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Spatial soliton formation in photonic crystal fibers

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Abstract

We demonstrate the existence of spatial soliton solutions in photonic crystal fibers (PCF’s). These guided localized nonlinear waves appear as a result of the balance between the linear and nonlinear diffraction properties of the inhomogeneous photonic crystal cladding. The spatial soliton is realized self-consistently as the fundamental mode of the effective fiber defined simultaneously by the PCF linear and the self-induced nonlinear refractive indices. It is also shown that the photonic crystal cladding is able to stabilize these solutions, which would be unstable otherwise if the medium was entirely homogeneous.

©2003 Optical Society of America

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Supplementary Material (1)

Media 1: GIF (2611 KB)     

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Figures (5)

Fig. 1.
Fig. 1. (a) Schematic representation of the transverse section of a PCF. (b) The box with dimensions D×D corresponds to the unit cell used to implement periodic boundary conditions. In our simulations we have chosen D=7Λ, Λ being the spatial periodicity, or pitch, of the photonic crystal cladding.
Fig. 2.
Fig. 2. Intensity distribution of different solutions of Eq. (1) for a PCF with pitch Λ=23µm, radius a=4µm, λ=1.55 µm and different nonlinear couplings: (a), linear mode (γ=0); (b) and (c), spatial soliton solutions for γ=0.0010 and γ=0.0015, respectively;(d), unstable nonlinear solution of the homogeneous medium (γ=γc=0.0017); and (e), self-focusing instability (γ>γc).
Fig. 3.
Fig. 3. (a) Dependence of the gap function Δ on the nonlinear coupling γ for different hole sizes. As in Fig. 2, Λ=23µm and λ=1.55µm. (b) Diagram of existence of solutions for a nonlinear PCF. The shaded region is the nonlinear soliton phase. The other region corresponds to the homogeneous-instability phase. The inter-phase is given by the γc(a) curve. As before, Λ=23 µm and λ=1.55 µm.
Fig. 4.
Fig. 4. (2.55 MB) Evolution of the field amplitude in z for a large-scale PCF with Λ=23µm, a=8µm and λ=1.55µm. We show the transient from an initial Gaussian profile towards an asymptotic spatial soliton solution.
Fig. 5.
Fig. 5. Typical evolution behavior in z of 〈ϕ|L(ϕ)|ϕ〉 for a large-scale PCF with Λ=23µm, a=8µm and λ=1.55µm.

Equations (2)

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[ t 2 + k 0 2 ( n 0 2 ( x ) + n 2 2 ( x ) ϕ 2 ) ] ϕ = β 2 ϕ ,
[ t 2 + k 0 2 ( n 0 2 ( x ) + n 2 2 ( x ) ϕ 2 ) ] ϕ = 2 ϕ z 2 .
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