Eur. Phys. J. D (2012) 66: 182
https://doi.org/10.1140/epjd/e2012-30204-4

Regular Article

Dark lattice solitons in one-dimensional waveguide arrays with defocusing saturable nonlinearity and alternating couplings

¹ Faculty of Electrical Engineering, Helmut Schmidt University, 22043 Hamburg, Germany
² Grupo de Física No Lineal, Departamento de Física Aplicada I, Universidad de Sevilla, Escuela Politécnica Superior, C/Virgen de África 7, 41011 Sevilla, Spain
³ Department of Mathematics and Statistics, University of Massachusetts, MA 01003-4515 Amherst, USA

^a e-mail: jcuevas@us.es

Received: 28 March 2012
Received in final form: 3 May 2012
Published online: 12 July 2012

Abstract

In the present work, we examine “binary” waveguide arrays, where the coupling between adjacent sites alternates between two distinct values C₁ and C₂ and a saturable nonlinearity is present on each site. Motivated by experimental investigations of this type of system in fabricated LiNbO₃ arrays, we proceed to analyze the nonlinear wave excitations arising in the self-defocusing nonlinear regime, examining, in particular, dark solitons and bubbles. We find that such solutions may, in fact, possess a reasonably wide, experimentally relevant parametric interval of stability, while they may also feature both prototypical types of instabilities, namely exponential and oscillatory ones, for the same configuration. The dynamical manifestation of the instabilities is also examined through direct numerical simulations.