Beam breakup and modulational instability in a bulk type I quadratic medium

The effect of a small modulation superimposed on a strip (1D) solitary wave propagating in a bulk quadratic medium was investigated both analytically and numerically near Type phase matching. General, exact results were obtai ned. By using first order perturbation theory, we obtained the gain coeffic ient for the modulational instability and the modulation cut-off frequency and we investigated their dependence on various beam and material parameter s. The wave evolves into a clean periodic sequence of solitary waves and do es not reproduce the incident beam. We showed that the beam breakup observe d experimentally is due entirely to noise induced modulational instability.