Phase matching of X-waves

This paper demonstrates a comprehensive analysis of phase-matching conditions of X-waves in various nonlinear optical processes. The single pulse (70 ps-duration) of the fourth harmonic of Nd:YAG cw-mode-locked laser is used as a pump beam of KDP crystal (type I phase-matching) based OPG. The angular frequency distribution of parametric superfluorescence is analyzed experimentally and good agreement of theoretical predictions with experimental results is obtained. This study also presents angular-frequency distribution of OPG output radiation in the air for different KDP crystal temperatures. Results show that angular dispersion of parametrically excited waves corresponds to angular dispersion of nondiffracting pulsed beams. The numerical fitting of experimental curve at degeneracy is also presented. So, the parametric downconversion of pump wave stimulates an excitation from quantum noise level the nondiffracting pulsed beams. Hence, these beams will obtain a typical X-shape if the components of spatial-temporal spectrum are phased. The appearance of conical emission in nonlinear optical process can be considered as a feature of the formation of nondiffracting waves.