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     

Beam scattering by a right-angled impedance wedge

Following earlier developments, a uniform asymptotic solution for two-dimensional high frequency scattering by a right-angled impedance wedge is presented. The wedge supports surface waves on both faces and numerical examples show the relative significance of these surface waves for different surface parameters, source directivities and positions of source and receiver. Surface parameters extracted from experimental data for buildings are used to show that for near grazing incidence surface waves can have a very significant effect along the direction of specular reflection even in the far field. These results should be important in urban propagation modeling.     

High-frequency surface field excited by a magnetic line source on an impedance cylinder

The evaluation of the transverse electric (TE) surface field on an impedance boundary circular cylinder, excited by a magnetic current on the same surface is discussed. The source is of infinite axial extent. The integral which describes the field due to a single surface ray is evaluated numerically and asymptotically. The results compare well with each other as well as with the eigenfunction solution. The surface ray field has a uniform representation in the sense that it remains valid in the immediate vicinity of the infinitesimal source as well as in the deep shadow region. A comparison is made with a flat impedance plane to indicate the influence of curvature on the surface field.     

High-frequency fields excited by a line source located on a concave cylindrical impedance surface

A previous study of high-frequency currents induced by a line source on a perfectly conducting concave cylindrical surface is extended to the case of nonvanishing surface impedanceZ_{s}. Alternative field representations are formulated and evaluated asymptotically as combinations of ray-optical, whispering gallery (WG) mode, surface wave, continuous spectrum, and canonical integral contributions. Numerical calculations provide an insight into the accuracy and utility of the various formulations. Sufficiently far from the source point, a combination of ray optical fields and tightly bound WG modes was previously found to be a most appealing form whenZ_{s} = 0. As the surface impedance becomes more dissipative, the WG modes axe weakened by attenuation and eventually render the ray optical fields adequate by themselves. A representation in terms of rays and a canonical integral is found to be useful for all parameter ranges. The canonical integral has been evaluated numerically and tabulated.     

High frequency scattering by a double impedance wedge

High-frequency diffraction coefficients are presented for up to and including the third-order interaction mechanisms associated with impedance double-wedge structures. The employed formulation is based on the extended spectral ray method (ESRM) accounting for all surface-wave contributions in a rigorous manner. Key identities are provided to enable an efficient asymptotic evaluation of the resulting integrals via a modified Paul-Clemmow steepest-descent method. The double-wedge structures considered are composed of a common face and outer faces which do not intersect. Examples of the structures studied are the thick impedance half-plane and the impedance insert in a full plane. Computations of the diffracted fields are also presented and found to be in good agreement with corresponding data generated with alternate methods. Some backscatter and bistatic patterns are presented for the purpose of examining the variation of the scattered fields as a function of the wedge angle and impedance     

High-frequency scattering by an isorefractive wedge with theparabolic equation method

The parabolic equation (PE) method is applied to the problem of the high-frequency scattering from a diaphanous wedge, that is, a wedge made of a material which is isorefractive with respect to the surrounding medium, illuminated by a plane wave or by a line current parallel to the edge. The proposed approach is able to handle any wedge aperture and incidence angle and presents some novelties that allows overcoming the problems arising in the numerical solution of the parabolic equation applied to penetrable wedges     

High-frequency scattering from the impedance discontinuity on a cylindrically curved surface

Explicit expressions for some diffraction coefficients related to the diffraction from the impedance discontinuity on a cylindrically curved impedance surface are obtained. When the radius of the curvature becomes infinitely large, the edge diffraction coefficient reduces to the known result related to the two-part impedance half-planes.     

Diffraction by a wedge with variable-impedance faces

The scattering from a wedge with nonuniform impedance faces illuminated by a plane wave, perpendicularly incident on its edge, is analyzed. The solution technique is in the framework of perturbative methods; it applies to surface impedances of the wedge faces having the form of a constant plus a small amplitude perturbation which exhibits an exponential dependence on the distance from the edge in a plane transverse to the edge. This is of remarkable importance for applications as it allows the modeling of the actual behavior of the equivalent surface impedance in the special case of wedges coated with dielectric slabs. Uniform asymptotic expressions for the fields are obtained in the context of the uniform geometrical theory of diffraction (UTD)     

Diffraction by an arbitrary-angled dielectric wedge. I. Physicaloptics approximation

A complete form is presented of the physical optics solution to diffraction by an arbitrary dielectric wedge angle with any relative dielectric constant in cases of both E- and H-polarized plane waves incident on one side of two dielectric interfaces. The solution, which is obtained by performing the physical optics (PO) approximation to the dual integral equation formulated in the spatial frequency domain, is constructed by the geometrical optics terms, including multiple reflection inside the wedge and the edge diffracted field. The diffraction coefficients of the edge diffracted field are represented in a simple form as two finite series of cotangent functions weighted by the Fresnel reflection coefficients. Far-field patterns of the PO solutions for a wedge angle of 45°, relative dielectric constants 2, 10, and 100, and an E-polarized incident angle of 150° are plotted in figures, revealing abrupt discontinuities at dielectric interfaces     

High-frequency scattering from the edges of impedance discontinuities on a flat plane

A high-frequency solution is presented for the scattering of a plane wave at the edges of surface impedance discontinuities on a fiat ground plane. Arbitrary uniform isotropic boundary conditions and a direction of incidence perpendicular to the edges of the discontinuities are considered for both the transverse electric (TE) and transverse magnetic (TM) cases. An asymptotic approximation of the exact solution given by Maliuzhinets and a spectral extension of the geometrical theory of diffraction (GTD) are used. Uniform expressions for the scattered field received at a point on the surface are given, including surface wave contributions. Numerical results are shown and in some examples they are compared with those obtained from a moment method (MM) solution.     

Diffraction by a wedge with anisotropic face impedances

When boundary conditions on a surface of a wedge are anisotropic impedance ones, the problem of diffraction is reduced to a coupled system of Maliuzhinets’ equations via Sommerfeld integral. For weak anisotropy a regular asymptotic method is developed to compute the leading terms and the first correction of spectral functions. Electromagnetic field which arises due to anisotropy is presented in closed form. Analytic properties of spectral functions are investigated. Uniform asymptotics for the scattered field are constructed via matching of local asymptotic expansions.     

High-frequency approximations for electromagnetic field near a face of an impedance wedge

We employ the exact solution given by G.D. Maliuzhinets (see Sov. Phys. Doklady, vol.3, p.752-5, 1958) for the canonical problem of diffraction of a plane wave by an arbitrarily angled impedance wedge to derive asymptotic approximations to the field components in a region contiguous to a face of the wedge. The asymptotic solution accounts for terms of order (k/spl rho/)/sup -3/2/ (k is the wave number and /spl rho/ is the distance from the edge), is uniform with respect to observation and illumination aspects and includes the case of grazing illumination of a wedge face, which is known to be particularly difficult for high-frequency analysis (Uflmtsev's singularity).     

Diffraction by a wide double wedge

Following an approximate technique by Karp and Russek for the diffraction by a wide slit, an asymptotic expression for the far diffracted field to a plane wave incident on two semi-infinite wedges is derived in terms of the unperturbed field due to the two wedges in isolation plus an interaction term due to an equivalent inhomogeneous line source at each edge. Numerical results for the diffraction pattern, transmission coefficient, equivalent line source intensity, and interaction term are presented and are in good agreement with previous results.     

Diffraction by a wide double wedge with rounded edges

The multiple diffraction by two conducting wedges with rounded edges is investigated, using an expression for the scattered field of a plane wave incident on a single wedge with rounded edge derived by Ross and Hamid, as well as the technique proposed by Karp and Keller for the diffraction by a slit in an infinite screen. Numerical results for the diffraction pattern, transmission coefficient and the effect of rounding are also presented. It is shown that small rounding of the two edges decreases the transmission coefficient for large separation distances between the wedges.     

Asymptotic solution for line source radiation from a curved perfectly conducting wedge

An asymptotic solution is presented for the radiation of an infinite line source located on a convex face of a perfectly-conducting curved cylindrical wedge. The solution employs a pair of new universal functions. Excellent agreement with a moment method solution is demonstrated for radiation from an original cylinder.<>     

Two-dimensional diffraction by a wedge with impedance boundary conditions

The two dimensional problem of diffraction by a wedge with impedance boundary conditions on its faces is explicitly solved in a form that admits effective numerical simulation by simple perfectly scalable algorithms with unlimited capability for parallel processing. The solution is represented as a superposition of the geometric field that is completely determined by elementary ray analysis and of the waves diffracted by the tip of the wedge. The diffracted field is explicitly represented as a mathematical expectation of a specified functional on trajectories of a random motion determined by the configurations of the problem and by the boundary conditions. The numerical results confirm the efficiency of this approach.     

Diffraction of a normally incident plane wave at a wedge withidentical tensor impedance faces

Diffraction of a normally incident plane wave by a wedge with identical tensor impedance faces is studied and an exact solution is obtained by reducing the original problem to two decoupled and already solved ones. A uniform asymptotic solution then follows from the exact one and agrees excellently with numerical results due to the method of parabolic equation     

TM scattering by a wedge with concaved edge

The TM scattering problem by a perfectly conducting wedge with concaved edge is formulated for a line source excitation using the mode-matching technique. The scattered and guided fields are represented in terms of an infinite series of radial waveguide modes with unknown coefficients. By applying the appropriate boundary conditions, the coefficients of scattered field are obtained. For small ka, the diffraction coefficient of concaved edge is derived from the scattered field     

Electromagnetic scattering by a wedge with anisotropic impedancefaces

Electromagnetic scattering from the edge of an anisotropic impedance wedge, illuminated at oblique incidence, is addressed. In particular, the paper provides a review of existing solutions for this important topic in diffraction theory. Both numerical and analytical techniques, suitable to properly account for the scattering properties of the wedge's anisotropic impedance faces, are considered