Role of walk-off in solitary-wave propagation in materials with quadratic nonlinearity

In the framework of second-harmonic generation with type I phase matching, we investigated the role played by temporal or spatial walk-off. Using a variational technique, we found that a two-parameter class of solutions always exists, even when nonnegligible spatial or temporal walk-off is present. We checked solitonlike behavior for the approximate stationary solutions by numerical integration of the governing equations; expressions of phase condition for stationary solutions and velocity of the locked waves were derived. To outline the possibilities offered by our approach in predicting the behavior of χ(2) devices, several examples for beam and pulse propagation in KTiOPO4 and LiNbO3 are presented.