Shielding Effect of a Thick Screen with Corrugations

— The shielding effectiveness of a corrugated thick screen is theoretically and experimentally investigated. This screen consists of a half-plane of ﬁnite thickness in which corrugations are etched on the smaller side. This structure provides a signiﬁcant attenuation in the shadow region for both polarizations of the incident ﬁeld; thus, it can be effectively used for protecting apparatuses from radiating interference as well as for decoupling nearby operating antennas. The shielding properties of the screen are described by a high-frequency formulation that involves closed-form expressions. An experimental setup at XXX band has been arranged to test the effectiveness of a corrugated screen; the ﬁeld in the shadow region is compared with that of a screen without corrugations. The experimental results compare very well with those obtained by the high-frequency expressions.


I. INTRODUCTION
O VERCROWDED platforms are often subjected to electromagnetic coupling between antennas and/or apparatuses operating close to each other. The engineering solutions for reducing interference and electromagnetic compatibility problems are of increasing importance, particularly for satellite environments. One of the most simple, but effective ways to reduce the radiating interference is to introduce barriers or fins between the two coupled systems. This solution can be also useful in reducing radiating interference in earth satellite stations [1]. In particular, interference that arises from microwave links operating at the same frequency often arrives from directions close to the horizon; they may sometimes be attenuated by diffraction losses at natural barriers occurring in terrain propagation. In other cases, introducing artificial shielding barriers may greatly alleviate these problems. The simplest canonical model of a barrier for interference protection is a perfectly conducting thick screen of a semiinfinite extent. When the source and the observer are optically shadowed, a field coupling still occurs due to double diffraction (DD) mechanisms at the two nearby parallel edges of the screen. Consequently, its shielding effectiveness significantly depends upon the thickness and the polarization of the incident field. In particular, when the incident electric field is parallel to the edges (TM pol, soft boundary condition), the diffracted field into the shadow region is very weak since the first-order diffracted field is short circuited by the conducting portion between the two edges. Then, the second-order diffraction essentially consists in a slope effect that becomes weaker as the thicknesses increases. On the other hand, when the incident electric field is perpendicular to the edges (TE pol, hard boundary condition), a stronger field propagates in shadow region because the first-order diffracted field does not vanish between the two edges. This results in a poor shielding. In order to improve the shielding effectiveness for this polarization, one can etch in the face joining the two edges a quarter of a wavelength deep corrugations, with a periodicity small with respect to the wavelength. For such configurations, the surface at the top of the corrugations may be appropriately modeled as a perfectly magnetic conducting (PMC) surface for the TE pol and a perfectly electric conducting (PEC) surface for the TM pol; thus, an artificially soft boundary condition (BC) is obtained [2], that leads to a similar behavior of the field for both polarizations.
In this paper, the shielding effectiveness of a thick corrugated screen of semi-infinite extent is investigated. In particular, in Section II, a brief description of the phenomena is given and a closed-form high-frequency solution is presented to calculate singly and doubly diffracted field contributions from the edges of the screen. In Section III, an -band experimental setup is described; in Section IV, numerical and experimental results are presented and compared.

II. HIGH-FREQUENCY SOLUTION
The cross section of the thick screen is shown in Fig. 1 in the cases of smooth top face and corrugated top face. Two parallel axes are defined along the two edges (normal to the plane of the paper and outcoming from it), and a cylindrical coordinate system ( ) is introduced at each edge ; denotes the exterior wedge angle at each edge and the thickness of the screen. In most practical cases . A spherical incident either TM or TE field is assumed. When the TE ray propagates along the corrugated surface after diffracting at the trailing edge, it excites TEM modes inside the corrugations. The -field tangent to the top face is short circuited by the /4 deep corrugations, thus yielding a vanishing grazing ray. In our high-frequency treatment, an artificially soft BC model is used at the top of the corrugations; i.e., PEC for TM and PMC for TE polarization. This assumption requires that both the source point and the observation point 0018-9375/98$10.00 © 1998 IEEE lie on the same plane perpendicular to the screen. Indeed, for oblique incidence, more sophisticated anisotropic BC are needed. The total field at the observation point is described as the sum of the following contributions (1) in which is the incident plus reflected geometrical optics (GO) field, denotes singly diffracted ray-field contributions and doubly diffracted field contributions. Each contribution may or may not exist, depending on both the incidence and observation aspects as can be easily inferred from simple ray tracing. Singly diffracted contributions are represented as (2) where is the ray-field singly diffracted at edge 1 (edge 2) that is calculated by (3) where is the incident field at the diffraction point on the edge 1 and the diffraction dyad is defined as (4) Here and henceforth, denote the wavenumber and a harmonic time dependence is assumed and suppressed. In (4), and are ordinary diffraction coefficients predicted by the uniform theory of diffraction (UTD) [3] that apply to perfectly conducting wedges in the TM and TE case, respectively; is the UTD diffraction coefficient for TE illuminated wedge with corrugations on the face [4], [5]. Here, the spreading factor and the distance parameter have been suitably modified to account for the spherical incident wavefront. This leads to csc csc csc csc (5) in which (6a) is the UTD transition function, whose arguments involve (6b) with denoting the integer that most nearly satisfies . Note that the expression of is identical to that of the ordinary UTD soft diffraction coefficient , except for the cosecant functions that replaces the typical cotangent functions. The analogous contribution is easily obtained by substituting subscript 1 with 2.
Doubly diffracted ray-field contribution is represented as (7) where is the doubly diffracted contribution that arises from edge after diffracting at edge . The contribution is obtained from the formulation presented in [6], [7] that is relevant to a line source illumination, by introducing a suitable modification in the spreading factor and in the distance parameters. This leads to (8) where the diffraction dyad is defined as (9) In (9), denotes the DD coefficient for soft BC that applies to TM pol, while and denote the DD diffraction coefficients for the hard and the artificially soft cases, respectively; these latter apply to the TE pol for smooth and corrugated screen, respectively. They are expressed as (10) (11) and csc (12) in which and . Equations (10)-(12) involve the transition functions (13) and (14) where is the generalized Fresnel integral (GFI) defined as in [8] where a very simple algorithm is suggested for its numerical computation.
The distance parameters in the transition functions are (15) and (16) where and are the integers that most nearly satisfy the relations and , respectively.

III. EXPERIMENTAL SETUP
An experimental setup at 8.2 GHz in an anechoic chamber has been arranged in order to test the shielding effectiveness of a corrugated screen (Fig. 2). A square corrugated screen 1 m 1 m has been constructed by two copper sheets supported by a frame of wood. On the top side, an aluminum rod is mounted, which is corrugated on one side and smooth on the other, so that by simply reversing it, both corrugated and smooth thick screens are obtained. This permits the comparison between the performances of these two different structures at the two polarizations. The space between the teeth and their thickness are mm (0.11 ) and mm (0.03 ), respectively [Fig 1(b)]. The depth of the corrugations is mm ( /4) and the thickness of the rod is mm (0.82 ), which contains six teeth. The transmitting and the receiving antennas are pyramidal horns with 5.5 cm 7.5 cm and 7.5 cm 7.5 cm apertures, respectively. The fundamental TE mode, with a quasiuniform phase distribution on the aperture is obtained in both horns, so that the phase center can be assumed on the aperture plane. The transmitting horn is connected via a rectangular -band waveguide to a TWT amplifier, fed by a HP8341B synthesized sweeper. A twist is used for changing the polarization of the transmitting antenna. The receiving antenna is connected via a 50-coaxial cable to a HP8566B spectrum analyzer.
The transmitting horn has been placed at 10 (36.6 cm) from the trailing edge, so that the edge is in the far-field region of the antenna. The receiving antenna is moved at a constant distance (10 ) from the second edge, from the lit to the shadow region. The angular scan of the receiving horn starts in the lit region at about 10 above the incidence shadow boundary of the leading edge, and stops at 30 from the shadowed face of the screen. In order to avoid gain variations, the aperture of the receiving horn has been maintained tangent to the scan circle for all the angular positions.

IV. NUMERICAL AND EXPERIMENTAL RESULTS
Calculations have been carried out to test the accuracy of the present formulation, as well as to demonstrate the effectiveness of the corrugations in shielding arbitrarily polarized incident fields. In Fig. 3, theoretical and experimental data for the total field are plotted by continuous lines and discrete symbols, respectively. The relevant geometries and observation scans are depicted in the insets. The phase center of the transmitting antenna is placed at from the leading edge and at 90 [ Fig. 3(a)] and 60 [ Fig. 3(b)] from the lit face of the screen.
The results relevant to a smooth PEC thick screen in TE pol (hard) are plotted by a short-dashed line (numerical) and black squares (experimental). The PEC TM (soft) results, are plotted by a long-dashed line (numerical) and white squares (experimental). Results for the corrugated screen in TE pol (artificially soft) are plotted by a continuous line (numerical) and black triangles (experimental). Experimental results have also been obtained for corrugated screen in the TM pol (white triangles). The latter practically coincide with those for the smooth screen, thus demonstrating that the TM pol is almost insensitive to the corrugations-as expected.
The agreement between numerical and experimental results has been found very satisfactory even at grazing illumination [ Fig. 3(a)]. It is worth noting that in this case the mathematical description of the physical phenomenon is complicated by the fact that the singly diffracted field exhibits a nonray optical behavior at the second edge, thus requiring the use of the transition functions defined in (13) and (14).
When the receiving antenna gets into the shadow region behind the screen, the artificially soft BC plays an important role, since the total field is dominated by the doubly diffracted field. Indeed, for the TE pol the field of the corrugated screen exhibits an attenuation, which is much stronger (more than 10 dB) than that of the smooth screen. This emphasizes that the corrugations provide a strong shielding effect even for TE pol, which becomes comparable to that for the TM pol. Then, when the receiving antenna approaches the shadowed face, the curves relevant to the soft and artificially soft cases gradually deviate one from the other. This gives evidence to the fact that there the field is mainly influenced by the BC of the shadowed face, as can be inferred from the slope of the two TE curves. Nevertheless, the attenuation of the corrugated screen is still several decibels stronger than that of the smooth screen for the same TE pol. Measurements have also been carried out for investigating the bandwidth of the shielding effectiveness. The results in Fig. 4 are relevant to the geometry shown in the inset. The data are properly normalized with respect to the field obtained by directly coupling the two antennas at a distance of 20.82 , which is the same length of the DD ray-path. This permits to avoid that the frequency dependence of the antenna gain may affect the field data. Measurements have been performed from 4 to 16.4 GHz while 8.2 GHz is the design frequency of the corrugations. Different horns have been used to cover the bandwidth. The experimental data are plotted by symbols in Fig. 4 where an averaging continuous line is also shown. An almost flat behavior of the normalized field is found for higher frequencies than the resonant frequency. This is probably due to the fact that the thickness of the screen increases in terms of the wavelength, and this compensates the loss of shielding effectiveness caused by the nonresonant behavior of the corrugations. At variance, at lower frequencies the field increases rapidly (until 20 dB over the attenuation in band). This rapid variation can be explained by observing that at lower frequency, the corrugations model a reactive impedance BC of inductive nature. This kind of BC supports surface waves excitation [9]- [12] so that the loss of shielding effectiveness may be attributed to the diffraction at the second edge of surface waves excited at the first edge.

V. CONCLUDING REMARKS
A theoretical and experimental investigation on the shielding effectiveness of a thick corrugated screen has been carried out. It is found that this structure can usefully be employed for decoupling nearby antennas operating in an overcrowded environment, since it provides a strong decoupling for both polarizations of the incident field. The theoretical analysis has been performed by applying a high-frequency solution, which is obtained by modeling the corrugated surface by an artificially soft BC. Experimental data have demonstrated that the screen may also be used at higher frequency with respect to the design frequency; at lower frequencies the properties of the screen rapidly degradates. The electromagnetic model presented here does not allow wide bandwidth description and a more complete analysis involving reactive impedance boundary condition is required, which is presently under progress.