Analysis of self-pulsing in absorptive optical bistability

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Abstract
We review and extend the theory of instabilities in absorptive optical bistability for ring cavities containing homogeneously broadened two-level media. The instabilities occur in the high-transmission branch and result in either a precipitation to the low-transmission branch or in pulsed multimode operation. Two numerical approaches are used to predict operation away from the simple mean-field limit. First, an iterative method is used to solve the general field eigenvalue equation for cavity modes with frequencies displaced from the input frequency. This work shows that the instability region decreases in size as the mirror transmission increases. These calculations are confirmed by the second numerical technique, consisting of direct integrations of the coupled Maxwell-Bloch equations. This second approach also provides time histories of the instability evolutions, and divides the instability range into a precipitation regime and a self-pulsing regime. The results are discussed in terms of first- and second-order phase transitions, and agree with the analytical results obtained within the dressed-mode description of optical bistability. They show that when the incident field is adiabatically decreased along the high-transmission branch, the spiking behavior always appears abruptly. By further decreasing the incident intensity, the self-pulsing disappears either continuously if the system remains in the high-transmission branch, or discontinuously if the system precipitates to the low-transmission branch. Connection is made with induced probe gain known in the saturation spectroscopy of absorbers (uninverted media), in which population pulsations transfer energy from a saturating wave to the probe waves. The very close relationship with multimode operation in homogeneously broadened unidirectional ring lasers is also established.