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.
Dispersive optical bistability with fluctuations is analyzed in the mean-field approximation. It is shown that the phase shift of the transmitted field in the purely dispersive case exhibits hysteresis and bistable behavior in a manner similar to that of the transmitted intensity. The Fokker-Planck equation describing the time evolution of the quasiprobability distribution for the transmitted-field amplitude is obtained. The time-dependent moments of the transmitted light are calculated with the use of a Monte Carlo integration scheme.