Surface solitons in quasiperiodic nonlinear photonic lattices

Abstract

We study discrete surface solitons in semi-infinite, one-dimensional, nonlinear (Kerr), quasiperiodic waveguide arrays of the Fibonacci and Aubry-Andr\'e types, and explore different families of localized surface modes, as a function of optical power content (``nonlinearity'') and quasiperiodic strength (``disorder''). We find a strong asymmetry in the power content of the mode as a function of the propagation constant, between the cases of focusing and defocusing nonlinearity, in both models. We also examine the dynamical evolution of a completely localized initial excitation at the array surface. We find that, in general, for a given optical power, a smaller quasiperiodic strength is required to effect localization at the surface than in the bulk. Also, for fixed quasiperiodic strength, a smaller optical power is needed to localize the excitation at the edge than inside the bulk.