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

A theoretical analysis is presented for second-harmonic generation in nonli near dielectric media. Mathematical expressions are derived for both the am plitude and phase evolution of optical waves for second-harmonic generation , wherein both second- and third-order nonlinear interactions are taken int o consideration. Based on the results, numerical examples of second-harmoni c generation in LiNbO3 are presented, and the effects of third-order intera ctions on the frequency conversion efficiency and the intensity-dependent p hase-matching condition are discussed. The derived result is amenable to a rigorous analysis of second-harmonic generation with a high-intensity incid ence to nonlinear dielectric media, where the intensity-dependent optical p arameters cannot be neglected.