Dynamical equations for wave packets in materials with both quadratic and cubic response

Abstract

The dynamical equations that govern the interaction between a weakly modulated plane wave and its second harmonic are derived for materials with asymmetric crystal structure, in which the effects of both the quadratic and the cubic nonlinear susceptibility tensors must be considered. Unlike in the case of pure quadratic nonlinearity, the equations for wave packets that describe temporal and spatial solitary waves do not have the same form unless the crystal structure of the material is nearly centrosymmetric, such that the lowest-order quadratic and cubic nonlinear terms balance. For lossless materials and nonresonant conditions the Hamiltonian structure of the equations is discussed, conserved quantities described, and a stable one-parameter family of bright ground-state solitary wave solutions found numerically for fixed material parameters.