有色噪声驱动的光学不稳定性

P. Hānggi, F. Moss
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引用次数: 0

摘要

在过去的几年里,人们对非线性系统的兴趣稳步增长,其中非线性耦合可以诱导诸如Hopf分岔,双稳态行为或混沌等现象。在这里,我们的重点将是非线性,噪声光学系统,它们要么经历一个连续的霍普夫分岔,要么表现出双稳性。控制参数也可能受到波动的影响。使用这些波动在完全不同的时间尺度上演变的标准假设,人们通常用白色(高斯)波动来近似噪声。典型的例子是单模激光或染料激光的阈值处理。超过阈值,整个问题会变得相当复杂。特别是,最近已经认识到,有限噪声相关效应,例如在泵浦激光波动中或在嘈杂的外部驱动激光场中,可以发挥至关重要的作用。因为具有双稳性的光学系统(5,6)对噪声特性的细节特别敏感;局部不稳定状态概率的指数抑制表明,这些系统非常适合对各种不同的理论和近似进行临界测试。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Optical Instabilities Driven by Colored Noise
Over the last years, there has been steadily growing interest in nonlinear systems in which the nonlinear coupling can induce phenomena such as a Hopf bifurcation, bistable behavior or chaos1). Here our focus will be on nonlinear, noisy optical systems which either undergo a continuous Hopf bifurcation or exhibit bistability. The control parameters may also be subject to fluctuations. Using the standard assumption that those fluctuations evolve on an entirely different time scale, one usually approximates the noise by white (Gaussian) fluctuations. Typical examples are the treatments of the single mode laser2) or a dye laser3) at threshold. Above threshold, the whole matter can complicate considerably. In particular, it has been realized recently, that finite noise correlation effects, e.g. in pump laser fluctuations4) or in noisy external driving laser fields, can play a crucial role. Because optical systems exhibiting bistability5,6) are particular sensitive to the details of the noise properties; as is manifested by the exponential suppression of probability of the locally unstable state, those systems are quite suitable to put to a critical test various different theories and approximations.
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