Super-diffusion in optical realizations of Anderson localization
Super-diffusion in optical realizations of Anderson localization
复制标题
安德森定位的光学实现中的超扩散
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
M. Wilkinson
中科院分区：
文献类型：
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作者：
Y. Krivolapov;Liad Levi;S. Fishman;M. Segev;M. Wilkinson
我们讨论的动力学粒子在一维的潜力是随机的空间和时间。结果被应用到最近的光学实验安德森本地化，其中的横向传播的光束被抑制的随机波动的折射率。如果折射率沿着光束的近轴传播方向波动，则局域化被破坏。我们分析这个破碎的本地化的潜力的谱分解。当势具有离散谱时，扩散由相空间中奇里科夫共振的重叠控制。随着傅立叶分量的数量增加，共振合并成一个连续谱，这是由福克-普朗克方程描述。我们用势的谱强度来表示扩散系数。对于光学中常用的一类势，福克-普朗克方程的解在相空间中表现出反常扩散，这意味着当安德森局域化被势的时间涨落打破时，结果是以类似于弹道的速率甚至更快的速率传输。对于一类在现有的安德森局部化实现中出现的势，发现了非典型行为.
We discuss the dynamics of particles in one dimension in potentials that are random in both space and time. The results are applied to recent optics experiments on Anderson localization, in which the transverse spreading of a beam is suppressed by random fluctuations in the refractive index. If the refractive index fluctuates along the direction of the paraxial propagation of the beam, the localization is destroyed. We analyze this broken localization in terms of the spectral decomposition of the potential. When the potential has a discrete spectrum, the spread is controlled by the overlap of Chirikov resonances in phase space. As the number of Fourier components is increased, the resonances merge into a continuum, which is described by a Fokker–Planck equation. We express the diffusion coefficient in terms of the spectral intensity of the potential. For a general class of potentials that are commonly used in optics, the solutions to the Fokker–Planck equation exhibit anomalous diffusion in phase space, implying that when Anderson localization is broken by temporal fluctuations of the potential, the result is transport at a rate similar to a ballistic one or even faster. For a class of potentials which arise in some existing realizations of Anderson localization, atypical behavior is found.