Nonlinear to geometric focusing transition: beam self-cleaning and self-focusing critical power

We propose an easy but effective approach to find a transition numerical aperture between the regimes of laser pulse filamentation with nonlinear focusing and with geometric focusing predominance. The suggested method based on the beam profile measurements allows correction of the data provided by spectra measurements. Using a simple semi-analytical model, we study the dependence of the transition numerical aperture on the pulse power and medium nonlinearity. The analysis shows that in condensed media the transition from the nonlinear to geometric focusing regime occurs at much tighter focusing than in air. Moreover, if the medium nonlinear refractive index is high enough, only the nonlinear focusing regime is observed even at numerical apertures close to one, which allows symmetric plasma channel formation.