Discrete localized modes supported by an inhomogeneous defocusing nonlinearity

TL;DR

This paper demonstrates that inhomogeneous defocusing nonlinear lattices support stable, localized bright solitons, including novel unstaggered types, with potential applications in optical waveguides and Bose-Einstein condensates.

Contribution

It introduces the existence of stable unstaggered bright solitons in inhomogeneous defocusing nonlinear lattices, a phenomenon absent in uniform systems, supported by numerical and variational methods.

Findings

Stable unstaggered bright solitons exist in inhomogeneous SDF lattices.

Surface solitons can be exactly produced with zero threshold norm.

Stability regions for these solitons are identified.

Abstract

We report that infinite and semi-infinite lattices with spatially inhomogeneous self-defocusing (SDF)\ onsite nonlinearity, whose strength increases rapidly enough toward the lattice periphery, support stable unstaggered (UnST) discrete bright solitons, which do not exist in lattices with the spatially uniform SDF nonlinearity. The UnST solitons coexist with stable staggered (ST) localized modes, which are always possible under the defocusing onsite nonlinearity. The results are obtained in a numerical form, and also by means of variational approximation (VA). In the semi-infinite (truncated) system, some solutions for the UnST surface solitons are produced in an exact form. On the contrary to surface discrete solitons in uniform truncated lattices, the threshold value of the norm vanishes for the UnST solitons in the present system. Stability regions for the novel UnST solitons are identified. The same results imply the existence of ST discrete solitons in lattices with the spatially growing self-focusing nonlinearity, where such solitons cannot exist either if the nonlinearity is homogeneous. In addition, a lattice with the uniform onsite SDF nonlinearity and exponentially decaying inter-site coupling is introduced and briefly considered too. Via a similar mechanism, it may also support UnST discrete solitons, under the action of the SDF nonlinearity. The results may be realized in arrayed optical waveguides and collisionally inhomogeneous Bose-Einstein condensates trapped in deep optical lattices. A generalization for a two-dimensional system is briefly considered too.