Abstract

We numerically study dispersive wave emission during femtosecond-pumped supercontinuum generation in photonic crystal fibres. We show that dispersive waves are primarily generated over a short region of high temporal compression. Despite the apparent complexity of the pump pulse in this region, we show that the dynamics of dispersive wave generation are dominated by a single fundamental soliton. However, any straightforward application of the theory that is thought to describe the blue emission, considerably underestimates the frequency shift. We show that in fact the red-shift of the soliton, caused by spectral recoil from the growing dispersive wave, causes an additional blue-shift of the resonant frequency which is in good agreement with full simulations.

©2006 Optical Society of America

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References

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  1. R. R. Alfano, The supercontinuum laser source: fundamentals with updated references, 2nd ed. (Springer, New York, 2006).
  2. A. V. Husakou and J. Herrmann, “Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers,” Phys. Rev. Lett. 87, 203901 (2001).
    [Crossref] [PubMed]
  3. J. Ranka, R. Windeler, and A. Stentz, “Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm,” Opt. Lett. 25, 25–27 (2000).
    [Crossref]
  4. J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006).
    [Crossref]
  5. N. Akhmediev and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fibers,” Phys. Rev. A 51, 2602–2607 (1995).
    [Crossref] [PubMed]
  6. P. K. A. Wai, H. H. Chen, and Y. C. Lee, “Radiations by “solitons” at the zero group-dispersion wavelength of single-mode optical fibers,” Phys. Rev. A 41, 426–439 (1990).
    [Crossref] [PubMed]
  7. A. S. 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. Hansch, “Direct Link betweenMicrowave and Optical Frequencies with a 300 THz Femtosecond Laser Comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
    [Crossref] [PubMed]
  8. 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 microstructure optical fiber,” Opt. Lett. 26, 608–610 (2001).
    [Crossref]
  9. H. N. Paulsen, K. M. Hilligsøe, J. Thogersen, S. R. Keiding, and J. J. Larsen, “Coherent anti-Stokes Raman scattering microscopy with a photonic crystal fiber based light source,” Opt. Lett. 28, 1123–1125 (2003).
    [Crossref] [PubMed]
  10. J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, “Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers,” Phys. Rev. Lett. 88, 173901 (2002).
    [Crossref] [PubMed]
  11. Y. Kodama and A. Hasegawa, “Nonlinear Pulse-Propagation In A Monomode Dielectric Guide,” IEEE J. Quantum Electron. 23, 510–524 (1987).
    [Crossref]
  12. J. P. Gordon, “Theory of the soliton self-frequency shift,” Opt. Lett. 11, 662–664 (1986).
    [Crossref] [PubMed]
  13. J. N. Elgin, T. Brabec, and S. Kelly, “A perturbative theory of soliton propagation in the presence of 3rd-order dispersion,” Opt. Commun. 114, 321–328 (1995).
    [Crossref]
  14. I. Cristiani, R. Tediosi, L. Tartara, and V. Degiorgio, “Dispersive wave generation by solitons in microstructured optical fibers,” Opt. Express 12, 124–135 (2004).
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  15. K. M. Hilligsøe, H. N. Paulsen, J. Thogersen, S. R. Keiding, and J. J. Larsen, “Initial steps of supercontinuum generation in photonic crystal fibers,” J. Opt. Soc. Am. B 20, 1887–1893 (2003).
    [Crossref]
  16. G. Genty, M. Lehtonen, and H. Ludvigsen, “Effect of cross-phase modulation on supercontinuum generated in microstructured fibers with sub-30 fs pulses,” Opt. Express 12, 4614–4624 (2004).
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  17. K. Blow and D Wood, “Theoretical description of transient stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. 25, 2665–2673 (1989).
    [Crossref]
  18. G. P. Agrawal, Nonlinear Fibre Optics, 3rd ed. (Academic Press, San Diego, 2001).
  19. Q. H. 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]
  20. B. Kibler, J. M. Dudley, and S. Coen, “Supercontinuum generation and nonlinear pulse propagation in photonic crystal fiber: influence of the frequency-dependent effective mode area,” Appl. Phys. B 81, 337–342 (2005).
    [Crossref]
  21. C.-M. Chen and P. L. Kelley, “Nonlinear pulse compression in optical fibers: scaling laws and numerical analysis,” J. Opt. Soc. Am. B 19, 1961–1967 (2002).
    [Crossref]
  22. D. Skryabin and A. Yulin, “Theory of generation of new frequencies by mixing of solitons and dispersive waves in optical fibers,” Phys. Rev. E 72, 016619 (2005).
    [Crossref]
  23. A. Efimov, A. Yulin, D. Skryabin, J. Knight, N. Joly, F. Omenetto, A. Taylor, and P. St. J. Russell, “Interaction of an Optical Soliton with a Dispersive Wave,” Phys. Rev. Lett. 95, 213902 (2005).
    [Crossref] [PubMed]
  24. A. Peleg, M. Chertkov, and I. Gabitov, “Inelastic interchannel collisions of pulses in optical fibers in the presence of third-order dispersion,” J. Opt. Soc. Am. B 21, 18–23 (2004).
    [Crossref]
  25. D. V. Skryabin, F. Luan, J. C. Knight, and P. St. J. Russell, “Soliton Self-Frequency Shift Cancellation in Photonic Crystal Fibers,” Science 301, 1705–1708 (2003).
    [Crossref] [PubMed]
  26. F. Biancalana, D. V. Skryabin, and A. V. Yulin, “Theory of the soliton self-frequency shift compensation by the resonant radiation in photonic crystal fibers,” Phys. Rev. E 70, 016615 (2004).
    [Crossref]

2006 (1)

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006).
[Crossref]

2005 (3)

B. Kibler, J. M. Dudley, and S. Coen, “Supercontinuum generation and nonlinear pulse propagation in photonic crystal fiber: influence of the frequency-dependent effective mode area,” Appl. Phys. B 81, 337–342 (2005).
[Crossref]

D. Skryabin and A. Yulin, “Theory of generation of new frequencies by mixing of solitons and dispersive waves in optical fibers,” Phys. Rev. E 72, 016619 (2005).
[Crossref]

A. Efimov, A. Yulin, D. Skryabin, J. Knight, N. Joly, F. Omenetto, A. Taylor, and P. St. J. Russell, “Interaction of an Optical Soliton with a Dispersive Wave,” Phys. Rev. Lett. 95, 213902 (2005).
[Crossref] [PubMed]

2004 (4)

2003 (3)

2002 (3)

2001 (2)

2000 (2)

A. S. 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. Hansch, “Direct Link betweenMicrowave and Optical Frequencies with a 300 THz Femtosecond Laser Comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
[Crossref] [PubMed]

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

1995 (2)

N. Akhmediev and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fibers,” Phys. Rev. A 51, 2602–2607 (1995).
[Crossref] [PubMed]

J. N. Elgin, T. Brabec, and S. Kelly, “A perturbative theory of soliton propagation in the presence of 3rd-order dispersion,” Opt. Commun. 114, 321–328 (1995).
[Crossref]

1990 (1)

P. K. A. Wai, H. H. Chen, and Y. C. Lee, “Radiations by “solitons” at the zero group-dispersion wavelength of single-mode optical fibers,” Phys. Rev. A 41, 426–439 (1990).
[Crossref] [PubMed]

1989 (1)

K. Blow and D Wood, “Theoretical description of transient stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. 25, 2665–2673 (1989).
[Crossref]

1987 (1)

Y. Kodama and A. Hasegawa, “Nonlinear Pulse-Propagation In A Monomode Dielectric Guide,” IEEE J. Quantum Electron. 23, 510–524 (1987).
[Crossref]

1986 (1)

Agrawal, G. P.

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

Akhmediev, N.

N. Akhmediev and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fibers,” Phys. Rev. A 51, 2602–2607 (1995).
[Crossref] [PubMed]

Alfano, R. R.

R. R. Alfano, The supercontinuum laser source: fundamentals with updated references, 2nd ed. (Springer, New York, 2006).

Biancalana, F.

F. Biancalana, D. V. Skryabin, and A. V. Yulin, “Theory of the soliton self-frequency shift compensation by the resonant radiation in photonic crystal fibers,” Phys. Rev. E 70, 016615 (2004).
[Crossref]

Blow, K.

K. Blow and D Wood, “Theoretical description of transient stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. 25, 2665–2673 (1989).
[Crossref]

Brabec, T.

J. N. Elgin, T. Brabec, and S. Kelly, “A perturbative theory of soliton propagation in the presence of 3rd-order dispersion,” Opt. Commun. 114, 321–328 (1995).
[Crossref]

Chen, C.-M.

Chen, H. H.

P. K. A. Wai, H. H. Chen, and Y. C. Lee, “Radiations by “solitons” at the zero group-dispersion wavelength of single-mode optical fibers,” Phys. Rev. A 41, 426–439 (1990).
[Crossref] [PubMed]

Chertkov, M.

Chudoba, C.

Coen, S.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006).
[Crossref]

B. Kibler, J. M. Dudley, and S. Coen, “Supercontinuum generation and nonlinear pulse propagation in photonic crystal fiber: influence of the frequency-dependent effective mode area,” Appl. Phys. B 81, 337–342 (2005).
[Crossref]

Cristiani, I.

Cundiff, S. T.

A. S. 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. Hansch, “Direct Link betweenMicrowave and Optical Frequencies with a 300 THz Femtosecond Laser Comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
[Crossref] [PubMed]

Degiorgio, V.

Diddams, A. S.

A. S. 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. Hansch, “Direct Link betweenMicrowave and Optical Frequencies with a 300 THz Femtosecond Laser Comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
[Crossref] [PubMed]

Dudley, J. M.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006).
[Crossref]

B. Kibler, J. M. Dudley, and S. Coen, “Supercontinuum generation and nonlinear pulse propagation in photonic crystal fiber: influence of the frequency-dependent effective mode area,” Appl. Phys. B 81, 337–342 (2005).
[Crossref]

Efimov, A.

A. Efimov, A. Yulin, D. Skryabin, J. Knight, N. Joly, F. Omenetto, A. Taylor, and P. St. J. Russell, “Interaction of an Optical Soliton with a Dispersive Wave,” Phys. Rev. Lett. 95, 213902 (2005).
[Crossref] [PubMed]

Eggleton, B.

Elgin, J. N.

J. N. Elgin, T. Brabec, and S. Kelly, “A perturbative theory of soliton propagation in the presence of 3rd-order dispersion,” Opt. Commun. 114, 321–328 (1995).
[Crossref]

Fujimoto, J. G.

Gabitov, I.

Genty, G.

Ghanta, R. K.

Gordon, J. P.

Griebner, U.

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

Hall, J. L.

A. S. 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. Hansch, “Direct Link betweenMicrowave and Optical Frequencies with a 300 THz Femtosecond Laser Comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
[Crossref] [PubMed]

Hansch, T. W.

A. S. 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. Hansch, “Direct Link betweenMicrowave and Optical Frequencies with a 300 THz Femtosecond Laser Comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
[Crossref] [PubMed]

Hartl, I.

Hasegawa, A.

Y. Kodama and A. Hasegawa, “Nonlinear Pulse-Propagation In A Monomode Dielectric Guide,” IEEE J. Quantum Electron. 23, 510–524 (1987).
[Crossref]

Herrmann, J.

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, “Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers,” Phys. Rev. Lett. 88, 173901 (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 (2001).
[Crossref] [PubMed]

Hilligsøe, K. M.

Holzwarth, R.

A. S. 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. Hansch, “Direct Link betweenMicrowave 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, P. St. J. Russell, and G. Korn, “Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers,” Phys. Rev. Lett. 88, 173901 (2002).
[Crossref] [PubMed]

Husakou, A. V.

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

Joly, N.

A. Efimov, A. Yulin, D. Skryabin, J. Knight, N. Joly, F. Omenetto, A. Taylor, and P. St. J. Russell, “Interaction of an Optical Soliton with a Dispersive Wave,” Phys. Rev. Lett. 95, 213902 (2005).
[Crossref] [PubMed]

Jones, D. J.

A. S. 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. Hansch, “Direct Link betweenMicrowave and Optical Frequencies with a 300 THz Femtosecond Laser Comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
[Crossref] [PubMed]

Karlsson, M.

N. Akhmediev and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fibers,” Phys. Rev. A 51, 2602–2607 (1995).
[Crossref] [PubMed]

Keiding, S. R.

Kelley, P. L.

Kelly, S.

J. N. Elgin, T. Brabec, and S. Kelly, “A perturbative theory of soliton propagation in the presence of 3rd-order dispersion,” Opt. Commun. 114, 321–328 (1995).
[Crossref]

Kibler, B.

B. Kibler, J. M. Dudley, and S. Coen, “Supercontinuum generation and nonlinear pulse propagation in photonic crystal fiber: influence of the frequency-dependent effective mode area,” Appl. Phys. B 81, 337–342 (2005).
[Crossref]

Knight, J.

A. Efimov, A. Yulin, D. Skryabin, J. Knight, N. Joly, F. Omenetto, A. Taylor, and P. St. J. Russell, “Interaction of an Optical Soliton with a Dispersive Wave,” Phys. Rev. Lett. 95, 213902 (2005).
[Crossref] [PubMed]

Knight, J. C.

D. V. Skryabin, F. Luan, J. C. Knight, and P. St. J. Russell, “Soliton Self-Frequency Shift Cancellation in Photonic Crystal Fibers,” Science 301, 1705–1708 (2003).
[Crossref] [PubMed]

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

Knox, W. H.

Ko, T. H.

Kodama, Y.

Y. Kodama and A. Hasegawa, “Nonlinear Pulse-Propagation In A Monomode Dielectric Guide,” IEEE J. Quantum Electron. 23, 510–524 (1987).
[Crossref]

Korn, G.

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

Larsen, J. J.

Lee, Y. C.

P. K. A. Wai, H. H. Chen, and Y. C. Lee, “Radiations by “solitons” at the zero group-dispersion wavelength of single-mode optical fibers,” Phys. Rev. A 41, 426–439 (1990).
[Crossref] [PubMed]

Lehtonen, M.

Li, X. D.

Liu, X.

Luan, F.

D. V. Skryabin, F. Luan, J. C. Knight, and P. St. J. Russell, “Soliton Self-Frequency Shift Cancellation in Photonic Crystal Fibers,” Science 301, 1705–1708 (2003).
[Crossref] [PubMed]

Ludvigsen, H.

Nickel, D.

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

Omenetto, F.

A. Efimov, A. Yulin, D. Skryabin, J. Knight, N. Joly, F. Omenetto, A. Taylor, and P. St. J. Russell, “Interaction of an Optical Soliton with a Dispersive Wave,” Phys. Rev. Lett. 95, 213902 (2005).
[Crossref] [PubMed]

Paulsen, H. N.

Peleg, A.

Ranka, J.

Ranka, J. K.

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 microstructure optical fiber,” Opt. Lett. 26, 608–610 (2001).
[Crossref]

A. S. 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. Hansch, “Direct Link betweenMicrowave and Optical Frequencies with a 300 THz Femtosecond Laser Comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
[Crossref] [PubMed]

Russell, P. St. J.

A. Efimov, A. Yulin, D. Skryabin, J. Knight, N. Joly, F. Omenetto, A. Taylor, and P. St. J. Russell, “Interaction of an Optical Soliton with a Dispersive Wave,” Phys. Rev. Lett. 95, 213902 (2005).
[Crossref] [PubMed]

D. V. Skryabin, F. Luan, J. C. Knight, and P. St. J. Russell, “Soliton Self-Frequency Shift Cancellation in Photonic Crystal Fibers,” Science 301, 1705–1708 (2003).
[Crossref] [PubMed]

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

Skryabin, D.

A. Efimov, A. Yulin, D. Skryabin, J. Knight, N. Joly, F. Omenetto, A. Taylor, and P. St. J. Russell, “Interaction of an Optical Soliton with a Dispersive Wave,” Phys. Rev. Lett. 95, 213902 (2005).
[Crossref] [PubMed]

D. Skryabin and A. Yulin, “Theory of generation of new frequencies by mixing of solitons and dispersive waves in optical fibers,” Phys. Rev. E 72, 016619 (2005).
[Crossref]

Skryabin, D. V.

F. Biancalana, D. V. Skryabin, and A. V. Yulin, “Theory of the soliton self-frequency shift compensation by the resonant radiation in photonic crystal fibers,” Phys. Rev. E 70, 016615 (2004).
[Crossref]

D. V. Skryabin, F. Luan, J. C. Knight, and P. St. J. Russell, “Soliton Self-Frequency Shift Cancellation in Photonic Crystal Fibers,” Science 301, 1705–1708 (2003).
[Crossref] [PubMed]

Stentz, A.

Tartara, L.

Taylor, A.

A. Efimov, A. Yulin, D. Skryabin, J. Knight, N. Joly, F. Omenetto, A. Taylor, and P. St. J. Russell, “Interaction of an Optical Soliton with a Dispersive Wave,” Phys. Rev. Lett. 95, 213902 (2005).
[Crossref] [PubMed]

Tediosi, R.

Thogersen, J.

Udem, T.

A. S. 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. Hansch, “Direct Link betweenMicrowave and Optical Frequencies with a 300 THz Femtosecond Laser Comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
[Crossref] [PubMed]

Wadsworth, W. J.

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

Wai, P. K. A.

P. K. A. Wai, H. H. Chen, and Y. C. Lee, “Radiations by “solitons” at the zero group-dispersion wavelength of single-mode optical fibers,” Phys. Rev. A 41, 426–439 (1990).
[Crossref] [PubMed]

Windeler, R.

Windeler, R. S.

Wood, D

K. Blow and D Wood, “Theoretical description of transient stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. 25, 2665–2673 (1989).
[Crossref]

Xu, C.

Yan, M. F.

Ye, J.

A. S. 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. Hansch, “Direct Link betweenMicrowave and Optical Frequencies with a 300 THz Femtosecond Laser Comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
[Crossref] [PubMed]

Ye, Q. H.

Yulin, A.

A. Efimov, A. Yulin, D. Skryabin, J. Knight, N. Joly, F. Omenetto, A. Taylor, and P. St. J. Russell, “Interaction of an Optical Soliton with a Dispersive Wave,” Phys. Rev. Lett. 95, 213902 (2005).
[Crossref] [PubMed]

D. Skryabin and A. Yulin, “Theory of generation of new frequencies by mixing of solitons and dispersive waves in optical fibers,” Phys. Rev. E 72, 016619 (2005).
[Crossref]

Yulin, A. V.

F. Biancalana, D. V. Skryabin, and A. V. Yulin, “Theory of the soliton self-frequency shift compensation by the resonant radiation in photonic crystal fibers,” Phys. Rev. E 70, 016615 (2004).
[Crossref]

Zhavoronkov, N.

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Supplementary Material (3)

» Media 1: AVI (2530 KB)     
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» Media 3: AVI (2543 KB)     

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Figures (7)

Fig. 1.
Fig. 1. Supercontinuum generation in 100 mm PCF using a 45 fs fifth-order soliton (N=5) as pump at 800 nm; (a) pump (blue) and output (red) temporal profiles; (b) pump (blue) and output (red) spectra, with dispersive wave marked by black vertical line; (c) temporal intensity; (d) spectral intensity, with dispersive wave generation region marked by white horizontal lines and dispersive wave marked by a white vertical line. Color plots are logarithmic with 40 dB range and normalized to the most intense pixel.

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Fig. 2.
Fig. 2. Animation of spectrum, temporal profile, spectrogram, and energy in the dispersive wave E DW for the simulation shown in Fig. 1 (2.5 MB). The dispersive wave energy is integrated over all spectral components above the dotted red line. A Gaussian gate function of T FWHM=80 fs was used for the spectrogram. In the upper axes, the dashed red curve shows the energy in the dispersive wave over the full propagation distance whilst the solid red curve is restricted to z values up to that of the animation frame. The still image above shows the state at z=z max=36 mm, the point of maximum temporal intensity of the field.

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Fig. 3.
Fig. 3. (a) Wavelength of dispersive wave vs soliton number; as extracted from simulations (red circles); and as predicted from soliton wavenumber using peak power (green stars), pump power (blue squares), and zero power (black diamonds). (b) Temporal intensity vs soliton number, launched pump peak power (blue squares), maximum power achieved over all (z, T) (red circles), and power that would be required to achieve the numerically observed blue-shift of the dispersive wave through the nonlinear phase-shift (magenta triangles).

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Fig. 4.
Fig. 4. Dispersive wave generation; (a) energy in dispersive wave vs z for N=4 (dashed green), N=5 (solid red) and N=6 (dotted blue); (b) Region of efficient dispersive wave generation vs N, defined by + signs (blue), point of maximum intensity (red dots) and approximate expression for soliton fission point L D,2/N (green dashed).

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Fig. 5.
Fig. 5. Nonlinear wavenumber in dispersive wave generation; (a) spectra at the start (blue dashed) and end (green solid) of the dispersive wave generation region for N=5 pump; (b) nonlinear (red solid), linear (blue dotted) and soliton (green dashed) wavenumber for N=5 pump; (c) nonlinear wavenumber for N=5 pump (red solid), N=7 (black dashed) and N=9 (green dot-dashed); (d) wavelength of dispersive waves as extracted from simulations (dashed green), predicted by nonlinear wavenumber (solid red) and predicted by soliton wavenumber (dotted blue). All nonlinear wavenumbers are calculated at the point of maximum intensity z=z max=36 mm.

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Fig. 6.
Fig. 6. (a) Animation (2.5MB) of evolution of nonlinear wavenumber for N=5 pump; temporal profile (upper axes), spectrum (lower-right y- axis, green), and linear and nonlinear wavenumbers (lower-left y-axis, red and dotted blue respectively). (b) Animation (2.5 MB) of spectrum, temporal profile, spectrogram and dispersive wave generation in supercontinuum using N=10 pump. Two black dashed lines also appear in the spectrum animation, indicating the original dispersive wave (at the end of the dispersive wave generation region at z=18 mm) and the subsequent blue-shift caused by additional nonlinear processes.

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Fig. 7.
Fig. 7. (a) Nonlinear wavenumber, and (b) wavelength of dispersive waves (left axis) and energy in dispersive waves (right axis), with full Raman response (blue dotted) and pure Kerr nonlinearity (solid red).

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Tables (1)

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Table 1. Simulation parameters

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Equations (7)

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β S ( ω ) = β ( ω S ) + β 1 ( ω S ) ( ω − ω S ) + γ ( ω S ) P S 2 ,
∑ n ≥ 2 β n ( ω S ) n ! ( ω R − ω S ) n = γ ( ω S ) P S 2 ,
∂ A ( T , z ) ∂ z = ∑ n ≥ 2 i n + 1 n ! β n ∂ n A ∂ T n + i γ ( 1 + i τ shock ∂ ∂ T ) ( A ( z , T ) ∫ − ∞ + ∞ R ( T ′ ) ∣ A ( z , T − T ′ ) ∣ 2 d T ′ )
∂ A ( ω ′ , z ) ∂ z = { i [ β NL ( ω , z ) − β ( ω 0 ) − β 1 ( ω 0 ) ω ′ ] − α NL ( ω , z ) 2 } A ( ω ′ , z ) ,
β NL ( ω , z ) = β ( ω ) + γ ( 1 + τ shock ω ′ ) Re FT [ A ( T , z ) R ( T ) * ∣ A ( T , z ) ∣ 2 ] A ( ω ′ , z ) ,
β NL ( ω ) = β ( ω ) + γ P 0 2 − N 2 β 2 ω ′ 2 ,
ω R f R + ω S ( 1 − f R ) = ω 0 ,

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