Interface optical phonons in k-component Fibonacci dielectric multilayers

We present the studies of the interface optical phonons in k-component Fibo nacci (KCF) dielectric multilyaers, in which k: different incommensurate in tervals are arranged according to a substitution rule. In the dielectric co ntinuum approximation, the dispersion relations and the frequency spectra a re obtained by the transfer-matrix method. Free-boundary and periodic-bound ary conditions are taken into account. With the free-boundary condition, th e dispersion relations of the interface optical phonons in the KCF multilay ers are demonstrated to possess two bands of dual structures. For the KCF m ultilayers with 1<k less than or equal to 5, each subband is a self-similar structure and contains k + 1 filial generations; for the KCF multilayers w ith k>5, the sub-bands do not show self-similarity, but they still have the hierarchical characteristic (where k is the number of different incommensu rate intervals). In the case of the periodic-boundary condition, the freque ncy 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 spe ctrum, f(alpha), demonstrates that in the KCF multilayers the interface opt ical phonons distribution presents a genuine multifractality. It is also sh own that by increasing the number of different incommensurate intervals in KCF multilayers, the fractal dimension of the corresponding support decreas es.