Quality deterioration of self-phase modulated Gaussian beams

The beam quality parameter M_x² for self-phase modulated Gaussian and super-Gaussian beams has been calculated analytically. These results can be used for experimental measurements of nonlinearities in optical materials. A super-Gaussian beam with a size comparable to a Gaussian one demonstrates much more stable behavior with propagation through Kerr media. The deteriorated beam quality parameter has also been calculated analytically in the case of higher order localized radial phase modes. The presented analysis of beam quality degradation due to localized phase aberrations is more efficient than the standard one based on polynomial aperture aberrations. (letter)