Bistable operation of a tunable laser with and without absorber coupled to an external resonator

The stationary states of a single-mode laser with feedback from a grating of high selectivity are investigated theoretically. The amplifying and absorbing media are contained in a Fabry-Perot cavity (FP) of lengthl. The grating and one of the FP end mirrors facing it are forming an external resonator (ER) of lengthL whereLl. The losses in the compound system consisting of the FP and ER depend on the refractive indices of both the media which change with light intensity. An inequality has been derived yielding conditions for unstable operation at lasing threshold connected with a transition of light intensity to the upper branch of a hysteresis cycle. It has been found that a hysteresis in a system without an absorber can arise by tuning the grating frequency towards a FP resonance from the high-frequency side provided that this resonance stands on the high-frequency side of the atomic transition. For the reversed tuning situation the FP resonance must be located on the low-frequency side of the atomic transition. If an absorber is present hysteresis cycles at both sides of a FP resonance can occur independently of its position with respect to the atomic resonances.