Power Controlled Soliton Stability and Steering in Lattices with Saturable Nonlinearity

Abstract

Dynamical properties of discrete solitons in nonlinear Schrödinger lattices with saturable nonlinearity are studied in the framework of the one-dimensional discrete Vinetskii-Kukhtarev model. Two stationary strongly localized modes, centered on site (A) and between two neighboring sites (B), are obtained. The associated Peierls-Nabarro potential is bounded and has multiple zeros indicating strong implications on the stability and dynamics of the localized modes. Besides a stable propagation of mode A, a stable propagation of mode B is also possible. The enhanced ability of the large power solitons to move across the lattice is pointed out and numerically verified.

Dark solitons in discrete lattices: Saturable versus cubic nonlinearities

“…This eigenvalue collides, in our numerical results, with the band edge of the continuous spectrum for ǫ ≈ 0.055 in the saturable model and ǫ ≈ 0.077 in the cubic one; this is in remarkable agreement with the theoretical predictions of 0.0538 for the saturable case and 0.07735 for the cubic one, respectively given by Eqs. (49) and (26). Notice that the latter case was the one examined previously in [27].…”

“…The above result also highlights a noteworthy difference between the saturable model in its defocusing and focusing [26] forms. The focusing version of the model has the remarkable feature of stability alternation between on-site and inter-site configurations (vanishing of the so-called Peierls-Nabarro barrier) as one of its most important characteristics.…”

“…The second model that we will consider is a discrete dynamical lattice exhibiting a saturable defocusing nonlinearity [26,35], which has recently been used in a variety of studies and pertains to the dark soliton experiments reported in [25]. In this case, the relevant discrete NLS equation is of the form:…”

“…We aim to mathematically justify the stability of the pertinent dark soliton modes (such as those centered on a site and those centered between two lattice sites) and to numerically corroborate our analytical findings. Furthermore, we intend to examine more quantitatively statements, such as those of [25] about improved stability of inter-site modes, and to examine whether phenomena similar to those emerging for bright solitons (such as the stability alternation between on-site and inter-site solutions [26]) can occur for dark solitons. Our work also builds on earlier theoretical work on such structures which considered them principally in the cubic nonlinearity setting such as e.g., [27,28,29].…”

Exact and explicit solutions to the discrete nonlinear Schrödinger equation with a saturable nonlinearity

“…It arises in nonlinear optics as a model of infinite wave guide arrays [15] and has been recently implemented to describe Bose-Einstein condensates in optical lattices [16]. The class of DNSE models with saturable nonlinearity is also of particular interest in their own right, due to a feature first unveiled in [17]. In this study, we focus on the so-called DNSE with a saturable nonlinearity [18,19] i ∂ψ n…”