Coupled wave equation study of non-collinear phase-matching second harmonic generation and nonlinear Cherenkov radiation generated on the surface of bulk lithium niobate crystals doped with magnesium medium

In this article, on the basis of our previous research on bandwidth of non-collinear phase-matching second harmonic generation (SHG) and nonlinear Cherenkov radiation (NCR) generated on the boundary of bulk nonlinear crystal, we demonstrated theoretically the coupled wave equation of SHG generated by a Gaussian beam on the boundary of 5%/mol MgO:LiNbO3. Using the Fourier-transform technique, we solved this coupled wave equation. The results can explain theoretically the generation mechanism of two different experimental phenomena which corresponded to non-collinear phase-matching SHG under anomalous-dispersion-like dispersion condition and nonlinear NCR under normal dispersion condition, respectively. The theoretical results show a good agreement with the experimental data. This work can provide theoretical fundamental for more complicated research on the boundary of nonlinear media.