Analysis of the weak localization of photons in fractal aggregated structures and its applications

通过光学实验和基于两种不同模型的计算机模拟，揭示了光子在分形聚集结构中的弱局域化特性。在一次模拟中，利用二维平面中的魏尔斯特拉斯函数生成的分维为1&D&lt；2的分形介质中的光子散射被跟踪。结果表明，增强后向散射光中的相干锥近似服从指数为1-D的幂函数，散射自由程的模拟概率密度近似等于理论密度。提出了一种自相似算法，将模拟扩展到三维空间。在另一种模拟中，通过在每个散射事件上使用随机数来计算自由路径来模拟散射过程。在该模拟中，介质的分形性仅被假定为自由路径的概率密度，该概率密度是我们在本研究中解析推导的。模拟结果表明，相干锥的形状依赖于介质的分维，并且这种依赖关系对于不同偏振分量的被检测光是不同的。利用PMMA水溶液产生的分形聚集体进行的光学实验表明，相干背向散射锥的形状服从指数近似为1-D的幂函数，并发现相干锥的高度取决于介质中分形团簇的平均尺寸。

By means of optical experiments and computer simulations on the basis of two different models, the following properties were revealed for the weak localization of photons in fractal aggregated structures.1. In one simulation, scattering of photons were traced in fractal media with fractal dimension 1<D<2 generated by means of the Weierstrass function in a two-dimensional plane. It is found that the coherent cone in the enhanced backscattering light obeys approximately a power law with the exponent of 1-D.Simulated probability density of the scattering free path was approximately equal to the theoretical density. A self-similar algorithm was developed to extend the simulation to the three-dimensional space.2. In the other simulation, the scattering process was simulated by calculating a free path by using random numbers at each scattering event. In this simulation, the fractality of the media was assumed only in the probability density of the free path, which we derived analytically in this study. This simulation revealed that the shape of the coherent cone depends on the fractal dimension of the media, and that this dependence is different for different polarization components of the detected light.3. The optical experiment using the fractal aggregates produced from the aqueous solution of PMMA particles showed the shape of the coherent backscattered cone to obey the power law with fractional exponent given approximately by 1-D.It is also found that the height of the coherent cone depends on the average size of fractal clusters of the media.