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

TL;DR

This paper investigates dark lattice solitons in one-dimensional waveguide arrays with alternating couplings and saturable defocusing nonlinearities, revealing their stability properties, spectral features, and differences from standard models.

Contribution

It introduces the analysis of dark solitons in binary waveguide arrays with saturable nonlinearities, highlighting stability ranges and spectral characteristics.

Findings

Dark solitons can be stable over a wide parameter range.

Solutions exhibit both exponential and oscillatory instabilities.

Spectral analysis reveals two bands and mini-gaps, differing from cubic models.

Abstract

In the present work, we examine "binary" waveguide arrays, where the coupling between adjacent sites alternates between two distinct values $C_1$ and $C_2$ and a saturable nonlinearity is present on each site. Motivated by experimental investigations of this type of system in fabricated LiNbO$_3$ 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 spectral properties of the linearization around the solutions and the presence of two bands and associated mini-gaps are discussed and the nontrivial differences from the standard cubic discrete nonlinear Schr{\"o}dinger model are highlighted.