Fraunhofer Diffraction by Koch Fractals

Abstract

Analytical expressions are derived for the complex amplitude in the Fraunhofer diffraction field of an arbitrary Koch fractal with a finite range of self-similarity. Results of the numerical evaluation for the intensity distribution of Fraunhofer diffraction patterns are compared with those obtained experimentally. It is shown that the diffraction pattern of the Koch fractal can be divided into two areas, a central fractal area and a periodic area, and that the former is surrounded by the latter. The existence of the periodic area is a consequence of the finite inner cut-off of the self-similarity of the object fractal. On the other hand, the outer cut-off gives rise to a small core area at the centre of the diffraction pattern.