Geodesic
Resonance Scattering by Infinite Sheets
Teoretičeskaâ i matematičeskaâ fizika, Tome 127 (2001) no. 1, pp. 21-33

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We study the scattering of Bloch waves in a crystal with impurities located on two parallel planes perpendicular to the wave propagation direction. We prove that the reduced scattering matrix has a pole with a small imaginary part and that the transmission coefficient suffers a sharp jump near the real part of the pole. 
@article{TMF_2001_127_1_a1,
     author = {A. A. Arsen'ev},
     title = {Resonance {Scattering} by {Infinite} {Sheets}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {21--33},
     publisher = {mathdoc},
     volume = {127},
     number = {1},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2001_127_1_a1/}
}
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A. A. Arsen'ev. Resonance Scattering by Infinite Sheets. Teoretičeskaâ i matematičeskaâ fizika, Tome 127 (2001) no. 1, pp. 21-33. http://geodesic.mathdoc.fr/item/TMF_2001_127_1_a1/