Intensity redistribution in diffractive pattern due to fractal phase changes

In this paper we are analyzing the influence of the non-binary (i.e. multi-level) changes in a fractal phase map (FPM) of a diffractive element (DE) upon the diffracted intensity. The diffraction efficiency dependence on the modified phase shift is presented. The fractal, bi-dimensional structures are obtained on an opto-electronic device: spatial light modulator (SLM). The FPMs were obtained via a recursive algorithm that generates regular gratings with spatial constants obeying a fractal rule. The spatial distribution of the diffracted intensity is exhibiting also a fractal structure. The contrast of the fractal structure in the screen plane increases significantly in some areas and decreases in others, for a selective phase shift in DE plane. The phase shifting rule obeys a non linear dependence of 1/q type with respect to the fractal stage of growth q. We also study the inverse problem which states the logical frame between the self-similar intensity distribution in the screen plane and the corresponding fractal phase map. The results of the numerical evaluation for the spatial intensity distribution of diffraction patterns are compared with those obtained experimentally.