A rigorous method for analyzing plane-wave scattering from perfectly conducting periodic surfaces is presented and applied to trapezoidal profiles. Both TE and TM polarizations of the incident plane wave are considered. An integral equation for the unknown current distribution in the scatter surface is formulated by invoking the extended boundary condition. Upon expressing the current density in terms of its physical optics approximation multiplied by a Fourier series, the integral equation reduces to a linear system of equations. For the case of a piecewise linear surface profile, the coefficient matrix of this system is amendable to efficient computer evaluation, which furnishes the Fourier coefficients of the current distribution. The method is applied to trapezoidal scatterers for which little data is available in the literature, and, by using appropriate limiting procedures, to triangular and rectangular profiles.
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