Spectrum and dynamic-response function of transmitted light in the absorptive optical bistability

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Abstract
We consider the dynamical behavior of the (nonlinear) amplitude fluctuations in the transmitted radiation of the optical bistability in the transition region. A Fokker-Planck model with nonlinear diffusion coefficient (multiplicative Gaussian white noise) is used to describe the system in the "good-quality" cavity limit. Choosing a parameter set corresponding to a numerically small but tractable tunneling rate between the stable and metastable states we study, as functions of the external coherent field and system size, the spectrum and the response to a small additional injected coherent signal. The numerical calculations are facilitated by the construction of complex-valued continued-fraction representations for the spectrum of amplitude fluctuations and for the response function. This representation allows us to discuss the memory effects caused by deviations from a simple Gaussian-Markov behavior around the transition region. In addition, such a representation enables the construction of "a posteriori" error bounds on the power spectrum.