In this article we propose a theoretical treatment of noncollinear phase-matched femtosecond parametric interaction process pumped by ultrashort optical pulses, and investigated the pulse characteristics of OPG in BBO crystal. The results show that the major factors, which a8ect the optical parametric conversion coe9cient and durations of the pulses, are the group velocity mismatch and the phase mismatch among the three ultra-short pulses. In addition, the material dispersion can cause the durations of the pulses to increase when pump pulse is below 20 fs, and its in:uence becomes more obvious at low pump intensity.

We describe oscillating loops in a laser cavity and optical paths in a laser crystal of different wavelength rays for a four-mirror cavity Kerr-lens mode-locked laser. The relation between different wavelength ray paths and laser resonator parameters is deduced. The analytical expressions of second- and thirdorder dispersion including angular dispersion of the crystal are presented. The variations of group-delay dispersion (GDD) and third-order dispersion (TOD) with cavity parameters are calculated exactly. The calculation shows that GDD and TOD increase rapidly when the spacing between two folding mirrors approaches the boundary of a cavity stability zone. The rapid dispersion increase influences the modelocked pulse width and the mode-locked stability.

We present analytical expressions of quadratic and cubic phases in a three-element resonator for Kerrlens mode locking. Variation of quadratic and cubic phases with wedge angles of Ti: sapphire and apex angles of a prismatic output coupler are calculated. The results provide a theoretical basis for the design of a three-element cavity.

We have theoretically analyzed the characteristics of an optical parametric amplifier system seeded by an optical parametric generation. We investigated the influences of the energy, pulse duration, material dispersion, and the third-order nonlinear effect in β-barium borate. The group-velocity mismatch (GVM) becomes the most important factor for the amplification of bandwidths. Even though tilting the wave front of the pump can decrease the GVM, it seems impossible to generate pulses smaller than 10-fs with 400-nm pumping. However, 10-fs pulses can be achieved with a 30-fs pump duration with pumping at 800nm.

In this paper, we investigate the group velocity matching based on tilting pulse front in type-III collinear phasematching configuration in BBO crystal. The design seems simple and practicable.