Dynamic fluctuations in optical bistability

Abstract

We present results on the time correlation function of a system undergoing absorptive optical bistability. We first use the Zwanzig-Mori formalism to calculate time correlation functions both near marginal stability points and in the coexistence region. Near marginal stability the theory predicts large deviations from a single exponential form of the correlation function. The truncated continued fraction expansion is shown to become inapplicable close to the coexistence point. The difficulties are due to the presence of long time scales, viz. the very large mean first passage times between the two metastable steady states. When these scales are important we show that the memory kernel relaxation is no longer faster than that of a field fluctuation. An increase in the size of the system increases the disparity of the time scales and thus exacerbates the problems of the projection operator formalism as used here following reference [14].

We next present an ansatz for the correlation function incorporating the four major time scales important near coexistence, the two single branch relaxation times and the two mean first passage times for transitions between the stable states. This form of the correlation function avoids the difficulties cited in connection with the use of the projection operator method.