Four-wave interaction in 2D periodic structures

The interaction of four SAWs is considered in a 2D periodic grating on the surface. In the isotropic case the grating reflects the incident wave with angles ±90°. Coupling-of-modes equations governing the four-wave interaction near the Bragg frequency are derived. For a rectangular shape of the area covered by the grid, they are solved analytically for zero detuning frequency and numerically for frequencies close to the Bragg frequency. The analytical solution shows resonant build-up of the amplitudes of the waves reflected in ±90° directions.