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

最近，首席研究小组证明了在平面扩散器的弗劳恩霍夫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夫区以外的地区产生这种场的方法，并通过分析这种场的统计特性，来扩展这项研究。假设漫射器被相干光照射，其强度分布遵循指数为-D的幂函数，对0 < D < 3进行了计算机模拟，结果表明，当2 <或等于> D < 3时，强度相关函数表现出非幂律行为，与理论预测一致。幂律强度相关性出现在0 < D【小于或等于】1的情况下，就像1 < D < 2的情况一样。理论和实验还表明，分形散斑可以在扩散器的菲涅耳区和像面以及弗劳恩霍夫区产生。通过计算机模拟研究了分形散斑裁剪强度和相位裁剪强度的统计特性，获得了从裁剪强度估计原始分形的一些基本知识。对分形散斑的相位统计进行了研究，发现其具有分形性。无衍射分形光束的产生研究表明，采用改进的无衍射光束光学结构可以产生无衍射分形光束。

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.