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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References

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Appl. Opt.

Electron. Lett.

M. J. Gander, R. McBride, J. D. C. Jones, D. Mogilevtsev, T. A. Birks, J. C. Knight, and P. St. J. Russell, �??Experimental measurement of group velocity dispersion in photonic crystal fibre,�?? Electron. Lett. 35, 63-64 (1999).
[CrossRef]

IEEE Photonics Technol. Lett.

C. Mazzali, D. F. Grosz, and H. L. Fragnito, �??Simple method for measuring dispersion and nonlinear coefficient near the zero-dispersion wavelength of optical fibers,�?? IEEE Photonics Technol. Lett. 11, 251-253 (1999).
[CrossRef]

T. A. Birks, D. Mogilevtsev, J. C. Knight, and P. St. J. Russell, �??Dispersion compensation using single-material fibers,�?? IEEE Photonics Technol. Lett. 11, 674-676 (1999).
[CrossRef]

J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blanch, W. J. Wadsworth, and P. St. J. Russell, �??Anomalous dispersion in photonic crystal fiber,�?? IEEE Photonics Technol. Lett. 12, 807-809 (2000).
[CrossRef]

J. Lightwave Technol.

J. Opt. Soc. Am. A

Opt. Fiber Technol.

F. Brechet, J. Marcou, D. Pagnoux, and P. Roy, �??Complete analysis of the characteristics of propagation into photonic crystal .bers, by the .nite element method,�?? Opt. Fiber Technol. 6, 181-191 (2000).
[CrossRef]

Opt. Lett.

Opt. Technol. Lett.

M. Qiu, �??Analysis of guided modes in photonic crystal fibers using the finite-difference time-domain method,�?? Microwave Opt. Technol. Lett. 30, 327-330 (2001).
[CrossRef]

Other

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed., Optics and Photonics Series (Academic, 2001).

A. Yariv, Optical Electronics in Modern Communications, 5th ed. The Oxford Series in Electrical and Computer Engineering (Oxford University Press, 1997).

BeamPROP Version 5.0c (RSoft Design Group, Inc., 2002).

G. K. L. Wong, A. Y. H. Chen, S. G. Murdoch, R. Leonhardt, J. D. Harvey, N. Y. Joly, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, �??Continuous-wave tunable optical parametric generation in a photonic-crystal .ber,�?? J. Opt. Soc. Am. B (to be published)

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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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