Group-velocity matched femtosecond parametric oscillation by noncollinear quasi-phase matching

A general model of noncollinear femtosecond parametric oscillation in periodically poled gratings is proposed, in which the group velocities of interacting waves are matched, based on a noncollinear quasi-phase matching (QPM) scheme. We demonstrate that group velocity matching and quasi-phase matching can be simultaneously achieved for ultrashort pulses. The corresponding noncollinear angles and grating periods are calculated for periodically poled lithium niobate (PPLN) and periodically poled KTP (PPKTP). With a suitable choice of parameters, the effective interaction length in the crystal can be remarkably increased, and an enhancement of parametric gain by orders of magnitude obtained, thus reducing the operational threshold significantly.