We study the properties of plasmon polaritons in one-dimensional photonic metamaterial superlattices resulting from the periodic repetition of a Fibonacci structure. We assume the system made up of positive refraction and metamaterial layers. A Drude-type dispersive response for both the dielectric permittivity and magnetic permeability of the left-handed material is considered. Maxwell’s equations are solved for oblique incidence by using the transfer-matrix formalism. Our results show that the plasmon-polariton modes are considerably affected by the increasing of the Fibonacci-sequence order of the elementary cell. The loss of the long-range spatial coherence of the electromagnetic field along the growth direction, which is due to the quasiperiodicity of the elementary cell, leads to the splitting of the plasmon-polariton frequencies, resulting in a Cantor-type frequency spectra. Moreover, the calculated photonic dispersion indicates that if the plasma frequency is chosen within the photonic $⟨n\left(\omega \right)⟩=0$ gap then the plasmon-polariton modes behave essentially as pure plasmon modes.

• Received 26 December 2009

DOI:https://doi.org/10.1103/PhysRevB.81.153101