Generation of fractal optical waves by means of light scattering and analysis of their statistical properties

最近，该课题组发现，在平面漫射体的夫琅和费区可以产生具有分形强度分布的随机光场。本研究旨在通过开发在弗劳恩霍费尔地区以外地区产生这种场的方法，并通过分析这种场的统计特性来扩大这项研究。假设漫射体被光强分布服从指数为-D的幂函数的相干光照射，对0&lt；D&lt；3进行了计算机模拟，发现2[小于或等于]D&lt；3的强度关联函数表现出非幂函数行为，与理论预测一致，并且0&lt；D[小于或等于]1与1&lt；D&lt；2.还从理论和实验上证明了散射体的菲涅耳区、像面以及夫琅和费区都可以产生分维散斑。通过计算机模拟研究了分维散斑的截断强度和相位截断强度，得到了从截断强度估计原始分形度的一些基本知识。研究了分形散斑的位相统计特性，发现其具有分形性。非衍射型分形束的产生研究表明，通过对非衍射束采用改进的光学结构，可以产生无衍射型的分形束。

Recently, it was shown by the head investigator's group that random optical fields with fractal intensity distributions can be generated in the Fraunhofer region of a plane diffuser. The present study aims at extending this research by developing methods for generating such fields in areas other than the Fraunhofer region, and by analyzing statistical properties of such fields.1. Properties of fractal speckles produced in various regionsAssuming that a diffuser is illuminated by coherent light with the intensity distribution following a power function with the exponent -D, computer simulations were conducted for 0 < D < 3, and revealed that the intensity correlation function shows non-power-law behaviors for 2 【less than or equal】 D < 3, agreeing with the theoretical predictions, and that power-law intensity correlations appear for 0 < D 【less than or equal】 1 as is in the case of 1 < D < 2.It was also shown theoretically and experimentally that fractal speckles can be generated in the Fresnel region and image plane as well as in the Fraunhofer region of the diffuser.2. Statistics of the clipped intensity and the phaseClipped intensity of fractal speckles was investigated by computer simulations and some fundamental knowledge for estimating the original fractality from the clipped intensity was obtained. Phase statistics of fractal speckles was also investigated, and was shown to have fractality.3. Generation of nondiffracting fractal beamsIt was shown that nondiffracting fractal beams can be generated by employing modified optical configurations for nondiffracting beams.