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 Sn is given by the inflation rule Sn=Sn−1Sn−2Sn−1 for n≥3, with initial conditions S1=A and S2=B. The metamaterial is characterized by a frequency dependent electric permittivity ε(ω) and magnetic permeability μ(ω). 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 kx.