Second harmonic generation in a two-dimensional diatomic lattice

Resonant interactions of modes in two-dimensional (2D) diatomic lattices are studied within the framework of the multiscale expansion. Equations governing three-wave processes and second harmonic generation are derived for a lattice having a finite number of cells. A particular example of the second harmonic generation in a two-dimensional lattice with nearest-neighbor interactions is considered in detail. It is shown that the 2D case reveals new features like, for example, possibility of simultaneous resonant interaction of one mode with two other ones, existence of solitary wave pulses localized in space and moving along the lattice, and creation of stationary spatial structures subject to proper boundary conditions.