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Characterization of chromatic dispersion in photonic crystal fibers using scalar modulation instability

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Abstract

A simple and accurate method is proposed for characterizing the chromatic dispersion of high air-filling fraction photonic crystal fibers. The method is based upon scalar modulation instability generated by a strong pump wave propagating near the zero-dispersion wavelength. Measuring the modulation instability sideband frequency shifts as a function of wavelength gives a direct measurement of the fiber’s chromatic dispersion over a wide wavelength range. To simplify the dispersion calculation we introduce a simple analytical model of the fiber’s dispersion, and verify its accuracy via a full numerical simulation. Measurements of the chromatic dispersion of two different types of high air-filling fraction photonic crystal fibers are presented.

©2005 Optical Society of America

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Figures (8)

Fig. 1.
Fig. 1. (a) Scanning electron microscope image of a photonic crystal fiber (fiber A) used in this paper. The light regions are fused silica; the dark regions are air. (b) Scanning electron microscope image of a second photonic crystal fiber (fiber B) used in this paper, where the air-filling fraction is lower.
Fig. 2.
Fig. 2. Group-velocity dispersion as a function of wavelength for (a) fiber A and (b) fiber B. Inset, model structure used in the numerical simulation.
Fig. 3.
Fig. 3. Modulation instability phase-matching diagram for a photonic crystal fiber with an effective core diameter of 1.624 μm and an effective air-filling fraction of 90%. The pump power was 1 W. Inset, dispersion of the fiber as a function of wavelength.
Fig. 4.
Fig. 4. Experimentally measured sideband wavelengths as a function of pump wavelength for fiber A. The solid curves are the least squares fit to the experimental data (circles), calculated using Eq. (3) based on our step-index fiber model.
Fig. 5.
Fig. 5. Optical spectra at the output of fiber A for pump wavelengths (i) 672.2, (ii) 670, and (iii) 667.6 nm (pump polarized to the high group-index mode). The peak power of the pump pulses was 1.5 W.
Fig. 6.
Fig. 6. Measured group-velocity dispersion of fiber A. Inset, close-up of β 2 near the zero-dispersion wavelength
Fig. 7.
Fig. 7. Experimentally measured sideband wavelengths as a function of pump wavelength for fiber B. The solid curves are the least squares fit to the experimental data (circles), calculated using Eq. (3) based on our step-index fiber model.
Fig. 8.
Fig. 8. Measured group-velocity dispersion of fiber B. Inset, close-up of β 2 near the zero-dispersion wavelength

Equations (4)

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g ( Ω ) = Im Δ β L ( Ω ) [ Δ β L ( Ω ) + 4 γP ] ,
Δ β L ( Ω ) = β ( ω p + Ω ) + β ( ω p Ω ) 2 β ( ω p ) .
Δ β L ( Ω ) + 2 γP = 0 .
n = 1 2 β 2 n Ω 2 n ( 2 n ) ! + 2 γ P = 0 .
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