Characteristics of second-harmonic generation including third-order nonlinear interactions

A theoretical analysis is presented for second-harmonic generation in nonlinear dielectric media. Mathematical expressions are derived for both the amplitude and phase evolution of optical waves for second-harmonic generation, wherein both second- and third-order nonlinear interactions are taken into consideration. Based on the results, numerical examples of second-harmonic generation in LiNbO/sub 3/ are presented, and the effects of third-order interactions on the frequency conversion efficiency and the intensity-dependent phase-matching condition are discussed. The derived result is amenable to a rigorous analysis of second-harmonic generation with a high-intensity incidence to nonlinear dielectric media, where the intensity-dependent optical parameters cannot he neglected.