induced electric and magnetic surface currents is derived. Then, a uniform asymptotic evaluation of the corresponding radiation integral provides the diffracted field in terms of the standard transition function relevant to the uniform theory of diffraction. The effectiveness of the solution is proved by many numerical tests     

A hybrid equation approach for the solution of electromagneticscattering problems involving two-dimensional inhomogeneous dielectriccylinders

A numerical procedure for the solution of electromagnetic scattering problems involving inhomogeneous dielectric cylinders of arbitrary cross section is discussed. The cases of illumination by both transverse magnetic (TM) and transverse electric (TE) plane waves are considered. The scattering problems are modeled via a hybrid integral-equation/partial-differential-equation approach. The method of moments is applied to obtain a system of simultaneous equations that can be solved for the unknown surface current densities and the interior electric field. The interior region partial differential equation and the exterior region surface integral equation are coupled in such a manner that many existing surface integral equation computer codes for treating problems involving scattering by homogeneous dielectric cylinders can be modified easily to generate the block of the matrix corresponding to the surface current interactions. The overall system matrix obtained using the method of moments is largely sparse. Numerical results are presented and compared with exact solutions for homogeneous and inhomogeneous circular cylinders     

The transient electromagnetic field of a pulsed line source located above a dispersively reflecting surface

An exact representation for the transient field of a pulsed line source above a plane reflecting surface is obtained as a finite integral over the transient plane-wave solution for complex angles of incidence. When applied to the reflection from a conducting half-space, a solution for the transient field is obtained as a finite double integral, which permits accurate calculations in a minimum of computer time. Comparison with early-time and late-time approximations available in the literature shows that there is a wide range of times for which neither is accurate.     

Hybrid solutions at internal resonances

The use of hybrid solutions for integral equation (IE) formulations in electromagnetics is illustrated at frequencies where a perfectly conducting scatterer exhibits internal resonances. Hybrid solutions, incorporating the Fock theory and physical optics Ansatzes, and the Galerkin representation, are compared with the method of moments (MM) solutions of the electric, magnetic, and combined field formulations at such frequencies. Numerical results are presented for spheres and a right circular cylinder.     

Plane wave scattering from 2-D perfectly conducting superquadriccylinders

The plane-wave scattering from perfectly conducting two-dimensional cylinders of arbitrary squareness parameter is investigated. A uniform geometrical optics (UGO) solution valid across the smooth caustics generated by the surface poles or zero curvature (inflection) points is developed based on physical optics (PO). The classical geometrical optics solution is modified using a multiplicative transition function that compensates for the caustic singularities and accounts for the complex ray contributions emanating from nonspecular scattering centers located near the surface poles. The transition function is heuristically derived on the basis of the PO radiation integral and involves a generalized (higher-order) form of Airy functions. The resulting UGO solution for the scattered field is simple, easy to apply, and computationally efficient for electrically large cylinders. It compares well with physical optics (numerical integration) and moment-method solutions for both backscatter and limited bistatic configurations     

The electromagnetic edge wave due to a point source of current radiating in the presence of a conducting wedge

Cylindrical wave expansions for the dyadic Green's functions for electric and magnetic fields of a point source of electric current radiating in the presence of a perfectly conducting wedge are derived using a scalarization procedure developed by Levine and Schwinger. The forms derived from this procedure involve a sum over angular wavenumbers and a continuous spectral integral which may be expressed either as an integration over a longitudinal or a radial spectral variable. Some relationships between these two representations are discussed. The longitudinal spectrum integral has a pair of branch points as its only singularities and may be evaluated asymptotically along a steepest descent path away from one of the branch points. The resulting asymptotic representation is found to agree with an earlier result obtained by Kouyoumjian and Buyukdura. The edge-guided wave interpretation of the asymptotic field is discussed, both in light of the longitudinal spectral representation and of the physical content of the asymptotic representation.     

An exact solution of the generalized exponential integral and itsapplication to moment method formulations

The generalized exponential integral is one of the most fundamental integrals in antenna theory and for many years exact solutions to this integral have been sought. This paper considers an exact solution to the generalized exponential integral which is completely general and independent of the usual restrictions involving the wavelength, field point distance and dipole length is considered. The exact series representation presented converges rapidly in the induction and near-field regions of the antenna, and therefore provides an alternative to numerical integration. Two method of moments formulations are considered. They use the exact expression for the generalized exponential integral in the computation of the impedance matrix elements. It is demonstrated that, for very thin straight-wire antennas, an asymptotic expansion can be used to obtain a numerically convenient form of the generalized exponential integral     

A numerical study of the separation wavenumber in the two-scalescattering approximation [ocean surface radar backscatter]

The modeling of radar backscatter from the ocean uses the two-scale scattering approximation. This approximation assumes that the continuous spectrum of the ocean can be separated at some wavenumber into large- and small-scale surfaces, allowing use of physical optics and small perturbation methods. The authors investigate the choice of the separation wavenumber by comparing two-scale calculations and exact numerical calculations for a randomly rough surface with a power law spectrum