Optimization of third harmonic generation for two coupled three-frequency interactions of waves with multiple frequencies in periodic crystals

Third harmonic generation with simultaneous excitation of degenerate two-frequency (2ω = ω + ω) and three-frequency (3ω = 2ω + ω) interactions of collinear waves in periodic crystals is considered. It is shown that the optimal condition for third harmonic generation, in this case, is determined by the ratio of the amplitudes of the fundamental and second harmonics at the entrance of the crystal. The optimal value of this ratio, for which the efficiency of the third harmonic generation may reach 96%, is found.