High-intensity light bullets at the competition of quadratic and cubic nonlinearities

Our studies are focused on high intensity spatiotemporal parametric processes in a microdispersive non-centrosymmetric medium. We solve numerically the system of coupled parabolic equations for second harmonic generation that are supplemented with terms responsible for self- and cross- modulations. Joint influence of quadratic and cubic nonlinearities is studied for the case of anomalous dispersion at both frequencies. Recently it was demonstrated that provided small phase mismatches a stable two-color light bullet may be generated and then it propagates in a medium with pure quadratic nonlinearity. At the same time, pure Kerr nonlinearity is responsible for bullet instability. In our investigations we reveal a threshold condition of the two-color bullet stability in the medium with combined quadraticcubic nonlinearity.