Diffraction of radiation on Cantor fractals

Oleg V. Angelsky; Alexander V. Kovalchuk; Peter P. Maksimyak; Volodymyr M. Rudeychuk

doi:10.1117/12.226678

10 November 1995 Diffraction of radiation on Cantor fractals

Oleg V. Angelsky, Alexander V. Kovalchuk, Peter P. Maksimyak, Volodymyr M. Rudeychuk

Proceedings Volume 2647, International Conference on Holography and Correlation Optics; (1995) https://doi.org/10.1117/12.226678
Event: International Conference on Holography and Correlation Optics, 1995, Chernivsti, Ukraine

Abstract

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.

Citation Download Citation

Oleg V. Angelsky, Alexander V. Kovalchuk, Peter P. Maksimyak, and Volodymyr M. Rudeychuk "Diffraction of radiation on Cantor fractals", Proc. SPIE 2647, International Conference on Holography and Correlation Optics, (10 November 1995); https://doi.org/10.1117/12.226678

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