Structural instabilities of a ring laser with optical back-scattering

The structure and stability region of the stationary ring laser states are essentially dependent on the spectral characteristic of the amplifier (homogeneuosly and inhomogeneuosly broadened gain line). In the case of inhomogeneuosly broadening only monostable states are found whereas for homogeneuosly broadening monostable states, bistable states and (anharmonic) limit cycles can occur depending on the strength and the phase difference of the back-reflected radiation. The transitions between those laser states correspond to first and second order phase transitions, respectively. The intensity oscillations of the counter-running waves are approximately calculated using an expansion in powers of the relative net gain of the ring laser.