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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  1. T. A. Birks , J. C. Knight , and P. St. J. Russell , “ Endlessly single-mode photonic crystal fiber ,” Opt. Lett.   22 , 961 – 963 ( 1997 ).
    [CrossRef] [PubMed]
  2. J. C. Knight , T. A. Birks , P. St. J. Russell , and J. P. de Sandro , “ Properties of photonic crystal fiber and the effective index model ,” J. Opt. Soc. Am. A   15 , 748 – 752 ( 1998 ).
    [CrossRef]
  3. A. Ferrando , E. Silvestre , J. J. Miret , P. Andrés , and M. V. Andrés , “ Full-vector analysis of a realistic photonic crystal fiber ,” Opt. Lett.   24 , 276 – 278 ( 1999 ).
    [CrossRef]
  4. T. M. Monro , D. J. Richardson , N. G. R. Broderick , and P. J. Bennett , “ Holey optical fibers: an efficient modal model ,” J. Lightwave Technol.   17 , 1093 – 1102 ( 1999 ).
    [CrossRef]
  5. D. Mogilevtsev , T. A. Birks , and P. St. J. Russell , “ Localized function method for modeling defect modes in 2-D photonic crystals ,” J. Lightwave Technol.   17 , 2078 – 2081 ( 1999 ).
    [CrossRef]
  6. F. Brechet , J. Marcou , D. Pagnoux , and P. Roy , “ Complete analysis of the characteristics of propagation into photonic crystal fibers, by the finite element method ,” Opt. Fiber Technol.   6 , 181 – 191 ( 2000 ).
    [CrossRef]
  7. M. J. Steel , T. P. White , C. Martijn de Sterke , R. C. McPhedran , and L. C. Botten , “ Symmetry and degeneracy in microstructured optical fibers ,” Opt. Lett.   26 , 488 – 490 ( 2001 ).
    [CrossRef]
  8. G. E. Town and J. T. Lizier , “ Tapered holey fibers for spot-size and numerical-aperture conversion ,” Opt. Lett.   26 , 1042 – 1044 ( 2001 ).
    [CrossRef]
  9. 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]
  10. 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]
  11. Q. Ye , C. Xu , X. Liu, , W. H. Knox , M. F. Yan , R. S. Windeler , and B. Eggleton , “ Dispersion measurement of tapered air-silica microstructure fiber by white-light interferometry ,” Appl. Opt.   41 , 4467 – 4470 ( 2002 ).
    [CrossRef] [PubMed]
  12. 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]
  13. 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]
  14. 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]
  15. A. Y. H. Chen , G. K. L. Wong , S. G. Murdoch , R. Leonhardt , J. D. Harvey , J. C. Knight , W. J. Wadsworth , and P. St. J. Russell , “ Widely tunable optical parametric generation in a photonic crystal fiber ,” Opt. Lett.   30 , 762 – 764 ( 2005 ).
    [CrossRef] [PubMed]
  16. G. P. Agrawal , Nonlinear Fiber Optics , 3rd ed., Optics and Photonics Series ( Academic , 2001 ).
  17. A. Yariv , Optical Electronics in Modern Communications , 5th ed. The Oxford Series in Electrical and Computer Engineering ( Oxford University Press , 1997 ).
  18. BeamPROP Version 5.0c ( RSoft Design Group, Inc. , 2002 ).
  19. 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 fiber ,” J. Opt. Soc. Am. B (to be published)

2005 (1)

2002 (1)

2001 (3)

2000 (2)

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]

F. Brechet , J. Marcou , D. Pagnoux , and P. Roy , “ Complete analysis of the characteristics of propagation into photonic crystal fibers, by the finite element method ,” Opt. Fiber Technol.   6 , 181 – 191 ( 2000 ).
[CrossRef]

1999 (6)

A. Ferrando , E. Silvestre , J. J. Miret , P. Andrés , and M. V. Andrés , “ Full-vector analysis of a realistic photonic crystal fiber ,” Opt. Lett.   24 , 276 – 278 ( 1999 ).
[CrossRef]

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]

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]

T. M. Monro , D. J. Richardson , N. G. R. Broderick , and P. J. Bennett , “ Holey optical fibers: an efficient modal model ,” J. Lightwave Technol.   17 , 1093 – 1102 ( 1999 ).
[CrossRef]

D. Mogilevtsev , T. A. Birks , and P. St. J. Russell , “ Localized function method for modeling defect modes in 2-D photonic crystals ,” J. Lightwave Technol.   17 , 2078 – 2081 ( 1999 ).
[CrossRef]

1998 (1)

1997 (1)

Agrawal, G. P.

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

Andrés, M. V.

Andrés, P.

Arriaga, J.

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]

Bennett, P. J.

Birks, T. A.

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]

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]

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]

D. Mogilevtsev , T. A. Birks , and P. St. J. Russell , “ Localized function method for modeling defect modes in 2-D photonic crystals ,” J. Lightwave Technol.   17 , 2078 – 2081 ( 1999 ).
[CrossRef]

J. C. Knight , T. A. Birks , P. St. J. Russell , and J. P. de Sandro , “ Properties of photonic crystal fiber and the effective index model ,” J. Opt. Soc. Am. A   15 , 748 – 752 ( 1998 ).
[CrossRef]

T. A. Birks , J. C. Knight , and P. St. J. Russell , “ Endlessly single-mode photonic crystal fiber ,” Opt. Lett.   22 , 961 – 963 ( 1997 ).
[CrossRef] [PubMed]

Botten, L. C.

Brechet, F.

F. Brechet , J. Marcou , D. Pagnoux , and P. Roy , “ Complete analysis of the characteristics of propagation into photonic crystal fibers, by the finite element method ,” Opt. Fiber Technol.   6 , 181 – 191 ( 2000 ).
[CrossRef]

Broderick, N. G. R.

Chen, A. Y. H.

A. Y. H. Chen , G. K. L. Wong , S. G. Murdoch , R. Leonhardt , J. D. Harvey , J. C. Knight , W. J. Wadsworth , and P. St. J. Russell , “ Widely tunable optical parametric generation in a photonic crystal fiber ,” Opt. Lett.   30 , 762 – 764 ( 2005 ).
[CrossRef] [PubMed]

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 fiber ,” J. Opt. Soc. Am. B (to be published)

de Sandro, J. P.

Eggleton, B.

Ferrando, A.

Fragnito, H. L.

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]

Gander, M. J.

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]

Grosz, D. F.

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]

Harvey, J. D.

A. Y. H. Chen , G. K. L. Wong , S. G. Murdoch , R. Leonhardt , J. D. Harvey , J. C. Knight , W. J. Wadsworth , and P. St. J. Russell , “ Widely tunable optical parametric generation in a photonic crystal fiber ,” Opt. Lett.   30 , 762 – 764 ( 2005 ).
[CrossRef] [PubMed]

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 fiber ,” J. Opt. Soc. Am. B (to be published)

Joly, N. Y.

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 fiber ,” J. Opt. Soc. Am. B (to be published)

Jones, J. D. C.

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]

Knight, J. C.

A. Y. H. Chen , G. K. L. Wong , S. G. Murdoch , R. Leonhardt , J. D. Harvey , J. C. Knight , W. J. Wadsworth , and P. St. J. Russell , “ Widely tunable optical parametric generation in a photonic crystal fiber ,” Opt. Lett.   30 , 762 – 764 ( 2005 ).
[CrossRef] [PubMed]

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]

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]

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]

J. C. Knight , T. A. Birks , P. St. J. Russell , and J. P. de Sandro , “ Properties of photonic crystal fiber and the effective index model ,” J. Opt. Soc. Am. A   15 , 748 – 752 ( 1998 ).
[CrossRef]

T. A. Birks , J. C. Knight , and P. St. J. Russell , “ Endlessly single-mode photonic crystal fiber ,” Opt. Lett.   22 , 961 – 963 ( 1997 ).
[CrossRef] [PubMed]

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 fiber ,” J. Opt. Soc. Am. B (to be published)

Knox, W. H.

Leonhardt, R.

A. Y. H. Chen , G. K. L. Wong , S. G. Murdoch , R. Leonhardt , J. D. Harvey , J. C. Knight , W. J. Wadsworth , and P. St. J. Russell , “ Widely tunable optical parametric generation in a photonic crystal fiber ,” Opt. Lett.   30 , 762 – 764 ( 2005 ).
[CrossRef] [PubMed]

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 fiber ,” J. Opt. Soc. Am. B (to be published)

Liu,, X.

Lizier, J. T.

Marcou, J.

F. Brechet , J. Marcou , D. Pagnoux , and P. Roy , “ Complete analysis of the characteristics of propagation into photonic crystal fibers, by the finite element method ,” Opt. Fiber Technol.   6 , 181 – 191 ( 2000 ).
[CrossRef]

Martijn de Sterke, C.

Mazzali, C.

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]

McBride, R.

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]

McPhedran, R. C.

Miret, J. J.

Mogilevtsev, D.

D. Mogilevtsev , T. A. Birks , and P. St. J. Russell , “ Localized function method for modeling defect modes in 2-D photonic crystals ,” J. Lightwave Technol.   17 , 2078 – 2081 ( 1999 ).
[CrossRef]

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]

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]

Monro, T. M.

Murdoch, S. G.

A. Y. H. Chen , G. K. L. Wong , S. G. Murdoch , R. Leonhardt , J. D. Harvey , J. C. Knight , W. J. Wadsworth , and P. St. J. Russell , “ Widely tunable optical parametric generation in a photonic crystal fiber ,” Opt. Lett.   30 , 762 – 764 ( 2005 ).
[CrossRef] [PubMed]

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 fiber ,” J. Opt. Soc. Am. B (to be published)

Ortigosa-Blanch, A.

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]

Pagnoux, D.

F. Brechet , J. Marcou , D. Pagnoux , and P. Roy , “ Complete analysis of the characteristics of propagation into photonic crystal fibers, by the finite element method ,” Opt. Fiber Technol.   6 , 181 – 191 ( 2000 ).
[CrossRef]

Qiu, M.

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]

Richardson, D. J.

Roy, P.

F. Brechet , J. Marcou , D. Pagnoux , and P. Roy , “ Complete analysis of the characteristics of propagation into photonic crystal fibers, by the finite element method ,” Opt. Fiber Technol.   6 , 181 – 191 ( 2000 ).
[CrossRef]

Russell, P. St. J.

A. Y. H. Chen , G. K. L. Wong , S. G. Murdoch , R. Leonhardt , J. D. Harvey , J. C. Knight , W. J. Wadsworth , and P. St. J. Russell , “ Widely tunable optical parametric generation in a photonic crystal fiber ,” Opt. Lett.   30 , 762 – 764 ( 2005 ).
[CrossRef] [PubMed]

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]

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]

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]

D. Mogilevtsev , T. A. Birks , and P. St. J. Russell , “ Localized function method for modeling defect modes in 2-D photonic crystals ,” J. Lightwave Technol.   17 , 2078 – 2081 ( 1999 ).
[CrossRef]

J. C. Knight , T. A. Birks , P. St. J. Russell , and J. P. de Sandro , “ Properties of photonic crystal fiber and the effective index model ,” J. Opt. Soc. Am. A   15 , 748 – 752 ( 1998 ).
[CrossRef]

T. A. Birks , J. C. Knight , and P. St. J. Russell , “ Endlessly single-mode photonic crystal fiber ,” Opt. Lett.   22 , 961 – 963 ( 1997 ).
[CrossRef] [PubMed]

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 fiber ,” J. Opt. Soc. Am. B (to be published)

Silvestre, E.

Steel, M. J.

Town, G. E.

Wadsworth, W. J.

A. Y. H. Chen , G. K. L. Wong , S. G. Murdoch , R. Leonhardt , J. D. Harvey , J. C. Knight , W. J. Wadsworth , and P. St. J. Russell , “ Widely tunable optical parametric generation in a photonic crystal fiber ,” Opt. Lett.   30 , 762 – 764 ( 2005 ).
[CrossRef] [PubMed]

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]

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 fiber ,” J. Opt. Soc. Am. B (to be published)

White, T. P.

Windeler, R. S.

Wong, G. K. L.

A. Y. H. Chen , G. K. L. Wong , S. G. Murdoch , R. Leonhardt , J. D. Harvey , J. C. Knight , W. J. Wadsworth , and P. St. J. Russell , “ Widely tunable optical parametric generation in a photonic crystal fiber ,” Opt. Lett.   30 , 762 – 764 ( 2005 ).
[CrossRef] [PubMed]

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 fiber ,” J. Opt. Soc. Am. B (to be published)

Xu, C.

Yan, M. F.

Yariv, A.

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

Ye, Q.

Appl. Opt. (1)

Electron. Lett. (1)

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. (3)

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. (2)

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (1)

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 fiber ,” J. Opt. Soc. Am. B (to be published)

Microwave Opt. Technol. Lett. (1)

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]

Opt. Fiber Technol. (1)

F. Brechet , J. Marcou , D. Pagnoux , and P. Roy , “ Complete analysis of the characteristics of propagation into photonic crystal fibers, by the finite element method ,” Opt. Fiber Technol.   6 , 181 – 191 ( 2000 ).
[CrossRef]

Opt. Lett. (5)

Other (3)

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 ).

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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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