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Topical Meeting on Optical Bistability (OB)

Fluctuations in Optical Bistability: Experiment with Shot Noise

S. L. McCall, Seth Ovadia, H. M. Gibbs, F. A. Hopf, D. L. Kaplan

Published Jan 1, 1983• 0 citations
Publisher

Abstract

The behavior of an optical bistable system in which the fluctuations play the dominant role has been studied on the basis of a Fokker-Planck description by Schenzle and Brand.1 However, all the analyses so far approximate the fluctuations as arising from a constant external noise source described by a δ-correlated, Gaussian random process.2,3 In this paper intensity-dependent shot noise fluctuations of a bistable system are experimentally studied for the first time, using a hybrid bistable optical device, and analyzed by a simple “ladder" model that fits the data well.

DOI
10.1364/obi.1983.wd4

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The behavior of an optical bistable system in which the fluctuations play the dominant role has been studied on the basis of a Fokker-Planck description by Schenzle and Brand.1 However, all the analyses so far approximate the fluctuations as arising from a constant external noise source described by a δ-correlated, Gaussian random process.2,3 In this paper intensity-dependent shot noise fluctuations of a bistable system are experimentally studied for the first time, using a hybrid bistable optical device, and analyzed by a simple “ladder" model that fits the data well.
A generalized Fokker-Planck equation is derived for a system undergoing optical bistability when the dominant source of fluctuations is due to fluctuations in the incident field rather than spontaneous emission. The fluctuations are treated as a time-dependent Gaussian process whose properties are determined by the individual laser's characteristics. Both amplitude and phase fluctuations are included on the incident laser field. The effect of fluctuations of the incident laser on optical bistability are different for amplitude and phase fluctuations and are different for absorptive and dispersive optical bistability. The combination of incident laser phase fluctuations and dispersive optical bistability leads to large amplitude fluctuations near the turning points of the optical bistability curve and causes the system to make a transition from one branch of the optical bistability curve to the other before reaching the mean-field turning points. We take the high-QQQ cavity limit of our generalized Fokker-Planck equation, solve the linearized equations, and provide criteria for the magnitude of fluctuations in optical bistability in terms of laser and cavity parameters. The magnitude of incident laser fluctuations are typically orders of magnitude larger than fluctuations due to spontaneous emission and are therefore important for practical applications of optical bistability devices.
In a recent paper (1) we formulated a running wave, singlemode model for purely dispersive optical bistability, which incorporates amplitude and frequency fluctuations in the incident field, cavity length fluctuations, thermal noise in the radiation field and in the material. In the bad-cavity case of miniaturized bistable devices which utilize semiconductor dispersive media, our model reduces to a single stochastic differential equation for the material variable, which contains several terms of additive and multiplicative noise. In the white-noise case, it is equivalent to a Fokker-Planck equation in one variable, whereas in the case of colored noise it is equivalent to a multidimensional Fokker-Planck equation. On the basis of this model, we examined both problem of practical (P) and of fundamental (F) interest.
We formulate a running wave, singlemode model for purely dispersive optical bistability, which incorporates amplitude and frequency fluctuations in the incident field, cavity length fluctuations, thermal noise in the radiation field and in the material (1). This model is given by a set of three Langevin-type equations for the real and the imaginary part of the slowly-varying electric field, and for the material variable. In the white noise limit, it is equivalent to a Fokker-Planck equation in three variables. Even if our model can describe also a Kerr medium or a two-level system in a suitable range of parameters, we are mainly interested in the case of miniaturized all–optical bistable devices which utilize semiconductor dispersive media. In this situation, we can adiabatically eliminate the field variables and therefore reduce the problem to a single stochastic differential equation in one variable, which contains several terms of additive and multiplicative noise. We find that noise in the imaginary part of the slowly varying electric field does not contribute to this equation. In the white, -noise case, our stochastic equation is equivalent to a Fokker-Planck equation in one variable, whereas in the case of colored noise we obtain a onedimensional Fokker-Planck equation only in the limit of short correlation times.