A generalized Fokker-Planck equation is derived for a system undergoing optical bistability when the dominant source of fluctuations is due to fluctuations in the incident field rather than spontaneous emission. The fluctuations are treated as a time-dependent Gaussian process whose properties are determined by the individual laser's characteristics. Both amplitude and phase fluctuations are included on the incident laser field. The effect of fluctuations of the incident laser on optical bistability are different for amplitude and phase fluctuations and are different for absorptive and dispersive optical bistability. The combination of incident laser phase fluctuations and dispersive optical bistability leads to large amplitude fluctuations near the turning points of the optical bistability curve and causes the system to make a transition from one branch of the optical bistability curve to the other before reaching the mean-field turning points. We take the high-
Q cavity limit of our generalized Fokker-Planck equation, solve the linearized equations, and provide criteria for the magnitude of fluctuations in optical bistability in terms of laser and cavity parameters. The magnitude of incident laser fluctuations are typically orders of magnitude larger than fluctuations due to spontaneous emission and are therefore important for practical applications of optical bistability devices.
We present phase control of the fluctuation-induced bistability in the three-level Λ-type system where a weak, amplitude-fluctuating component and a strong coherent component are used as a control field. With the addition of the stochastic component, optical bistability can be produced even if detunings of the probe and control fields from corresponding atomic transition frequencies are equal; without the addition, the medium is transparent to the input light. Depending on the relative phase between the stochastic and coherent parts, bistability appears or disappears and the threshold intensity is raised or lowered.