Abstract
Scattering calculations via the Schwinger variational principle are exemplified for the canonical model of E ∥ plane waves incident on a planarsinusoidal perfect-reflector surface. The complete solution is obtained in terms of a contour integral from which analytic limits are derived that agree with exact results. The contour integral is then evaluated by principal-value and asymptotic techniques, furnishing an explicit solution in Bessel and digamma functions. The variational solution is cast finally into the form of a linear algebraic system, whence we derive various analytic expansions that reproduce further exact results and confirm the efficacy of a simple form of our trial functions. Computations employing this trial function are compared with other approximations and the exact solution. Alternative variational solution representations involving incomplete Anger–Weber or half-range Anger functions are appended.
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