Dissipative surface solitons in periodic structures

TL;DR

This paper demonstrates the formation and stability of dissipative surface solitons at the interface of a semi-infinite lattice and a Kerr medium, highlighting the conditions for their existence in focusing and defocusing media.

Contribution

It introduces the concept of dissipative surface solitons at the lattice-medium interface, detailing their existence conditions and stability criteria in various spectral gaps.

Findings

Stable dissipative surface solitons exist in both focusing and defocusing media.

Surface solitons form when amplification exceeds a threshold and are limited by an upper gain in finite gaps.

Existence depends on the propagation constants falling into specific spectral gaps.

Abstract

We report dissipative surface solitons forming at the interface between a semi-infinite lattice and a homogeneous Kerr medium. The solitons exist due to balance between amplification in the near-surface lattice channel and two-photon absorption. The stable dissipative surface solitons exist in both focusing and defocusing media, when propagation constants of corresponding states fall into a total semi-infinite and or into one of total finite gaps of the spectrum (i.e. in a domain where propagation of linear waves is inhibited for the both media). In a general situation, the surface solitons form when amplification coefficient exceeds threshold value. When a soliton is formed in a total finite gap there exists also the upper limit for the linear gain.