Dark Solitons and Grey Solitons in Waveguide Arrays with Long-Range Linear Coupling Effects

Zhijie Mai,Fang Lin,Yongyao Li,Yan Liu,Shenhe Fu,Haitao Xu

doi:10.3390/app7030311

Zhijie Mai, Fang Lin + Show 4 more

Open Access

https://doi.org/10.3390/app7030311

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Abstract

In J. Phys. Soc. Jpn. 83, 034404 (2014), we designed a scheme of waveguide arrays with long-range linear coupling effects and studied the bright solitons in this system. In this paper, we further study the dynamics of dark and grey solitons in such waveguide arrays. The numerical simulations show that the stabilities of dark solitons and grey solitons depend on the normalized decay length and the scaled input power. The width of dark solitons and the grey level of grey solitons are studied. Our results may contribute to the understanding of discrete solitons in long-range linear coupling waveguide arrays, and may have potential applications in optical communications and all-optical networks.

Highlights

Nonlinear discrete systems attract considerable attention in many branches of physics, and exhibit various physical characteristics [1,2,3]
In 2012, Noskov and colleagues conducted significant studies of the nonlinear dipolar field in a nanoparticle train [14,15,16]—which can be viewed as a discrete nonlinear system—and reported that a linear coupling effect can exist among all lattice sites because of long-range dipole–dipole interactions
We further study the dynamics of dark and grey solitons in such a waveguide array, which was not considered before

Summary

Introduction

Nonlinear discrete systems attract considerable attention in many branches of physics, and exhibit various physical characteristics [1,2,3]. DS formation is the result of a balance between on-site nonlinearity and the discrete diffraction induced by linear coupling among adjacent waveguides or lattice sites. In 2012, Noskov and colleagues conducted significant studies of the nonlinear dipolar field in a nanoparticle train [14,15,16]—which can be viewed as a discrete nonlinear system—and reported that a linear coupling effect can exist among all lattice sites because of long-range dipole–dipole interactions. This system can produce all non-zero off-diagonal elements in the linear coupling matrix.

Model and Basic Equations

Dark Solitons

Grey Solitons

Conclusions