We present the studies of the interface optical phonons in k-component Fibonacci (KCF) dielectric multilyaers, in which k different incommensurate intervals are arranged according to a substitution rule. In the dielectric continuum approximation, the dispersion relations and the frequency spectra are obtained by the transfer-matrix method. Free-boundary and periodic-boundary conditions are taken into account. With the free-boundary condition, the dispersion relations of the interface optical phonons in the KCF multilayers are demonstrated to possess two bands of dual structures. For the KCF multilayers with (Formula presented) each subband is a self-similar structure and contains (Formula presented) filial generations; for the KCF multilayers with (Formula presented) the sub-bands do not show self-similarity, but they still have the hierarchical characteristic (where k is the number of different incommensurate intervals). In the case of the periodic-boundary condition, the frequency span of interface optical phonons in the KCF multilayers is singularly continuous and the frequency spectra are analyzed by a multifractal concept. A dimensional spectrum of singularities associated with the frequency spectrum, (Formula presented) demonstrates that in the KCF multilayers the interface optical phonons distribution presents a genuine multifractality. It is also shown that by increasing the number of different incommensurate intervals in KCF multilayers, the fractal dimension of the corresponding support decreases. © 1999 The American Physical Society.
Peng R. W.;Jin G. J.;Wang Mu;Hu A.;Jiang S. S.;Feng D.
Physical Review B Condensed Matter and Materials Physics