A Uniform Geometrical Theory of Diffraction for predicting fields of sources near or on thin planar positive/negative material discontinuities

Abstract

[1] Relatively simple and accurate closed form Uniform Geometrical Theory of Diffraction (UTD) solutions are obtained for describing the radiated and surface wave fields, respectively, which are excited by sources near or on thin, planar, canonical twodimensional (2-D) double positive/double negative (DPS/DNG) material discontinuities. Unlike most previous works, which analyze the plane wave scattering by such DPS structures via the Wiener-Hopf (W-H) or Maliuzhinets methods, the present development can also treat problems of the radiation by and coupling between antennas near or on finite material coatings on large metallic platforms. The latter is made possible mainly through the introduction of important higher-order UTD slope diffraction terms which are developed here in addition to first-order UTD. The present solutions are simpler to use because, in part, they do not contain the complicated split functions of the W-H solutions nor the complex Maliuzhinets functions. Unlike the latter methods based on approximate boundary conditions, the present solutions, which are developed via a heuristic spectral synthesis approach, recover the proper local plane wave Fresnel reflection and transmission coefficients and surface wave constants of the DPS/DNG material. They also include the presence of backward surface waves in DNG media. Besides being asymptotic solutions of the wave equation, the present UTD diffracted fields satisfy reciprocity, the radiation condition, boundary conditions on the conductor, and the Karp-Karal lemma which dictates that the first-order UTD space waves vanish on a material interface.Citation: Lertwiriyaprapa, T., P. H. Pathak, and J. L. Volakis (2007), A Uniform Geometrical Theory of Diffraction for predicting fields of sources near or on thin planar positive/negative material discontinuities, Radio Sci., 42, RS6S18,

An Approximate Utd Ray Solution for the Radiation and Scattering by Antennas Near a Junction Between Two Different Thin Planar Material Slab on Ground Plane

“…1(a) can be obtained by extending the two dimensional (2-D) solution [7] via an approach similar to that in [8]. It is known that the normal field components E y and H y satisfy the Helmholtz scalar equation and impedance boundary conditions independently.…”

“…1(b) contains a PEC for the n-face (x < 0, y = 0, z). The "perturbed" fieldŪ p y can be expressed in a manner similar to that done earlier in [7] for the 2-D case. One can start to rewrite (5) in [7] as…”

“…This unknown constant W will be determined later. It is noted that one can obtain the same PWS integral as shown in (13) if the same ansatz as explained in [7] is used to heuristically synthesize the PWS integral from the available 3-D W-H in [8]. TheR in (13) is given bȳ…”

“…However, the analytical expression for the approximate diffractedŪ d pw in (31) does not satisfy reciprocity, but is expected to provide numerical results which nearly satisfy the reciprocity principle. On the other hand, the technique shown in [7] can be easily applied to restore the reciprocity condition into thē U d pw in (31). The desired ansatz is now established by the set of Equations (34)- (36) and (23), respectively which allows one to obtain a corresponding solution for the case of spherical wave incidence.…”

“…In this paper, it is of interest to extend the normal incidence solution as discussed in [7] in order to treat the more general case of skew (or oblique) incidence (three-dimensional 3-D). Plane wave (for oblique or skew incidence) and spherical wave illumination are considered here.…”