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Solitary vortices in two-dimensional waveguide matrix

Guihua Chen

Department of Electronic Engineering, Dongguan University of Technology, Dongguan 523808, P. R. China

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Hongcheng Huang

Department of Electronic Engineering, Dongguan University of Technology, Dongguan 523808, P. R. China

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, and

Muying Wu

Department of Electronic Engineering, Dongguan University of Technology, Dongguan 523808, P. R. China

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https://doi.org/10.1142/S0218863515500125Cited by:6 (Source: Crossref)

Abstract

We consider the nonlinear propagation of an optical beam in a two-dimensional waveguide matrix, which is described by the discrete nonlinear Schrödinger equation with a self-focusing nonlinearity. Our study focuses on the stability domain of the discrete vortex solitons with its topological invariant S equal to 1. Such domain is identified with the propagation constant k and the coupling constant C. Our simulations show that there is a critical value C_cr for any fixed value of k. At C ≤ C_cr, the stable domain is continuous. However, at C > C_cr, the stable domain becomes discontinuous and fuzzy. The distribution of the continuous stable regions is identified and plotted. Moreover, we give the relation of the total power P to C and k, which enable us to figure out the continuous stability area through the (P, C) plane.

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