Scattering from a corrugated thick screen

A closed form, high-frequency solution is presented for the scattering in the near zone by a semi-infinite thick screen, when it is illuminated by a line source at finite distance. This solution is derived for a thick screen with perfectly conducting side walls, and either perfectly conducting or artificially soft boundary condition on the top face joining the two wedges. This last condition is practically obtained by etching on this face a quarter of a wavelength deep corrugations with a small periodicity with respect to the wavelength. Owing to the particular properties of the artificially soft surface, a strong decoupling effect in the shadow region is achieved for both polarizations; thus, an effective shielding from undesired interferences is obtained. The formulation adopted is based on the spectral approach, which is summarized. The artificially soft boundary condition is accounted for by the spectral Green's function. The procedure leads to a double spectral integral that is asymptotically evaluated. Thus, a high-frequency solution is obtained, that is described as a superposition of different diffracted field contributions, including doubly diffracted rays. This solution uniformly describes the total field, including those aspects where the transition regions of the diffracted fields from the two edges overlap, and an ordinary application of standard UTD fails. Numerical results are presented and discussed in order to emphasize the shielding effectiveness of the corrugated screen.


INTRODUCTION
A closed form, high-frequency solution is presented for the scattering in the near zone by a semi-infinite thick screen, when it is illuminated by a line source at finite distance.This solution is derived for a thick screen with perfectly conducting side walls, and either perfectly conducting or artificially soft boundary condition [l] on the top face joining the two wedges.This last condition is practically obtained by etching on this face a quarter of wavelength deep corrugations with a small periodicity with respect t o the wavelength.Owing to the particular properties of the artificially soft surface, a strong decoupling effect in the shadow region is achieved for both polarizations; thus, an effective shielding from undesired interferences is obtained.
The formulation adopted in this paper, which is based on the spectral approach presented in [2],[3], is briefly summarized in Sect. 2. The artificially soft boundary condition is accounted for by the spectral Green's function derived in [4],[5].The above procedure leads to a double spectral integral that is asymptotically evaluated in Sect.3. Thus, a high-frequency solution is obtained, that is described as a superposition of different diffracted field contributions, including doubly diffracted rays.This solution uniformly describes the total field: including those aspects where the transition regions of the diffracted fields from the two edges overlap, and an ordinary application of standard UTD [6] fails.Numerical results are presented and discussed in Sect. 4 in order to emphasize the shielding effectiveness of the corrugated screen.

FORMULATION
The geometry of the problem is shown in For the sake of simplicity in the notation we deal with the normalized scalar potential $.
The total field is represented as the sum of the GO field plus singly diffracted fields from edges 1 and 2, and doubly diffracted fields.In order to calculate the doubly diffracted contribution, the same formulation as that used in [2],[3] is used, which is summarized hereinafter.First, the response of the first edge to the line source excitation is represented in terms of a cylindrical wave spectrum.Next, each cylindrical spectral source is used as the incident field at the second edge.Then, the near field response of the second wedge is employed to obtain, by spectral synthesis, a double integral representation of the doubly diffracted field An anolougus double diffraction contribution $$," arises from the reverse mechanism 2 4 1 .

Fig. 1 Geometry of the problem
The double spectral integral representation for $ !! is now asymptotically evaluated to find a uniform high-frequency expression.To this end, it is seen that the integrand in (8)  = (O,O), that provides the dominant contribution.Furthermore, Fl(@f, q ) and Fz(@& a2) exhibit pole singularities that independently occur in the two spectral variables.These poles may occur close to and at the stationary point; thus, they have to be appropriately accounted for.The uniform asymptotic evaluation of $f," is performed by considering the nearest poles to the saddle point.It is worth noting that the functions F, are either even or odd with respect to the integration variable for either hard ( h ) or artificially soft (a) and soft ( 5 ) cases.In these latter cases, the integrand vanish at the saddle point; thus, requiring a more accurate asymptotic evaluation, as that in in which is the Generalized Fresnel Integral defined as in [7] where a very simple algorithm is suggested for its numerical computation.The distance parameters involved in the transition functions are:

<
Fig. I. Let US define a cylindrical coordinate system ( p i , 4;) 11 at each edge i = 1,2.A uniform either electric (TMJ or magnetic ($' E,) line source illumination is assumed.Also, let us denote by P' E ( p ; , 6;) the source point and by the thickness of the screen.The incident field at any point P (pl, 4') is eitherE,=-jkCI,$(P,P') or H,=-j k Im$(P,P') for either TM, or TE, case, respectively, where and I,, I, are the amplitudes of the electric and magnetic currents.