Photonic band gap spectra in Octonacci metamaterial quasicrystals

Abstract 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 = S n − 1 S n − 2 S n − 1 for n ≥ 3 , with initial conditions S 1 = A and S 2 = B . The metamaterial is characterized by a frequency dependent electric permittivity e ( 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 k x .