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

分形聚集结构中光子的弱局域化分析及其应用

基本信息

批准号：
07832001
负责人：
UOZUMI Jun
金额：
$ 1.47万
依托单位：
HOKKAIDO UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1995
资助国家：
日本
起止时间：
1995 至 1996
项目状态：
已结题

项目摘要

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.

通过两个不同模型的光学实验和计算机模拟，揭示了以下特性，即在分形聚集结构中光子的弱定位。1。在一个模拟中，将光子的散射追溯到分形介质的分形介质1 <d <2通过在二维平面中生成的weierstrass函数。已经发现，增强的反向散射光中的相干锥体遵守大约具有1-D指数的功率定律。散射自由路径的概率密度大约等于理论密度。开发了一种自相似算法，以将模拟扩展到三维空间2。在另一个模拟中，通过在每个散射事件中使用随机数来计算自由路径来模拟散射过程。在此模拟中，仅在自由路径的概率密度中假定了介质的分形，这是我们在本研究中分析得出的。该模拟表明，相干锥的形状取决于培养基的分形维，并且对于检测到的光的不同极化成分，这种依赖性不同。3。使用PMMA颗粒水溶液产生的分形聚集体的光学实验显示了相干反向散射锥的形状，以大约1-D给出的分数指数遵守功率定律，这也发现相干锥的高度取决于培养基的平均大小。