Nonlinear Phenomena in Complex Systems, 2004, Vol.7, No.2, pp.140-149

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2004, Vol.7, No.2, pp.140-149

Scaling Properties and Spectral Self-Similarity in Generalized Quarter-Wave Fractal Multilayers
S.V. Zhukovsky, A.V. Lavrinenko, and S.V. Gaponenko

It is shown analytically that fractal quarter-wave multilayers possess spectral scalability (earlier found numerically in these kind of structures), and that this scaling directly corresponds to the geometrical scaling relations of the multilayers themselves. It has been found that scalability can be separated into phase and amplitude parts, for which the corresponding scaling relations have been derived. The effects of a finite structure size have been analyzed. Additionally, we have numerically found that fractal multilayers also exhibit spectral self-similarity, and compared it with a known spectral self-similarity in quasiperiodic structures.
Key words: fractal multilayers, spectral scalability, self-similarity

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