Symmetry of the spatial structure of radiation upon transverse mode locking in an astigmatic resonator laser

The influence of the astigmatic resonator parameters on the symmetry of the spatial structure of the radiation intensity is analysed upon transverse mode locking in a nonuniformly pumped laser. Conditions for the transition from the circular symmetry to its violation are found. At a fixed astigmatism of the resonator, the symmetry is determined, first of all, by the resonator length and losses. The theoretical conclusions are confirmed by the experiments with diode end-pumped Nd:YAG and Nd:YLF lasers.