When two synchronized laser beams illuminate the inner surface of bulk lithium niobate crystals with magnesium doping (5%/mol MgO:LiNbO3) under the condition of total reflection, semi-degenerate four-wave mixing (FWM) is generated. On this basis, a more sophisticated frequency conversion process on the interface of nonlinear crystal has been researched. The generation mechanism of FWM is associated with the fundamental waves reflected on the inner surface of the nonlinear crystal. Analysis of the phase-matching mechanism confirms that the FWM is radiated by the third-order nonlinear polarized waves, which are stimulated by the third-order nonlinear susceptibility coefficient of the nonlinear crystal. Theoretically calculated and experimentally measured corresponding data have been presented in this article. These results are expected to provide new inspiration for further experimental and theoretical research on frequency conversion in nonlinear crystals.

In this Letter, a new method is presented to calculate the interactive length between the fundamental wave and second harmonic generation (SHG) for the configuration of total internal reflection on the inner surface of a nonlinear crystal. Three independent experiments are designed to measure the bandwidths of this second harmonic wave. The theoretical expression of the intensity of SHG is obtained through a nonlinear coupled wave equation. The interactive length of this phase-matched SHG can be calculated mathematically by utilizing the measured bandwidths and the intensity equation. There is no existing method to obtain the interactive length either from theoretical calculations or by experimental measurement. This method can be applied to estimate the extremely short interactive volume in nonlinear processes.