Second-harmonic generation taking into account dispersion of nonlinear susceptibility

Second-harmonic generation in the field of an ultrashort pulse and the propagation of extremely short pulses in a medium with quadratic nonlinearity are analyzed. Second-harmonic generation is analyzed taking into account the effect of second-and third-order group velocity dispersion and dispersion of nonlinear susceptibility up to the second order. Corrections, whose order of smallness is determined by the parameter (ω_L t _p)^?1, where t _p is the pulse duration and ω_L is the carrier frequency of the pump wave, are obtained. For a large phase mismatch, two new solutions are found that describe the stationary evolution of solitary pump and second-harmonic waves in the regions of both anomalous and normal group velocity dispersions.