Stable two-dimensional solitons supported by radially inhomogeneous self-focusing nonlinearity

Hidetsugu Sakaguchi, Boris A. Malomed

Research output: Contribution to journalArticlepeer-review

Abstract

We demonstrate that modulation of the local strength of the cubic self-focusing (SF) nonlinearity in the twodimensional geometry, in the form of a circle with contrast Δg of the SF coefficient relative to the ambient medium with a weaker nonlinearity, stabilizes a family of fundamental solitons against the critical collapse. The result is obtained in an analytical form, using the variational approximation and Vakhitov-Kolokolov stability criterion, and corroborated by numerical computations. For the small contrast, the stability interval of the soliton's norm scales as ΔN ∼ Δg (the replacement of the circle by an annulus leads to a reduction of the stability region by perturbations breaking the axial symmetry). To further illustrate this mechanism, we demonstrate, in an exact form, the stabilization of one-dimensional solitons against the critical collapse under the action of a locally enhanced quintic SF nonlinearity.

Original languageEnglish
Pages (from-to)1035-1037
Number of pages3
JournalOptics Letters
Volume37
Issue number6
DOIs
StatePublished - 15 Mar 2012

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