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

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