Dynamics of Multipole Solitons and Vortex Solitons in PT-Symmetric Triangular Lattices with Nonlocal Nonlinearity

Jing Huang,Yuanhang Weng,Peijun Chen,Hong Wang

doi:10.3390/app9183731

Jing Huang, Yuanhang Weng + Show 2 more

Open Access

https://doi.org/10.3390/app9183731

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Abstract

We investigate the evolution dynamics of solitons with complex structures in the PT-symmetric triangular lattices with nonlocal nonlinearity, including dipole solitons, six-pole solitons, and vortex solitons. Dipole solitons can be linearly stable with a small degree of gain/loss, while six-pole solitons can only be stable when both the degree of gain/loss and the degree of nonlocality are small. For unstable solitons, some humps will decay quickly or new hotspots will appear during propagation. According to the existence range of dipole solitons, the multipole solitons tend to exist in PT-symmetric triangular lattices whose nonlocal nonlinearity is intermediate. We also consider the vortex solitons with high topological charges in the same triangular lattices and find that their profiles are codetermined by the propagation constant, degree of nonlocality, and topological charge.

Highlights

Optical modes tend to diffract after transmitting in a waveguide, which is detrimental to the long-haul transmission of optical signals
We first consider dipole solitons, because they are the basic type of multipole solitons
We find that dipole solitons in PT-symmetric triangular lattices can be generated with different degrees of that dipole solitons in PT-symmetric triangular lattices can be generated with different degrees of nonlocality, d, and with different PT-symmetric potentials

Summary

Introduction

Optical modes tend to diffract after transmitting in a waveguide, which is detrimental to the long-haul transmission of optical signals. Nonlocal nonlinearity strongly affects the propagation of light, providing the potential to form and stabilize many types of solitons, such as defect solitons [7], breather solitons [8], surface solitons [9], multipole solitons [10], and vortex solitons [11]. We investigate in detail the propagation and stability of the multipole solitons, as well as the evolution of the vortex solitons in a nonlocal triangular optical lattice with PT-symmetric complex potentials. These two types of soliton have complex phases and wave fronts, which means that they will have more complex dynamics and carry more information than fundamental solitons. The profiles of these vortex solitons are influenced by the propagation constant, the degree of nonlocality, and the topological charge

Theoretical Model

Dipole Solitons

Six-Pole Solitons

Vortex Solitons

12. The evolution of of the solitonswith withmm

Conclusions