Properties of a Lorentz-broadened single-mode unidirectional ring laser

We study some properties of a single-mode unidirectional ring laser characterized by a Lorentzian inhomogeneous broadening. The emphasis is on the derivation of analytic results. First we determine the various classes of stationary solutions and demonstrate the existence of low-intensity and high-intensity optical bistability. Both types of optical bistability require a finite detuning and inhomogeneous broadening. Next we study the linear stability of the steady solutions and determine the conditions for the occurrence of a Casperson instability in various limits but on resonance.