Focused beam self-cleaning during laser filamentation

The beam self-cleaning phenomenon is theoretically predicted by the two-dimensional nonlinear Schrödinger equation, which describes self-focusing, and is observed in the case of femtosecond laser filamentation in the collimated regime of propagation. However, the impact of external focusing on the self-cleaning has not been investigated so far. In this paper we systematically study this impact in a wide range of focusing conditions. We show that the energy range, in which self-cleaning can be observed, shrinks monotonically with the numerical aperture growth at some point vanishing at all.