مرکز منطقه ای اطلاع رساني علوم و فناوري - On the scatttering of waves by an infinite grating

Abstract :

Using Green\´s function methods, we express the field of a grating of cylinders excited by a plane wave as certain sets of plane waves: a transmitted set, a reflected set, and essentially the sum of the two "inside" the grating. The transmitted set is given by $psi_{o} + 2\\Sigma C_{\\upsilon }G(\\theta_{\\upsilon }, \\theta_{o})psi_{\\upsilon }$ , where the $\\psi$ \´s are the usual infinite number of plane wave (propagating and surface) modes; $G(\\theta_{\\upsilon }, \\theta_{o})$ is the "multiple scattered amplitude of a cylinder in the grating" for direction of incidence $\\theta_{o}$ and observation $\\theta_{\\upsilon }$ ; and the C\´s are known constants. (For a propagating mode, $C_{\\upsilon }$ is proportional to the number of cylinders in the first Fresnel zone corresponding to the direction of mode $v$ .) We show (for cylinders symmetrical to the plane of the grating) that $G(\\theta,\\theta_{o})= g(\\theta,\\theta_{o}) +(\\Sigma _{\\upsilon } - \\int dv)C_{\\upsilon }[g(\\theta,\\theta_{\\upsilon } + g (\\theta,\\pi - \\theta_{\\upsilon })G(\\pi-\\theta_{\\upsilon },\\theta_{o})]$ , where $g$ is the scattering amplitude of an isolated cylinder. This inhomogeneous "sum-integral" equation for $G$ is applied to the "Wood anomalies" of the analogous reflection grating; we derive a simple approximation indicating extrema in the intensity at wavelengths slightly longer than those having a grazing mode. These extrema suggest the use of gratings as microwave filters, polarizers, etc.