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Vortex solitons in photonic crystal fibers

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Abstract

We demonstrate the existence of vortex soliton solutions in photonic crystal fibers. We analyze the role played by the photonic crystal fiber defect in the generation of optical vortices. An analytical prediction for the angular dependence of the amplitude and phase of the vortex solution based on group theory is also provided. Furthermore, all the analysis is performed in the non-paraxial regime.

©2004 Optical Society of America

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Supplementary Material (2)

Media 1: GIF (997 KB)     
Media 2: GIF (965 KB)     

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Figures (5)

Fig. 1.
Fig. 1. (a) Schematic representation of a PCF. (b)–(d) Amplitudes of several vortices for increasing values of γ in a PCF with Λ=31µm and a=6µm (λ=1064nm): (b) γ=0,45×10-3; (c) γ=0,95×10-3; (d) γ=1,75×10-3.
Fig. 2.
Fig. 2. Effective index of a family of vortex solutions as a function of γ (solid line). Same for a family of fundamental solitons (dashed line), as in Ref. [10]. The shadow region corresponds to the conduction band, constituted by Bloch modes, of the 2D photonic cladding with Λ=31µm and a=10µm (λ=1064nm).
Fig. 3.
Fig. 3. Phase of a vortex with l=1 at r=21µm. We represent both the total phase arg(ϕl ) (solid line) and the group phase arg(ϕl )- (dashed line).
Fig. 4.
Fig. 4. (997 KB) Evolution of the field amplitude in z under a diagonal perturbation (ε=0.095) for a large-scale PCF with Λ=31µm, a=10µm and λ=1064nm. We show the transient from an initial profile towards an asymptotic vortex solution.
Fig. 5.
Fig. 5. (965 KB) Evolution of the field amplitude in z under a non-diagonal perturbation (ε=0.05) for a large-scale PCF with Λ=31µm, a=10µm and λ=1064nm.

Equations (3)

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[ t 2 + k 0 2 ( n 0 2 ( x ) + n 2 2 ( x ) E 2 ) ] E = 2 E z 2 ,
L ( ϕ ) ϕ = β 2 ϕ L ( ϕ ) = L 0 + L NL ( ϕ ) ,
ϕ l = r l e i l θ ϕ l s ( r , θ ) exp [ i ϕ l p ( r , θ ) ] l = 1 , 2 ,
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