A method for approximate computation of the scattering matrix in acoustic diffraction gratings

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.