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Optics Communications

Relaxation from a marginal state in optical bistability. Anomalous fluctuations and first-passage time statistics

Angel Valle A, Luis Pesquera, Miguel A. Rodríguez

Published Oct 1, 1990• 5 citations
Publisher
DOI
10.1016/0030-4018(90)90193-w

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Characteristic decay times for relaxation close to the marginal point of optical bistability are studied. A model-independent formula for the decay time is given which interpolates between Kramers time for activated decay and a deterministic relaxation time. This formula gives the decay time as a universal scaling function of the parameter which measures deviation from marginality. The standard deviation of the first-passage-time distribution is found to vary linearly with the decay time, close to marginality, with a slope independent of the noise intensity. Our results are substantiated by numerical simulations and their experimental relevance is pointed out.
As a result of quantum fluctuations, a bistable system will undergo spontaneous transitions from one state to the other. For a bistable two-mode laser we present a theoretical analysis of the switching statistics by treating it as a one-dimensional first-passage---time (FPT) problem for the intensity of one of the modes. The methodology is also applicable to other bistable systems, such as in optical bistability. Several new asymptotic results for the small- and large-time behavior of various FPT distributions are given. The switching-time distribution is introduced as a weighted integral over FPT distributions and asymptotic expressions for this distribution are given. Several results of Monte Carlo computer simulations of the FPT problem are presented.