Photonic band gap spectra in Octonacci metamaterial quasicrystals

In this work we study theoretically the photonic band gap spectra for a one-dimensional quasicrystal made up of SiO2 (layer A) and a metamaterial (layer B) organized following the Octonacci sequence, where its nth-stage S-n is given by the inflation rule S-n = Sn-1Sn-2Sn-1, for n >= 3, with initial conditions S-1 = A and S-2 = B. The metamaterial is characterized by a frequency dependent electric permittivity epsilon(omega) and magnetic permeability mu(omega). The polariton dispersion relation is obtained analytically by employing a theoretical calculation based on a transfer-matrix approach. A quantitative analysis of the spectra is then discussed, stressing the distribution of the allowed photonic band widths for high generations of the Octonacci structure, which depict a self-similar scaling property behavior, with a power law depending on the common in-plane wavevector k(x). (C) 2016 Elsevier B.V. All rights reserved.