Nonlinear Phenomena in Complex Systems, 2001, Vol.4, No.4, pp.383-389

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2001, Volume 4, Number 4, pp.383-389

Spectral Properties of Fractal and Quasi-periodic Multilayered Media
S. V. Zhukovsky, S. V. Gaponenko, and A. V. Lavrinenko

Non-conventional layered dielectric media, including quasi-periodic Fibonacci stacks and model fractal Cantor-like structures are analyzed in terms of their spectral properties. Optical transmission spectra for such media are found to exhibit scalability and self-similarity. For Cantor structures, strong correlation between geometrical and spectral properties is discovered. Fractal behavior of Cantor spectra are discussed and investigated. Qualitative estimation reveals that the spectral curve represents a fractal with a dimension between 1 and 2, while the transmission peaks are distributed in a non-fractal way. The results obtained are also applicable for the eigenvalue problem in a Cantor-like potential, as well as to propagation of elastic waves in stratified media
Key words: dielectric multilayers, cantor structures, fractal spectra, PBGs

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