Localization of plasmon-polaritons in n–i–p–i quasi-periodic semiconductor superlattices

In this communication we investigate the plasmon-polariton spectra of a semiconductor superlattice arranged in a quasi-periodic n–i–p–i sequence. The n–i–p–i periodic superlattice consists of alternate layers of n- and p-doped semiconductors, with an insulating material in-between. We use a convenient theoretical model based on a transfer matrix formalism to simplify the algebra, which is otherwise quite involved. The n–i–p–i layers are characterized by a frequency-dependent dielectric function, including effects of retardation. We present numerical results to discuss the fractal aspect of the spectra as well as their localization and scaling behavior. We show that the total allowed bandwidth of the plasmon-polariton spectrum Δ scales as the power law Δ∼(2n+1)−δ.