VIBRATIONS OF FRACTALS AND SCATTERING OF LIGHT FROM AEROGELS
VIBRATIONS OF FRACTALS AND SCATTERING OF LIGHT FROM AEROGELS
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DOI：
10.1103/physrevb.40.7953
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发表时间：
1989-10-15
影响因子：
3.7
通讯作者：
ALEXANDER, S
中科院分区：
文献类型：
--
作者：
ALEXANDER, S
Courtens，Vacher和合作者最近实验研究的气凝胶中的振动光的非弹性偏振和去偏振散射进行了分析，使用分形模型的缩放和交叉的考虑。我们讨论了短程分形结构的影响和强烈的本地化振动的方式上的短程分形结构的凝胶（fractons）显示在散射。为了这个目的，我们扩展现有的讨论假设一个连接的自相似分形结构的振动的影响，并讨论了弹性散射理论和安德森本地化的分形的关系。通过将非弹性光散射视为振动分形斑点的Mie散射，包含了底层质量密度的无序分形结构和振动的三维特征。当散射光的波长与分形子的大小相当且小于结构的相干长度时，我们发现散射截面中存在一个极大值，并讨论了偏振和去偏振散射的不同频率依赖性。结果矛盾的布里渊散射表达式从低频瑞利政权外推。我们还讨论了振动本征模的结构，并表明所测得的指数是新的唯象指数，它与标准分形维数或超局域化无关。
The inelastic polarized and depolarized scattering of light from the vibrations in aerogels recently studied experimentally by Courtens, Vacher, and collaborators are analyzed with use of fracton-model scaling and crossover considerations. We discuss the implications of the short-range fractal structure and the way the strongly localized vibrations on the short-range fractal structure of the gel (fractons) show up in the scattering. For this purpose we extend existing discussions of the implications of assuming a connected self-similar fractal structure for the vibrations, and also discuss the relationship of fractons to elastic-scattering theory and to Anderson localization. The disordered fractal structure of the underlying mass density and the three-dimensional character of the vibrations are included by treating the inelastic light scattering as Mie scattering from the vibrating fractal blobs. We find a maximum in the scattering cross section when the wavelength of the scattered light is comparable to the size of the fracton and smaller than the coherence length of the structure, and discuss the different frequency dependence of the polarized and depolarized scattering. The results contradict extrapolations of the Brillouin-scattering expressions from the low-frequency Rayleigh regime. We also discuss the structure of the vibrational eigenmodes and show that the indices measured are new phenomenological indices which are not related to standard fractal dimensions or to superlocalization.