Geodesic
A method for approximate computation of the scattering matrix in acoustic diffraction gratings
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 52, Tome 516 (2022), pp. 238-252

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A two-dimensional reflection acoustic grating is considered. We formulate and justify a method for approximate computation of the scattering matrix describing the scattering of plane waves on the periodic boundary of this grating. To this purpose, the problem in the grating is reduced to a problem in an auxiliary waveguide. The known method for computing waveguide scattering matrices is expanded to the obtained waveguide. The suggested method is not influenced by surface waves in the grating. 
@article{ZNSL_2022_516_a8,
     author = {B. A. Plamenevsky and A. S. Poretsky and O. V. Sarafanov},
     title = {A method for approximate computation of the scattering matrix in acoustic diffraction gratings},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {238--252},
     publisher = {mathdoc},
     volume = {516},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2022_516_a8/}
}
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B. A. Plamenevsky; A. S. Poretsky; O. V. Sarafanov. A method for approximate computation of the scattering matrix in acoustic diffraction gratings. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 52, Tome 516 (2022), pp. 238-252. http://geodesic.mathdoc.fr/item/ZNSL_2022_516_a8/