Noise Effects In Optical Bistability

R. Horowicz, L. Lugiato
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Abstract

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.
光学双稳中的噪声效应
我们建立了一个纯色散光双稳的行波单模模型,该模型考虑了入射场的振幅和频率波动、腔长波动、辐射场和材料中的热噪声(1)。该模型由三个朗格万型方程给出,分别用于慢变电场的实部和虚部,以及材料变量。在白噪声极限下,它相当于三个变量的Fokker-Planck方程。即使我们的模型也可以在适当的参数范围内描述克尔介质或两能级系统,我们主要对利用半导体色散介质的小型化全光双稳器件感兴趣。在这种情况下,我们可以绝热地消除场变量,从而将问题简化为一个单变量的随机微分方程,其中包含几项加性和乘性噪声。我们发现在缓慢变化的电场的虚部的噪声对这个方程没有贡献。在白噪声的情况下,我们的随机方程相当于一个变量的Fokker-Planck方程,而在有色噪声的情况下,我们只在短相关时间的极限下得到一个一维的Fokker-Planck方程。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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