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

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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.