Multi-stable Operation of a Semiconductor Ring Laser Due to Spatial Hole-Burning

We have theoretically analyzed multi-stability of a symmetric ring laser operating in one single longitudinal mode in the presence of coherent back scattering and inversion-grating-induced mutual coupling of the clockwise and counter-clockwise modes. Our model takes into account the inversion grating created by the standing-wave pattern of the interfering counter-propagating fields and avoids the frequently used ad-hoc introduction of cross and self-saturation coefficients. Our study confirms that linear coupling due to waveguide irregularities or weak interface reflections leads to an effective pump strength below which the clock and anti-clock wise modes are symmetrically coupled whereas above which the grating-induced coupling leads to multi-stability.