Spontaneous phase symmetry breaking in a four-frequency ring gas laser

Lasing regimes of a single-mode four-frequency class-A ring gas laser with elliptical polarization of the emitted waves are studied numerically. Stationary regimes typical of both standing-and traveling-wave lasing are discovered. Self-oscillations exhibiting the properties of asymmetric and symmetric limit cycles are also found. It is shown that transition between cycles with different symmetry may result in the spontaneous phase symmetry breaking and the appearance of chaos arising due to the period doubling bifurcation cascade of the asymmetric limit cycle.