Cherenkov type high-order harmonic processes on nonlinear crystal surface

Cherenkov type sum-frequency and frequency doubling process, which has relatively high converscion efficiency with relaxed phase matching requirements, is a good way for high-order harmonic generation. Cascaded high order Cherenkov harmonic generation on the interface with second order nonlinear coefficient χ
⁽²⁾
from −1 to +1 (i.e., domain wall) has been research in the past. The high-order harmonic generation is produced via enhanced second-order nonlinear susceptibility at domain wall, where Cherenkov second harmonic cascaded with successive multistep sum-frequency generation with simultaneously longitudinal phase-matching. On the nonlinear crystal surface, i.e., the interface with χ
⁽²⁾
from 1 to 0, the nonlinear wave-mixing effect is much more complex, because of the presence of total internal reflection. Besides the high-order nonlinear Cherenkov radiation, there are many other types of cascaded processes, which interplays with each other. This research sorted out the complex high-order nonlinear processes on crystal surface by analysis of their phase matching angles, wavelengths, spot morphology and so on. Through the polarization analysis of phase mismatched high-order nonlinear process on crystal surface, we can determine the cascaded process with χ
⁽²⁾
rather than high-order susceptibility. Cherenkov sum-frequency of the two laser beams with different wavelengths proved that the nonlinear polarization wave propagating is confined on the surface of the nonlinear crystal as on the domain wall, which is an important basis to analyze high-order Cherenkov process. We demonstrate that on the crystal surface high-order Cherenkov type harmonics phase matches several ways, including cascade mode with lower-order Cherenkov radiation participation and without. In addition, a four-wave mixing process at the frequency of third harmonic generation is found, which only appears at the position meeting the complete phase matching, and is relatively weak to the cascaded Cherenkov harmonics, since the third-order nonlinear coefficient is less affected by surface symmetry breaking.