Localization of electrons and electromagnetic waves in a deterministic aperiodic system

Electron localization and optical transmission in one-dimensional systems with two components distributed according to the Rudin-Shapiro sequence are investigated. The nature of the eigenstates in the diagonal tight-binding model is studied by making use of nonlinear recurrence relations satisfied by the associated transfer matrices and their traces. It is shown that the wave functions display a wide range of features going from weak to exponential localization. Numerical computations lead to the conjecture that the localization property is generic. Nevertheless, a countable dense set of critical values of the on-site potential amplitude is found for which a class of extended states exists. Accordingly, the numerical investigation of the time evolution of the electronic wave packets displays a subdiffusive behavior when the potential amplitude becomes critical. Finally, a study of the optical properties of the Rudin-Shapiro dielectric multilayer shows strong similarities with the behavior of the disordered multilayers regarding the development of gaps in the transmission spectra.