Deflection of nematicon-vortex vector solitons in liquid crystals

Gaetano Assanto, Antonmaria A. Minzoni, and Noel F. Smyth

Phys. Rev. A 89, 013827 – Published 22 January 2014

Abstract

The deflection of a vector soliton formed by a solitary wave and an optical vortex in nematic liquid crystals is investigated upon interaction with a localized refractive index defect. The azimuthal instability of the vortex can be triggered by the index perturbation and enhanced by the distortion of the copropagating solitary wave when in the vicinity of the defect. A modulation theory is developed to study the refraction of the vector soliton and is found to be in good agreement with numerical solutions. This model reveals the crucial role of the diffractive radiation shed by both beam components as they evolve, showing that radiation reduces the destabilizing effect of the solitary wave interaction with the vortex, thus enlightening the effect of this continuous spectrum on the evolution of the nonlinear wave packets.

Received 14 November 2013

DOI:https://doi.org/10.1103/PhysRevA.89.013827

Authors & Affiliations

Gaetano Assanto¹, Antonmaria A. Minzoni², and Noel F. Smyth³

¹NooEL–Nonlinear Optics and Optoelectronics Lab, University of Rome “Roma Tre,” Via della Vasca Navale 84, 00146 Rome, Italy
²Fenomenos Nonlineales y Mecánica (FENOMEC), Department of Mathematics and Mechanics, Instituto de Investigación en Matemáticas Aplicadas y Sistemas, Universidad Nacional Autónoma de México, 01000 México D.F., México
³School of Mathematics, University of Edinburgh, Edinburgh EH9 3JZ, Scotland, United Kingdom

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Vol. 89, Iss. 1 — January 2014

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Figure 1
Numerical solution for linear vortex $| v |$ given by (40, 41, 42) at (a) $z = 0$ , (b) $z = 60$ for $a_{u} = 0.0$ , and (c) $z = 100$ for $a_{u} = 1.0$ . The other parameter values are $a_{v} = 0.5$ , $w_{u} = 5.0$ , $w_{v} = 4.0$ , $V_{u} = V_{v} = 0.5$ , $ξ_{u} = ξ_{v} = 0$ at $z = 0$ with $q = 2$ , $ν = 200$ , $(X, Z) = (- 10, 20)$ , $W = 20$ , and $A_{D} = 0.3$ .
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Figure 2
Evolution of nematicon and vortex in the $(x, z)$ plane. The parameter values are $a_{v} = 0.15$ , $w_{u} = 4.0$ , $w_{v} = 5.0$ , $V_{u} = V_{v} = 0.5$ , $ξ_{u} = ξ_{v} = 0$ at $z = 0$ with $q = 2$ , $ν = 200$ , $(X, Z) = (0, 40)$ , $W = 20$ , and $A_{D} = 0.25$ . (a) Vortex $| v |$ for $a_{u} = 0$ , $A_{D} = 0$ ; (b) vortex $| v |$ for $a_{u} = 0$ , $A_{D} = 0.25$ ; (c) nematicon $| u |$ for $a_{u} = 0.75$ , $A_{D} = 0.25$ ; and (d) vortex $| v |$ for $a_{u} = 0.75$ , $A_{D} = 0.25$ .
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Figure 3
Comparison between full numerical and modulation solutions. The parameter values are $a_{u} = 0.75$ , $a_{v} = 0.15$ , $w_{u} = 4.0$ , $w_{v} = 5.0$ , $V_{u} = V_{v} = 0.5$ , $ξ_{u} = ξ_{v} = 0$ at $z = 0$ with $q = 2$ , $ν = 200$ , $(X, Z) = (0, 40)$ , $W = 20$ , and $A_{D} = 0.25$ . Full numerical solution for nematicon: red (solid) line; full numerical solution for vortex: green (dashed) line; modulation solution for nematicon: blue (dotted) line; modulation solution for vortex: pink (small dots) line. (a) Nematicon amplitude $a_{u}$ and vortex amplitude $A_{v}$ . (b) Nematicon position $ξ_{u}$ and vortex position $ξ_{v}$ .
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Figure 4
Comparison between full numerical solution and solution of modulation equations with no radiative loss. The parameter values are $a_{u} = 0.75$ , $a_{v} = 0.15$ , $w_{u} = 4.0$ , $w_{v} = 5.0$ , $V_{u} = V_{v} = 0.5$ , $ξ_{u} = ξ_{v} = 0$ at $z = 0$ with $q = 2$ , $ν = 200$ , $(X, Z) = (0, 40)$ , $W = 20$ , and $A_{D} = 0.25$ . Full numerical solution for nematicon: red (solid) line; full numerical solution for vortex: green (dashed) line; modulation solution for nematicon: blue (dotted) line; modulation solution for vortex: pink (small dots) line. (a) Nematicon amplitude $a_{u}$ and vortex amplitude $A_{v}$ . (b) Nematicon position $ξ_{u}$ and vortex position $ξ_{v}$ .
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Figure 5
Stable and unstable vortex beams. The parameter values are $a_{v} = 0.15$ , $w_{u} = 4.0$ , $w_{v} = 5.0$ , $V_{u} = V_{v} = 0.5$ , $ξ_{u} = ξ_{v} = 0$ at $z = 0$ with $q = 2$ , $ν = 200$ , $(X, Z) = (0, 40)$ , $W = 20$ , and $A_{D} = 0.25$ . (a) Vortex $| v |$ at $z = 100$ for $a_{u} = 0.75$ , (b) vortex $| v |$ at $z = 100$ for $a_{u} = 1.2$ , (c) vortex $| v |$ at $z = 150$ for $a_{u} = 1.2$ , and (d) amplitude evolution for $a_{u} = 1.2$ . Full numerical solution for $a_{u}$ : red (solid) line; full numerical solution for $A_{v}$ : green (dashed) line; modulation solution for $a_{u}$ : blue (dotted) line; modulation solution for $A_{v} = a_{v} w_{v} e^{- 1}$ : pink (small dots) line.
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Figure 6
Comparison of vortex stability boundary. The parameter values are $w_{u} = 4$ , $a_{v} = 0.15$ , $w_{v} = 5.0$ , $V_{u} = V_{v} = 0.5$ , $ξ_{u} = ξ_{v} = 0$ at $z = 0$ with $q = 2$ , $ν = 200$ , $(X, Z) = (0, 40)$ , and $W = 20$ . Numerical solution: red triangle; modulation solution: green cross; modulation solution without radiation loss: blue star.
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