Temporal Solitary Waves with Walk-Off in Nonlinear Quadratic Media and their Stability

Abstract

Recently solitary waves based on a quadratically nonlinear interaction attracted a lot of attention in nonlinear optics. They were found to exist as selfguided beams in planar waveguides [1]. Both spatial and temporal solitary waves are described by the same evolution Until now only a one-parameter family of such solutions is known. In the spatial case this corresponds to the fundamental and second harmonics propagating in the same direction. No spatial walk-off is induced, e.g. by birefringence. The spatial walk-off can be avoided in a planar waveguide, whereas in the temporal case the situation is much more complicated. The known one-parameter family of solitary wave solutions corresponds to a certain carrier frequency where the group velocities of the two pulses (fundamental and second harmonics) are equal. In most materials such a frequency does not exist. Here we concentrate on the more common situation where the two pulses may move away from each other due to a group velocity difference. The family of solitary wave solutions obtained is two-parametric and applies to the case of spatial walk-off as well.