Self-focusing of elliptic beams: an example of the failure of the aberrationless approximation

We show that the increase in critical power for elliptic input beams is onl y 40% of what had been previously estimated based on the aberrationless app roximation. We also find a theoretical upper bound for the critical power, above which elliptic beams always collapse. If the power of an elliptic bea m is above critical, the beam self-focuses and undergoes partial beam blowu p, during which the collapsing part of the beam approaches a circular Towne sian profile. As a result, during further propagation additional small mech anisms, which are neglected in the derivation of the nonlinear Schrodinger equation (NLS) from Maxwell's equations, can have large effects, which are the same as in the case of circular beams. Our simulations show that most p redictions for elliptic beams based on the aberrationless approximation are either quantitatively inaccurate or simply wrong. This failure of the aber rationless approximation is related to its inability to capture neither the partial beam collapse nor the subsequent delicate balance between the Kerr nonlinearity and diffraction. We present an alternative two-stage approach and use it to analyze the effect of nonlinear saturation, nonparaxiality, and time dispersion on the propagation of elliptic beams. The results of th e two-stage found to be in good agreement with NLS simulations. (C) 2000 Op tical Society of America.