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

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{ö}dinger model are highlighted.

In comparison to the printed version, a typo has been corrected in Eqs. (4)-(5), where βhas been replaced with -β

References in corpus (5)

• Observation of discrete gap solitons in binary waveguide arrays
• The Discrete Nonlinear Schrödinger equation - 20 Years on
• Formation and light guiding properties of dark solitons in one-dimensional waveguide arrays
• Dark Solitons in Discrete Lattices: Saturable versus Cubic Nonlinearities
• Dark-bright gap solitons in coupled-mode one-dimensional saturable waveguide arrays

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