Review of hybrid methods on antenna theory

Hybrid methods are robust analysis tools for a large class of complex scattering and radiation problems not amenable to traditional classical methods. In the hybrid technique, a complex radiator is decomposed into parts solved by a combination of numerical and asymptotic methods. Three methods are reviewed here: the hybrid MM/Green’s function method; the field-based hybrid method which combines the method of moments (MM) and the geometrical theory of diffraction (GTD); and the current-based hybrid method which incorporates MM, physical theory of diffraction (PTD), and the Fock theory. The domain of applicability of each method is illustrated with examples.     

Electromagnetic scattering from extended wires and two- and three-dimensional surfaces

Efficient numerical solutions for the electromagnetic scattering for classes of electrically large one-, two-, and three-dimensional perfectly conducting scatterers are presented. The formulation is based on solution of the electric field integral equation (EFIE) using the method of moments (MM). An entire domain Galerkin representation is used for wires and two-dimensional surfaces and a combination of entire and subdomain representations is applied to surfaces in three dimensions. The analysis is extendable to corrugated surfaces formed from sections of surfaces of translation or rotation. Numerical results are presented for wires, infinite strips, and finite strips (or plates). The behavior of the solutions with the number of terms in the entire domain expansion is examined. The reconstruction of the traveling-wave contribution to the scattering cross section using various approximations is discussed, and representative examples are given.     

Integral equation formulations for imperfectly conducting scatterers

Integral equation formulations are presented for characterizing the electromagnetic (EM) scattering interaction for nonmetallic surfaced bodies. Three different boundary conditions are considered for the surfaces: namely, the impedance (Leontovich), the resistive sheet, and its dual, the magnetically conducting sheet boundary. The integral equation formulations presented for a general geometry are specialized for bodies of revolution and solved with the method of moments (MM). The current expansion functions, which are chosen, result in a symmetric system of equations. This system is expressed in terms of two Galerkin matrix operators that have special properties. The solutions of the integral equation for the impedance boundary at internal resonances of the associated perfectly conducting scatterer are examined. The results are compared with the Mie solution for impedance-coated spheres and with the MM solutions of the electric, magnetic, and combined field formulations for impedance-coated bodies.     

Electromagnetic scattering from finite circular and elliptic cones

A formulation based on the physical theory of diffraction (PTD) is presented for finite conical surfaces with circular and elliptic cross sections. The base-rim discontinuity is represented by equivalent currents, including second-order terms extended for elliptic boundaries. Tip-rim interactions are examined as a function of the tip-rim distance, cone angle, and illumination angle for circular cones; and their implication for elliptic cones is noted. The diffraction contribution from tip-rim interactions is shown to be dependent on the cone angle and the illumination angle but to be relatively insensitive to the tip-rim distance. The Fock Ansatz is used to enlarge the validity of the PTD formulation to cases where nonspecular effects arising from surface curvature and shadow boundaries are significant. The formulation is applied to cones with varying ellipticity for axial and oblique illumination. Correlation is made with published results for circular cones and with experimental data for an elliptic cone.     

Hybrid solutions for scattering from large bodies of revolution with material discontinuities and coatings

A formulation is presented for electromagnetic scattering from electrically large convex bodies of revolution (BOR's) having material discontinuities. Hybrid solutions are developed for the resulting integral equations, using the method of moments (MM) technique together with the Fock or physical optics (PO) Ansatz for large convex conducting bodies where the use of the MM approach by itself is computationally impractical. The analysis is developed for arbitrary oblique illumination. The solutions are shown to yield accurate results for nonspecular, surface wave dominated scattering. The method is illustrated for spheres, cylinders and conespheres having material discontinuities. Generalization of this formulation applies also to graded, nonuniform lossy coatings on BOR scatterers.     

Combined field integral equation formulation for inhomogeneous two and three-dimensional bodies: the junction problem

A combined field integral equation (CFIE) formulation is presented for two- and three-dimensional bodies having discrete dielectric and conducting regions. A three-dimensional case is restricted to bodies of revolution (BORs). The two-dimensional case is analogous to the BOR case when the Fourier mode number is zero. The method of moments (MM) is used to solve the CFIE in terms of two integral operators. It is shown that the CFIE formulation yields accurate answers for scattering problems where the scatterer may be internally resonant. The CFIE results were validated using Mie series results and measured data. The junction problem associated with the CFIE-based formulation is explicated, and several geometries with multiple junctions are used to validate the general CFIE formulation. A number of configurations are tested where the penetrable region consisted of a free-space coating. Extensive numerical studies have shown that such limiting cases are sensitive indicators of the stability of MM solutions and allow direct comparison of different configurations     

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.     

Electromagnetic scattering from ducts with irregular edges. II.Noncircular case

For pt.I see ibid., vol.AP-36, no.3, p.383-97 (1988). Electromagnetic scattering from finite noncircular ducts terminated with irregular edges is investigated. An edge-dependent entire-domain Galerkin expansion is proposed for the current variation on the duct wall, rigorously satisfying the edge conditions. The electric field integral equation is solved using this expansion for arbitrary noncircular ducts. Convergence of these solutions is examined and compared to results obtained with a simpler edge-independent formulation. The solutions are shown to agree with previously published results for circular ducts and recently obtained experimental data     

Hybrid methods for analysis of complex scatterers

Depending on the angle of illumination, electrically large scatterers can support a variety of electromagnetic (EM) phenomena, such as traveling waves, creeping waves, and edge/surface diffraction effects. The electrical size of a body limits the tractability of numerical methods such as the method of moments (MM), and the geometric complexity of an object circumscribes the applicability of optics-derived methods. Hybrid methods incorporating both numerical and high-frequency asymptotic techniques have the potential to substantially enlarge the class of EM scattering problems that can be treated. In this discussion, the current-based hybrid formulation is summarized for classes of two- and three-dimensional scatterers. The use of Ansatz solutions derived from physical optics, the physical theory of diffraction, and the Fock theory is illustrated for perfectly conducting, partially penetrable, and totally coated bodies. For the latter, a generalization rooted in the impedance boundary (Leontovich) condition is used. Complementing these Ansatz solutions, the Galerkin representation is used for regions where the foregoing are computationally or physically intractable. The above cases are illustrated by representative solutions explicating the approach