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Physical Review A

Effect of laser-frequency fluctuations on optical bistability

C. R. Willis

Published Jan 1, 1983• 12 citations
Publisher

Abstract

We derive, solve, and analyze the linearized master equation and evaluate the spectrum for absorptive optical bistability in the high-$Q$ cavity when the incident laser has jitter or frequency fluctuation. The fluctuations are treated as a time-dependent Gaussian process whose properties are determined by the individual laser's characteristics. With our results we can explain the qualitative results of machine simulations and provide criteria for the magnitude of fluctuations in optical bistability in terms of laser and cavity parameters.

DOI
10.1103/physreva.27.375

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We derive, solve, and analyze the linearized master equation and evaluate the spectrum for absorptive optical bistability in the high-QQQ cavity when the incident laser has jitter or frequency fluctuation. The fluctuations are treated as a time-dependent Gaussian process whose properties are determined by the individual laser's characteristics. With our results we can explain the qualitative results of machine simulations and provide criteria for the magnitude of fluctuations in optical bistability in terms of laser and cavity parameters.
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We derive and analyze the master equation for absorptive and dispersive optical bistability in the high-Q cavity limit where the driving laser has both amplitude and phase fluctuations which are larger than the small amplitude and phase fluctuations caused by incoherent spontaneous emission in the cavity. We treat the amplitude and phase fluctuations of the driving laser as independent time dependent Gaussian processes. The causes of jitter and amplitude fluctuations will vary from laser to laser and the fluctuations need not be Gaussian. However, we use Gaussian processes for mathematical tractability and because we expect them to be qualitatively correct. Recently,1 we have shown in the case of absorptive optical bistability when the driving laser has phase fluctuations the fundamental process which determines the statistical properties of the internal field is the competition between locking of the internal field phase to the phase of the driving laser and the diffusion of the phase of the internal field as a consequence of the driving laser fluctuations. The driving laser fluctuations have little effect if the phase locking rate is larger than the phase diffusion rate caused by the driving laser’s fluctuations. However, when the diffusion rate becomes comparable to the locking rate we find the amplitude of the 2 internal field is reduced and the dimensionless parameter2 measuring the importance of transitions from one branch of the OB curve to the other due to fluctuations takes on a value which leads to an appreciable transition rate due to fluctuations.
In this paper we discuss the influence of laser fluctuations on the hysteresis cycle in Optical Bistability. For the simplest case of an Absorptive Optical Bistability in a good cavity driven by an external laser light with non-white Gaussian amplitude fluctuations we derive a Fokker-Planck equation in the limit of large laser linewidth and good amplitude stabilization. This Fokker-Planck equation has a nonconstant diffusion term which shifts the most probable values of the steady state probability distribution from its deterministic positions. From the form of the steady state solution of the Fokker-Planck equation with non-white amplitude fluctuations we discuss the relative stability of the bistable branches. As in the case of quantum fluctuations the random amplitude of the laser field leads to a small range of values of the injected laser intensity in which the two bistable peaks have a comparable area. The transmitted field averaged with respect to the stationary distribution function coincides with one of the two deterministic branches except on the narrow transition region where we have large fluctuations.