Geodesic
Wood's anomalies and surface waves in the~problem of scattering by a~periodic boundary.~I
Sbornik. Mathematics, Tome 190 (1999) no. 1, pp. 111-141

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The solution of the problem of diffraction of an acoustic plane wave by a periodic boundary for frequencies close to threshold values is studied. Wood's well-known experiments show that deviations from the threshold frequency values by a small quantity bring about drastic changes in the diffraction pattern. The asymptotic formula with respect to the small parameter $\varepsilon$ is obtained for the corresponding scattering matrix. 
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     author = {I. V. Kamotskii and S. A. Nazarov},
     title = {Wood's anomalies and surface waves in the~problem of scattering by a~periodic {boundary.~I}},
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     url = {http://geodesic.mathdoc.fr/item/SM_1999_190_1_a3/}
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I. V. Kamotskii; S. A. Nazarov. Wood's anomalies and surface waves in the~problem of scattering by a~periodic boundary.~I. Sbornik. Mathematics, Tome 190 (1999) no. 1, pp. 111-141. http://geodesic.mathdoc.fr/item/SM_1999_190_1_a3/