Dark-bright gap solitons in coupled-mode one-dimensional saturable waveguide arrays

TL;DR

This paper explores the existence and stability of dark-bright gap solitons in coupled-mode one-dimensional saturable waveguide arrays, extending experimental observations with theoretical analysis of various coupled states.

Contribution

It introduces a theoretical framework for dark-bright gap solitons in saturable waveguide arrays, including symbiotic and non-symbiotic states, and analyzes their stability properties.

Findings

Coupled dark-bright solitons can exist in the first gap of the spectrum.

Most states are unstable but with small growth rates, allowing experimental observation.

Theoretical models extend experimental results to various coupling scenarios.

Abstract

In the present work, we consider the dynamics of dark solitons as one mode of a defocusing photorefractive lattice coupled with bright solitons as a second mode of the lattice. Our investigation is motivated by an experiment which illustrates that such coupled states can exist with both components in the first gap of the linear band spectrum. This finding is further extended by the examination of different possibilities from a theoretical perspective, such as symbiotic ones where the bright component is supported by states of the dark component in the first or second gap, or non-symbiotic ones where the bright soliton is also a first-gap state coupled to a first or second gap state of the dark component. While the obtained states are generally unstable, these instabilities typically bear fairly small growth rates which enable their observation for experimentally relevant propagation distances.