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Octonacci Photonic Crystals with Negative Refraction Index Materials

We investigate the optical transmission spectra for $s$-polarized (TE) and $p$-polarized (TM) waves in one-dimensional photonic quasicrystals on a quasiperiodic multilayer structure made up by alternate layers of SiO$_{2}$ and \textit{metamaterials}, organized by following the Octonacci sequence. Maxwell's equations and the transfer-matrix technique are used to derive the transmission spectra for the propagation of normaly and obliquely incident optical fields. We assume Drude-Lorentz-type dispersive response for the dielectric permittivity and magnetic permeability of the metamaterials. For normally incident waves, we observe that the spectra does not have self-similar behavior or mirror symmetry and it also features the absence of optical band gap. Also for normally incident waves, we show regions of full transmittance when the incident angle $θ_{C} = 0^{\circ}$ in a particular frequency range.