Abstract

The onset of supercontinuum generation in a photonic crystal fiber is investigated experimentally and numerically as a function of pump wavelength and intensity with 100-fs pulses. Soliton formation is found to be the determining factor in the initial step. The formation and behavior of a blueshifted, nonsolitonic component, emitted as the soliton evolves towards the stable regime, is investigated and the role of phase matching through higher-order dispersion is highlighted. Good agreement between experiments and simulations is obtained.

© 2003 Optical Society of America

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  1. J. K. Ranka, R. S. Windeler, and A. J. Stentz, “Visible continuum generation in air-silica microstructure fibers with anomalous dispersion at 800 nm,” Opt. Lett. 25, 25–27 (2000).
    [CrossRef]
  2. An overview of the field can be found in the special issue on nonlinear optics of photonic crystals of J. Opt. Soc. Am. B 19, 2046–2296 (2002).
  3. S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hänsch, “Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
    [CrossRef] [PubMed]
  4. I. Hartl, X. D. Li, C. Chudoba, R. K. Ghanta, T. H. Ko, J. G. Fujimoto, J. K. Ranka, and R. S. Windeler, “Ultrahigh-resolution optical coherence tomography using continuum generation in an air-silica microstructured optical fiber,” Opt. Lett. 26, 608–610 (2001).
    [CrossRef]
  5. G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, San Diego, Calif., 2001).
  6. J. M. Dudley, L. Provino, N. Grossard, H. Maillotte, R. S. Windeler, B. J. Eggleton, and S. Coen, “Supercontinuum generation in air-silica microstructured fibers with nanosecond and femtosecond pulse pumping,” J. Opt. Soc. Am. B 19, 765–771 (2002).
    [CrossRef]
  7. A. B. Fedotov, A. N. Naumov, A. M. Zheltikov, I. Bugar, J. D. Chorvat, A. P. Tarasevitch, and D. von der Linde, “Frequency-tunable supercontinuum generation in photonic-crystal fibers by femtosecond pulses of an optical parametric amplifier,” J. Opt. Soc. Am. B 19, 2156–2164 (2002).
    [CrossRef]
  8. A. V. Husakou and J. Herrmann, “Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers,” Phys. Rev. Lett. 87, 203901–203904 (2001).
    [CrossRef] [PubMed]
  9. J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers,” Phys. Rev. Lett. 88, 173901–173904 (2002).
    [CrossRef] [PubMed]
  10. A. V. Husakou and J. Herrmann, “Supercontinuum generation, four-wave mixing, and fission of higher-order solitons in photonic-crystal fibers,” J. Opt. Soc. Am. B 19, 2171–2182 (2002).
    [CrossRef]
  11. S. Coen, A. H. C. Chau, R. Leonhardt, J. D. Harvey, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “Supercontinuum generation by stimulated Raman scattering and parametric four-wave mixing in photonic crystal fibers,” J. Opt. Soc. Am. B 19, 753–764 (2002).
    [CrossRef]
  12. A. L. Gaeta, “Nonlinear propagation and continuum generation in microstructured optical fibers,” Opt. Lett. 27, 924–926 (2002).
    [CrossRef]
  13. B. R. Washburn, S. E. Ralph, and R. S. Windeler, “Ultrashort pulse propagation in air-silica microstructure fiber,” Opt. Express 10, 575–580 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10–13–575.
    [CrossRef] [PubMed]
  14. A. Ortigosa-Blanch, J. C. Knight, and P. St. J. Russell, “Pulse breaking and supercontinuum generation with 200-fs pump pulses in photonic crystal fibers,” J. Opt. Soc. Am. B 19, 2567–2572 (2002).
    [CrossRef]
  15. P. K. A. Wai, C. R. Menyuk, Y. C. Lee, and H. H. Chen, “Nonlinear pulse propagation in the neighborhood of the zero-dispersion wavelength of monomode optical fibers,” Opt. Lett. 11, 464–466 (1986).
    [CrossRef] [PubMed]
  16. J. N. Elgin, T. Brabec, and S. M. J. Kelly, “A perturbative theory of soliton propagation in the presence of third order dispersion,” Opt. Commun. 114, 321–328 (1995).
    [CrossRef]
  17. For numerical convenience the slowly-varying-envelope approximation is used in this work. The results have been compared to results from a model identical to the one used in Ref. 8 and only negligible difference was found.
  18. J. Broeng, Crystal Fibre A/S, Blokken 84, DK-3460 Birkerød, Denmark (personal communication, 2002).

2002 (8)

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers,” Phys. Rev. Lett. 88, 173901–173904 (2002).
[CrossRef] [PubMed]

S. Coen, A. H. C. Chau, R. Leonhardt, J. D. Harvey, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “Supercontinuum generation by stimulated Raman scattering and parametric four-wave mixing in photonic crystal fibers,” J. Opt. Soc. Am. B 19, 753–764 (2002).
[CrossRef]

J. M. Dudley, L. Provino, N. Grossard, H. Maillotte, R. S. Windeler, B. J. Eggleton, and S. Coen, “Supercontinuum generation in air-silica microstructured fibers with nanosecond and femtosecond pulse pumping,” J. Opt. Soc. Am. B 19, 765–771 (2002).
[CrossRef]

A. L. Gaeta, “Nonlinear propagation and continuum generation in microstructured optical fibers,” Opt. Lett. 27, 924–926 (2002).
[CrossRef]

B. R. Washburn, S. E. Ralph, and R. S. Windeler, “Ultrashort pulse propagation in air-silica microstructure fiber,” Opt. Express 10, 575–580 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10–13–575.
[CrossRef] [PubMed]

A. V. Husakou and J. Herrmann, “Supercontinuum generation, four-wave mixing, and fission of higher-order solitons in photonic-crystal fibers,” J. Opt. Soc. Am. B 19, 2171–2182 (2002).
[CrossRef]

A. B. Fedotov, A. N. Naumov, A. M. Zheltikov, I. Bugar, J. D. Chorvat, A. P. Tarasevitch, and D. von der Linde, “Frequency-tunable supercontinuum generation in photonic-crystal fibers by femtosecond pulses of an optical parametric amplifier,” J. Opt. Soc. Am. B 19, 2156–2164 (2002).
[CrossRef]

A. Ortigosa-Blanch, J. C. Knight, and P. St. J. Russell, “Pulse breaking and supercontinuum generation with 200-fs pump pulses in photonic crystal fibers,” J. Opt. Soc. Am. B 19, 2567–2572 (2002).
[CrossRef]

2001 (2)

2000 (2)

J. K. Ranka, R. S. Windeler, and A. J. Stentz, “Visible continuum generation in air-silica microstructure fibers with anomalous dispersion at 800 nm,” Opt. Lett. 25, 25–27 (2000).
[CrossRef]

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hänsch, “Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
[CrossRef] [PubMed]

1995 (1)

J. N. Elgin, T. Brabec, and S. M. J. Kelly, “A perturbative theory of soliton propagation in the presence of third order dispersion,” Opt. Commun. 114, 321–328 (1995).
[CrossRef]

1986 (1)

Brabec, T.

J. N. Elgin, T. Brabec, and S. M. J. Kelly, “A perturbative theory of soliton propagation in the presence of third order dispersion,” Opt. Commun. 114, 321–328 (1995).
[CrossRef]

Bugar, I.

Chau, A. H. C.

Chen, H. H.

Chorvat, J. D.

Chudoba, C.

Coen, S.

Cundiff, S. T.

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hänsch, “Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
[CrossRef] [PubMed]

Diddams, S. A.

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hänsch, “Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
[CrossRef] [PubMed]

Dudley, J. M.

Eggleton, B. J.

Elgin, J. N.

J. N. Elgin, T. Brabec, and S. M. J. Kelly, “A perturbative theory of soliton propagation in the presence of third order dispersion,” Opt. Commun. 114, 321–328 (1995).
[CrossRef]

Fedotov, A. B.

Fujimoto, J. G.

Gaeta, A. L.

Ghanta, R. K.

Griebner, U.

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers,” Phys. Rev. Lett. 88, 173901–173904 (2002).
[CrossRef] [PubMed]

Grossard, N.

Hall, J. L.

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hänsch, “Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
[CrossRef] [PubMed]

Hänsch, T. W.

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hänsch, “Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
[CrossRef] [PubMed]

Hartl, I.

Harvey, J. D.

Herrmann, J.

A. V. Husakou and J. Herrmann, “Supercontinuum generation, four-wave mixing, and fission of higher-order solitons in photonic-crystal fibers,” J. Opt. Soc. Am. B 19, 2171–2182 (2002).
[CrossRef]

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers,” Phys. Rev. Lett. 88, 173901–173904 (2002).
[CrossRef] [PubMed]

A. V. Husakou and J. Herrmann, “Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers,” Phys. Rev. Lett. 87, 203901–203904 (2001).
[CrossRef] [PubMed]

Holzwarth, R.

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hänsch, “Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
[CrossRef] [PubMed]

Husakou, A.

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers,” Phys. Rev. Lett. 88, 173901–173904 (2002).
[CrossRef] [PubMed]

Husakou, A. V.

A. V. Husakou and J. Herrmann, “Supercontinuum generation, four-wave mixing, and fission of higher-order solitons in photonic-crystal fibers,” J. Opt. Soc. Am. B 19, 2171–2182 (2002).
[CrossRef]

A. V. Husakou and J. Herrmann, “Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers,” Phys. Rev. Lett. 87, 203901–203904 (2001).
[CrossRef] [PubMed]

Jones, D. J.

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hänsch, “Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
[CrossRef] [PubMed]

Kelly, S. M. J.

J. N. Elgin, T. Brabec, and S. M. J. Kelly, “A perturbative theory of soliton propagation in the presence of third order dispersion,” Opt. Commun. 114, 321–328 (1995).
[CrossRef]

Knight, J. C.

Ko, T. H.

Lee, Y. C.

Leonhardt, R.

Li, X. D.

Maillotte, H.

Menyuk, C. R.

Naumov, A. N.

Nickel, D.

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers,” Phys. Rev. Lett. 88, 173901–173904 (2002).
[CrossRef] [PubMed]

Ortigosa-Blanch, A.

Provino, L.

Ralph, S. E.

Ranka, J. K.

Russell, P. St. J.

Stentz, A. J.

Tarasevitch, A. P.

Udem, T.

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hänsch, “Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
[CrossRef] [PubMed]

von der Linde, D.

Wadsworth, W. J.

S. Coen, A. H. C. Chau, R. Leonhardt, J. D. Harvey, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “Supercontinuum generation by stimulated Raman scattering and parametric four-wave mixing in photonic crystal fibers,” J. Opt. Soc. Am. B 19, 753–764 (2002).
[CrossRef]

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers,” Phys. Rev. Lett. 88, 173901–173904 (2002).
[CrossRef] [PubMed]

Wai, P. K. A.

Washburn, B. R.

Windeler, R. S.

Ye, J.

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hänsch, “Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
[CrossRef] [PubMed]

Zhavoronkov, N.

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers,” Phys. Rev. Lett. 88, 173901–173904 (2002).
[CrossRef] [PubMed]

Zheltikov, A. M.

J. Opt. Soc. Am. B (5)

Opt. Commun. (1)

J. N. Elgin, T. Brabec, and S. M. J. Kelly, “A perturbative theory of soliton propagation in the presence of third order dispersion,” Opt. Commun. 114, 321–328 (1995).
[CrossRef]

Opt. Express (1)

Opt. Lett. (4)

Phys. Rev. Lett. (3)

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hänsch, “Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
[CrossRef] [PubMed]

A. V. Husakou and J. Herrmann, “Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers,” Phys. Rev. Lett. 87, 203901–203904 (2001).
[CrossRef] [PubMed]

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers,” Phys. Rev. Lett. 88, 173901–173904 (2002).
[CrossRef] [PubMed]

Other (4)

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, San Diego, Calif., 2001).

For numerical convenience the slowly-varying-envelope approximation is used in this work. The results have been compared to results from a model identical to the one used in Ref. 8 and only negligible difference was found.

J. Broeng, Crystal Fibre A/S, Blokken 84, DK-3460 Birkerød, Denmark (personal communication, 2002).

An overview of the field can be found in the special issue on nonlinear optics of photonic crystals of J. Opt. Soc. Am. B 19, 2046–2296 (2002).

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Figures (10)

Fig. 1
Fig. 1

Recorded spectra for three pump wavelengths: λP= (a) 710 nm, (b) 883 nm, (c) 941 nm. The inset shows a scanning-electron micrograph of the central region of the fiber.

Fig. 2
Fig. 2

Measurement of the wavelength (λNSR) of the blueshifted NSR versus the pump wavelength (λP). As the pump wavelength is increased from 710 nm to 988 nm, λNSR decreases from 622 nm to 372 nm. The inset shows the behavior of λNSR calculated on the basis of phase matching.

Fig. 3
Fig. 3

NSR wavelength dependence on input power: λP= (a) 836 nm, (b) 883 nm, (c) 934 nm. The solid curves are linear fits.

Fig. 4
Fig. 4

NSR amplitude dependence on input power: λP= (a) 836 nm, (b) 883 nm, (c) 934 nm. The solid curves are exponential fits.

Fig. 5
Fig. 5

Examples of simulated spectra for the following pump wavelengths: (a) 780 nm, (b) 836 nm, (c) 934 nm. The pump peak intensities are (a) 9×109 W/cm2, (b) 2.9×1010 W/cm2, (c) 8×1010 W/cm2.

Fig. 6
Fig. 6

Blueshift of the NSR as extracted from the simulations. The intensity corresponding to a given soliton number [Eq. (1)] is indicated by the vertical dotted lines. The pump wavelengths are (a) 780 nm, (b) 836 nm, (c) 934 nm.

Fig. 7
Fig. 7

Growth of the blue signal as extracted from the simulations. The intensity corresponding to a given soliton number [Eq. (1)] is indicated by the vertical dotted lines. The pump wavelengths are (a) 780 nm, (b) 836 nm, (c) 934 nm.

Fig. 8
Fig. 8

Pulse spectra for a 934-nm, 100-fs pulse at (a) the entrance of the fiber, (b) 2.0 cm into the fiber, (c), (d) after 10.1 cm, corresponding to one soliton period. The peak intensity in (a)–(c) is 8×1010 W/cm2, (d) 2×1010 W/cm2.

Fig. 9
Fig. 9

Temporal shape of a 934-nm, 100-fs pulse at (a) the entrance of the fiber, (b) 2.0 cm into the fiber, (c), (d) after 10.1 cm. The peak intensity in (a)–(c) is 8×1010 W/cm2, (d) 2×1010 W/cm2.

Fig. 10
Fig. 10

Phase-matching curve for generation of NSR. The solid curve is the phase matching as given by Eqs. (2) and (3). The crosses show the position of the NSR from the simulations.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

N2=γP0T02|β2|,
ϕS=n(ωS)ωSc z-ωSvS z+n2I0ωSc z,
ϕNSR=n(ωNSR)ωNSRc z-ωNSRvS z,
dA(z, t)dz=DˆA(z, t)+iγ1+iω0t×A(z, t)-tdtR(t)|A(z, t-t)|2,
hR(t)=τ12+τ22τ1τ22exp(-t/τ2)sin(t/τ1),

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