ASTIGMATISM IN GAUSSIAN-BEAM SELF-FOCUSING AND IN RESONATORS FOR KERR-LENS MODE-LOCKING

An analytical treatment for the propagation of astigmatic Gaussian bea ms in Kerr media is presented. This method, which is valid to the firs t order in the beam power, allows us to calculate in closed form the n onlinear variations of the spot size and the radius of curvature. This formalism is applied to the calculation of the self-consistent Gaussi an mode of an astigmatic resonator with a Kerr medium, such as those u sed for Kerr-lens mode-locked lasers. Theoretical predictions are conf irmed by the experimental results obtained with a femtosecond Ti:sapph ire laser. In particular, the design of an optimized resonator permits self-starting of the mode-locking mechanism.