Abstract
We carry out a theoretical analysis for the spectra of plasmon polaritons in multiple semiconductor layers arranged in a quasiperiodical fashion. This quasiperiodicity can be of the type of so-called substitutional sequences. They are characterized by the nature of their Fourier spectrum, which can be dense pure point (Fibonacci sequences) or singular continuous (Thue-Morse and double-period sequences). These substitutional sequences are described in terms of a series of generations that obey peculiar recursion relations. In order to study the plasmon-polariton spectra, we use a convenient theoretical model based on a transfer-matrix treatment, with the layers characterized by a frequency-dependent dielectric function, including the effect of retardation. We present numerical results to discuss the fractal aspect of the spectra, and compare it with the nonfractal spectra presented in the periodic case.
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