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Diffraction of radiation on Cantor fractals

In this paper we investigate some properties of the diffraction field due to Cantor bars, which are a 1-D fractal and are one of the most well known regular fractals. By 1-D fractal we mean that the smallest Euclidian dimension of a space where a fractal exists is one. We investigate spatial complexity in optical fields resulting from diffraction of a plane wave by such fractals. For this purpose we employ the theory of stochastic and chaotic oscillations. There are several parameters which are commonly used to characterize the dimension of a chaotic system, namely, Liapunov exponent, dimension, and entropy. We use fractal dimension d for fractals and correlation exponent v for the diffraction field. In the present paper, the correlation exponent v is used as a parameter characterizing the spatial complexity of an optical field. This parameter gives the quantity of spatial harmonics with uncommesurable periods.