Instabilities in Optical Bistability:Transform from CW to Pulsed

Abstract

This paper reviews the results obtained by our group on the stationary solution for OB in a ring cavity and on the instabilities that can arise in these solutions. First, we solve exactly and analytically the Maxwell-Bloch equations with the proper boundary conditons both in the absorptive and in dispersive case, both for homogeneous broadening and for Lorentzian inhomogeneous broadening. In the limit αL → 0, T → 0, with αL/T arbitrary, the exact solution reduces to the previously calculated mean field state equation. In this case, we give explicit analytic bistability conditions which show in particular that the purely absorptive case is the one in which one finds the largest hysteresis cycle. On the other hand, the exact solution shows that the mean field limit case is the optimal situation to observe bistability. In fact, an increase of T causes a decrease of the size of the cycle, until for T large enough the bistable behavior disappears. We show also that under suitable conditions a part of the curve of transmitted vs. incident light with positive slope can become unstable. In the dispersive case, this situation can occur also in the absence of bistability, whereas in the purely absorptive case this instability can arise only in bistable situations, and precisely in the high transmission branch of the hysteresis cycle. When there is instability the system either precipitates to the low transmission branch, thereby producing a net reduction of the cycle, or evolves towards an undamped spiking situation (self-pulsing). In the latter case, the system works as an all-optical device which transforms CW light into pulsed light. We give analytic instability conditions in the case aL ≪ 1, T ≪ 1 (mean field limit, again!), in which the dynamics of the system is governed by the modes of the cavity. The self-pulsing instability occurs when the nonlinear dynamics of the system transfers part of the incident energy from the resonant mode to other cavity modes, thereby producing the spiking behavior. Hence, with respect to these off-resonance modes, the system behaves as a type of laser that works without population inversion. Finally, we have analyzed the instabilities in the case of a Fabry-Perot. It turns out that self-pulsing is much more difficult to be achieved than in the case of the ring cavity.