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- W2169727283 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 <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>psi_{o} + 2SigmaC_{upsilon}G(theta_{upsilon}, theta_{o})psi_{upsilon}</tex> , where the <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>psi</tex> 's are the usual infinite number of plane wave (propagating and surface) modes; <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>G(theta_{upsilon}, theta_{o})</tex> is the multiple scattered amplitude of a cylinder in the grating for direction of incidence <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>theta_{o}</tex> and observation <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>theta_{upsilon}</tex> ; and the C's are known constants. (For a propagating mode, <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>C_{upsilon}</tex> is proportional to the number of cylinders in the first Fresnel zone corresponding to the direction of mode <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>v</tex> .) We show (for cylinders symmetrical to the plane of the grating) that <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>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})]</tex> , where <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>g</tex> is the scattering amplitude of an isolated cylinder. This inhomogeneous sum-integral equation for <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>G</tex> 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." @default.
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- W2169727283 date "1956-07-01" @default.
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- W2169727283 title "On the scatttering of waves by an infinite grating" @default.
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- W2169727283 doi "https://doi.org/10.1109/tap.1956.1144408" @default.
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