Scattering by a Two-Dimensional Periodic Array of Narrow Plate

Abstract

Theoretical and experimental studies of the scattering by a two‐dimensional periodic array of narrow, perfectly‐conducting plates have been carried out. The scattering in the resonance region is treated. The present work is restricted to a normally incident plane wave; however, the approach described here can be extended to the case of oblique incidence. The surface current on a single plate is expanded in a series of N terms. An integral equation is obtained for by enforcing the boundary condition on the tangential electric field. The N unknown coefficients of are found by satisfying the integral equation exactly at N points. The solution for the scattered field was found to be highly sensitive to the location of the N points at which the integral equation is satisfied. A set of N points is found by introducing a suitable error gauge which involves ∫ J_s · E^Tds, where the integral is taken over a single plate and is the calculated total electric field. Within the frequency band considered, the reflectivity of the array is seen to range from unity at its first resonance to zero at certain frequencies where Wood's anomalies occur. Also, the frequency shift of the array resonance from single element resonance is observed. Values of the reflection coefficient calculated as a function frequency compare well with experimental values.