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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.
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Chrostowski et al. (1981) studied this question.
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