Abstract

We present a numerical study of the polarization properties of the broadband supercontinuum (SC) generated in birefringent photonic crystal fibers (PCFs). The simulations are based on generalized coupled nonlinear Schrödinger equations with quantum noise taken into account. The simulations illustrate the complicated polarization behavior in the SC spectra and show that the pulse-to-pulse polarization state of SC spectra fluctuates because of vector modulation instability. We investigate the polarization stability and uniformity of SC spectra under several simulation conditions and discuss generation of the SC in birefringent PCFs for applications with various polarization requirements.

© 2004 Optical Society of America

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  1. J. C. Knight, T. A. Birks, P. St. J. Russell, and D. M. Atkin, “All-silica single mode optical fiber with photonic crystal cladding,” Opt. Lett. 21, 1547–1549 (1996).
    [CrossRef] [PubMed]
  2. T. M. Monro, D. J. Richardson, and P. J. Bennett, “Developing holey fibres for evanescent field devices,” Electron. Lett. 35, 1188–1189 (1999).
    [CrossRef]
  3. 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]
  4. N. G. R. Broderick, T. M. Monro, P. J. Bennett, and D. J. Richardson, “Nonlinearity in holey optical fibers: measurement and future opportunities,” Opt. Lett. 24, 1395–1397 (1999).
    [CrossRef]
  5. T. P. Hansen, J. Broeng, S. E. B. Libori, E. Knudsen, A. Bjarklev, J. R. Jensen, and H. Simonsen, “Highly birefringent index-guiding photonic crystal fibers,” IEEE Photon. Technol. Lett. 13, 588–590 (2001).
    [CrossRef]
  6. 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 Photon. Technol. Lett. 12, 807–809 (2000).
    [CrossRef]
  7. A. Ferrando, E. Silvestre, J. J. Miret, and P. Andres, “Nearly zero ultraflattened dispersion in photonic crystal fibers,” Opt. Lett. 25, 790–792 (2000).
    [CrossRef]
  8. J. K. Ranka, R. S. Windeler, and A. J. Stentz, “Visible continuum generation in air–silica microstructure optical fibers with anomalous dispersion at 800 nm,” Opt. Lett. 25, 25–27 (2000).
    [CrossRef]
  9. T. A. Birks, W. J. Wadsworth, and P. St. J. Russell, “Supercontinuum generation in tapered fibers,” Opt. Lett. 25, 1415–1417 (2000).
    [CrossRef]
  10. 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]
  11. R. Holzwarth, T. Udem, T. W. Hänsch, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “Optical frequency synthesizer for precision spectroscopy,” Phys. Rev. Lett. 85, 2264–2267 (2000).
    [CrossRef] [PubMed]
  12. 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]
  13. S. Coen, A. H. L. Chan, R. Leonhardt, J. D. Harvey, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “White-light supercontinuum generation with 60-ps pump pulses in a photonic crystal fiber,” Opt. Lett. 26, 1356–1358 (2001).
    [CrossRef]
  14. A. L. Gaeta, “Nonlinear propagation and continuum generation in microstructured optical fibers,” Opt. Lett. 27, 924–926 (2002).
    [CrossRef]
  15. A. Apolonski, B. Povazay, A. Unterhuber, W. Drexler, W. J. Wadsworth, J. C. Knight, and P. St. J. Russell, “Spectral shaping of supercontinuum in a cobweb photonic-crystal fiber with sub-20-fs pulses,” J. Opt. Soc. Am. B 19, 2165–2170 (2002).
    [CrossRef]
  16. S. Coen, A. H. L. 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]
  17. G. Genty, M. Lehtonen, H. Ludvigsen, J. Broeng, and M. Kaivola, “Spectral broadening of femtosecond pulses intocontinuum radiation in microstructured fibers,” Opt. Express 10, 1083–1098 (2002), http://www.opticsexpress.org.
    [CrossRef] [PubMed]
  18. 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]
  19. 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]
  20. W. J. Wadsworth, A. Ortigosa-Blanch, J. C. Knight, T. A. Birks, T. P. M. Man, and P. St. J. Russell, “Supercontinuum generation in photonic crystal fibers and optical fiber tapers: a novel light source,” J. Opt. Soc. Am. B 19, 2148–2155 (2002).
    [CrossRef]
  21. 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.
    [CrossRef] [PubMed]
  22. 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 gen-eration by fission of higher-order solitons in photonic fibers,” Phys. Rev. Lett. 88, 173901 (2002).
    [CrossRef]
  23. 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]
  24. J. M. Dudley and S. Coen, “Numerical simulations and coherence properties of supercontinuum generation in photonic crystal and tapered optical fibers,” IEEE J. Sel. Top. Quantum Electron. 8, 651–659 (2002).
    [CrossRef]
  25. J. M. Dudley and S. Coen, “Coherence properties of supercontinuum spectra generated in photonic crystal and tapered optical fibers,” Opt. Lett. 27, 1180–1182 (2002).
    [CrossRef]
  26. M. Lehtonen, G. Genty, H. Ludvigsen, and M. Kaivola, “Supercontinuum generation in a highly birefringent microstructured fiber,” Appl. Phys. Lett. 82, 2197–2199 (2003).
    [CrossRef]
  27. G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, San Diego, Calif., 2002).
  28. K. J. Blow and D. Wood, “Theoretical description of transient stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. 25, 2665–2673 (1989).
    [CrossRef]

2003

M. Lehtonen, G. Genty, H. Ludvigsen, and M. Kaivola, “Supercontinuum generation in a highly birefringent microstructured fiber,” Appl. Phys. Lett. 82, 2197–2199 (2003).
[CrossRef]

2002

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

A. Apolonski, B. Povazay, A. Unterhuber, W. Drexler, W. J. Wadsworth, J. C. Knight, and P. St. J. Russell, “Spectral shaping of supercontinuum in a cobweb photonic-crystal fiber with sub-20-fs pulses,” J. Opt. Soc. Am. B 19, 2165–2170 (2002).
[CrossRef]

S. Coen, A. H. L. 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]

G. Genty, M. Lehtonen, H. Ludvigsen, J. Broeng, and M. Kaivola, “Spectral broadening of femtosecond pulses intocontinuum radiation in microstructured fibers,” Opt. Express 10, 1083–1098 (2002), http://www.opticsexpress.org.
[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. 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]

W. J. Wadsworth, A. Ortigosa-Blanch, J. C. Knight, T. A. Birks, T. P. M. Man, and P. St. J. Russell, “Supercontinuum generation in photonic crystal fibers and optical fiber tapers: a novel light source,” J. Opt. Soc. Am. B 19, 2148–2155 (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.
[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 gen-eration by fission of higher-order solitons in photonic fibers,” Phys. Rev. Lett. 88, 173901 (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]

J. M. Dudley and S. Coen, “Numerical simulations and coherence properties of supercontinuum generation in photonic crystal and tapered optical fibers,” IEEE J. Sel. Top. Quantum Electron. 8, 651–659 (2002).
[CrossRef]

J. M. Dudley and S. Coen, “Coherence properties of supercontinuum spectra generated in photonic crystal and tapered optical fibers,” Opt. Lett. 27, 1180–1182 (2002).
[CrossRef]

2001

T. P. Hansen, J. Broeng, S. E. B. Libori, E. Knudsen, A. Bjarklev, J. R. Jensen, and H. Simonsen, “Highly birefringent index-guiding photonic crystal fibers,” IEEE Photon. Technol. Lett. 13, 588–590 (2001).
[CrossRef]

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. 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]

S. Coen, A. H. L. Chan, R. Leonhardt, J. D. Harvey, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “White-light supercontinuum generation with 60-ps pump pulses in a photonic crystal fiber,” Opt. Lett. 26, 1356–1358 (2001).
[CrossRef]

2000

R. Holzwarth, T. Udem, T. W. Hänsch, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “Optical frequency synthesizer for precision spectroscopy,” Phys. Rev. Lett. 85, 2264–2267 (2000).
[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 Photon. Technol. Lett. 12, 807–809 (2000).
[CrossRef]

A. Ferrando, E. Silvestre, J. J. Miret, and P. Andres, “Nearly zero ultraflattened dispersion in photonic crystal fibers,” Opt. Lett. 25, 790–792 (2000).
[CrossRef]

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

T. A. Birks, W. J. Wadsworth, and P. St. J. Russell, “Supercontinuum generation in tapered fibers,” Opt. Lett. 25, 1415–1417 (2000).
[CrossRef]

1999

T. M. Monro, D. J. Richardson, and P. J. Bennett, “Developing holey fibres for evanescent field devices,” Electron. Lett. 35, 1188–1189 (1999).
[CrossRef]

N. G. R. Broderick, T. M. Monro, P. J. Bennett, and D. J. Richardson, “Nonlinearity in holey optical fibers: measurement and future opportunities,” Opt. Lett. 24, 1395–1397 (1999).
[CrossRef]

1997

1996

1989

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

Andres, P.

Apolonski, A.

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 Photon. Technol. Lett. 12, 807–809 (2000).
[CrossRef]

Atkin, D. M.

Bennett, P. J.

T. M. Monro, D. J. Richardson, and P. J. Bennett, “Developing holey fibres for evanescent field devices,” Electron. Lett. 35, 1188–1189 (1999).
[CrossRef]

N. G. R. Broderick, T. M. Monro, P. J. Bennett, and D. J. Richardson, “Nonlinearity in holey optical fibers: measurement and future opportunities,” Opt. Lett. 24, 1395–1397 (1999).
[CrossRef]

Birks, T. A.

Bjarklev, A.

T. P. Hansen, J. Broeng, S. E. B. Libori, E. Knudsen, A. Bjarklev, J. R. Jensen, and H. Simonsen, “Highly birefringent index-guiding photonic crystal fibers,” IEEE Photon. Technol. Lett. 13, 588–590 (2001).
[CrossRef]

Blow, K. J.

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

Broderick, N. G. R.

Broeng, J.

G. Genty, M. Lehtonen, H. Ludvigsen, J. Broeng, and M. Kaivola, “Spectral broadening of femtosecond pulses intocontinuum radiation in microstructured fibers,” Opt. Express 10, 1083–1098 (2002), http://www.opticsexpress.org.
[CrossRef] [PubMed]

T. P. Hansen, J. Broeng, S. E. B. Libori, E. Knudsen, A. Bjarklev, J. R. Jensen, and H. Simonsen, “Highly birefringent index-guiding photonic crystal fibers,” IEEE Photon. Technol. Lett. 13, 588–590 (2001).
[CrossRef]

Chan, A. H. L.

Chau, A. H. L.

Chudoba, C.

Coen, S.

Drexler, W.

Dudley, J. M.

Eggleton, B. J.

Ferrando, A.

Fujimoto, J. G.

Gaeta, A. L.

Genty, G.

M. Lehtonen, G. Genty, H. Ludvigsen, and M. Kaivola, “Supercontinuum generation in a highly birefringent microstructured fiber,” Appl. Phys. Lett. 82, 2197–2199 (2003).
[CrossRef]

G. Genty, M. Lehtonen, H. Ludvigsen, J. Broeng, and M. Kaivola, “Spectral broadening of femtosecond pulses intocontinuum radiation in microstructured fibers,” Opt. Express 10, 1083–1098 (2002), http://www.opticsexpress.org.
[CrossRef] [PubMed]

Ghanta, R. K.

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 gen-eration by fission of higher-order solitons in photonic fibers,” Phys. Rev. Lett. 88, 173901 (2002).
[CrossRef]

Grossard, N.

Hänsch, T. W.

R. Holzwarth, T. Udem, T. W. Hänsch, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “Optical frequency synthesizer for precision spectroscopy,” Phys. Rev. Lett. 85, 2264–2267 (2000).
[CrossRef] [PubMed]

Hansen, T. P.

T. P. Hansen, J. Broeng, S. E. B. Libori, E. Knudsen, A. Bjarklev, J. R. Jensen, and H. Simonsen, “Highly birefringent index-guiding photonic crystal fibers,” IEEE Photon. Technol. Lett. 13, 588–590 (2001).
[CrossRef]

Hartl, I.

Harvey, J. D.

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 gen-eration by fission of higher-order solitons in photonic fibers,” Phys. Rev. Lett. 88, 173901 (2002).
[CrossRef]

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 (2001).
[CrossRef] [PubMed]

Holzwarth, R.

R. Holzwarth, T. Udem, T. W. Hänsch, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “Optical frequency synthesizer for precision spectroscopy,” Phys. Rev. Lett. 85, 2264–2267 (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 gen-eration by fission of higher-order solitons in photonic fibers,” Phys. Rev. Lett. 88, 173901 (2002).
[CrossRef]

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 (2001).
[CrossRef] [PubMed]

Jensen, J. R.

T. P. Hansen, J. Broeng, S. E. B. Libori, E. Knudsen, A. Bjarklev, J. R. Jensen, and H. Simonsen, “Highly birefringent index-guiding photonic crystal fibers,” IEEE Photon. Technol. Lett. 13, 588–590 (2001).
[CrossRef]

Kaivola, M.

M. Lehtonen, G. Genty, H. Ludvigsen, and M. Kaivola, “Supercontinuum generation in a highly birefringent microstructured fiber,” Appl. Phys. Lett. 82, 2197–2199 (2003).
[CrossRef]

G. Genty, M. Lehtonen, H. Ludvigsen, J. Broeng, and M. Kaivola, “Spectral broadening of femtosecond pulses intocontinuum radiation in microstructured fibers,” Opt. Express 10, 1083–1098 (2002), http://www.opticsexpress.org.
[CrossRef] [PubMed]

Knight, J. C.

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]

W. J. Wadsworth, A. Ortigosa-Blanch, J. C. Knight, T. A. Birks, T. P. M. Man, and P. St. J. Russell, “Supercontinuum generation in photonic crystal fibers and optical fiber tapers: a novel light source,” J. Opt. Soc. Am. B 19, 2148–2155 (2002).
[CrossRef]

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 gen-eration by fission of higher-order solitons in photonic fibers,” Phys. Rev. Lett. 88, 173901 (2002).
[CrossRef]

S. Coen, A. H. L. 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]

A. Apolonski, B. Povazay, A. Unterhuber, W. Drexler, W. J. Wadsworth, J. C. Knight, and P. St. J. Russell, “Spectral shaping of supercontinuum in a cobweb photonic-crystal fiber with sub-20-fs pulses,” J. Opt. Soc. Am. B 19, 2165–2170 (2002).
[CrossRef]

S. Coen, A. H. L. Chan, R. Leonhardt, J. D. Harvey, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “White-light supercontinuum generation with 60-ps pump pulses in a photonic crystal fiber,” Opt. Lett. 26, 1356–1358 (2001).
[CrossRef]

R. Holzwarth, T. Udem, T. W. Hänsch, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “Optical frequency synthesizer for precision spectroscopy,” Phys. Rev. Lett. 85, 2264–2267 (2000).
[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 Photon. Technol. Lett. 12, 807–809 (2000).
[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]

J. C. Knight, T. A. Birks, P. St. J. Russell, and D. M. Atkin, “All-silica single mode optical fiber with photonic crystal cladding,” Opt. Lett. 21, 1547–1549 (1996).
[CrossRef] [PubMed]

Knudsen, E.

T. P. Hansen, J. Broeng, S. E. B. Libori, E. Knudsen, A. Bjarklev, J. R. Jensen, and H. Simonsen, “Highly birefringent index-guiding photonic crystal fibers,” IEEE Photon. Technol. Lett. 13, 588–590 (2001).
[CrossRef]

Ko, T. H.

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 gen-eration by fission of higher-order solitons in photonic fibers,” Phys. Rev. Lett. 88, 173901 (2002).
[CrossRef]

Lehtonen, M.

M. Lehtonen, G. Genty, H. Ludvigsen, and M. Kaivola, “Supercontinuum generation in a highly birefringent microstructured fiber,” Appl. Phys. Lett. 82, 2197–2199 (2003).
[CrossRef]

G. Genty, M. Lehtonen, H. Ludvigsen, J. Broeng, and M. Kaivola, “Spectral broadening of femtosecond pulses intocontinuum radiation in microstructured fibers,” Opt. Express 10, 1083–1098 (2002), http://www.opticsexpress.org.
[CrossRef] [PubMed]

Leonhardt, R.

Li, X. D.

Libori, S. E. B.

T. P. Hansen, J. Broeng, S. E. B. Libori, E. Knudsen, A. Bjarklev, J. R. Jensen, and H. Simonsen, “Highly birefringent index-guiding photonic crystal fibers,” IEEE Photon. Technol. Lett. 13, 588–590 (2001).
[CrossRef]

Ludvigsen, H.

M. Lehtonen, G. Genty, H. Ludvigsen, and M. Kaivola, “Supercontinuum generation in a highly birefringent microstructured fiber,” Appl. Phys. Lett. 82, 2197–2199 (2003).
[CrossRef]

G. Genty, M. Lehtonen, H. Ludvigsen, J. Broeng, and M. Kaivola, “Spectral broadening of femtosecond pulses intocontinuum radiation in microstructured fibers,” Opt. Express 10, 1083–1098 (2002), http://www.opticsexpress.org.
[CrossRef] [PubMed]

Maillotte, H.

Man, T. P. M.

Miret, J. J.

Monro, T. M.

N. G. R. Broderick, T. M. Monro, P. J. Bennett, and D. J. Richardson, “Nonlinearity in holey optical fibers: measurement and future opportunities,” Opt. Lett. 24, 1395–1397 (1999).
[CrossRef]

T. M. Monro, D. J. Richardson, and P. J. Bennett, “Developing holey fibres for evanescent field devices,” Electron. Lett. 35, 1188–1189 (1999).
[CrossRef]

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 gen-eration by fission of higher-order solitons in photonic fibers,” Phys. Rev. Lett. 88, 173901 (2002).
[CrossRef]

Ortigosa-Blanch, A.

Povazay, B.

Provino, L.

Ralph, S. E.

Ranka, J. K.

Richardson, D. J.

T. M. Monro, D. J. Richardson, and P. J. Bennett, “Developing holey fibres for evanescent field devices,” Electron. Lett. 35, 1188–1189 (1999).
[CrossRef]

N. G. R. Broderick, T. M. Monro, P. J. Bennett, and D. J. Richardson, “Nonlinearity in holey optical fibers: measurement and future opportunities,” Opt. Lett. 24, 1395–1397 (1999).
[CrossRef]

Russell, P. St. J.

A. Apolonski, B. Povazay, A. Unterhuber, W. Drexler, W. J. Wadsworth, J. C. Knight, and P. St. J. Russell, “Spectral shaping of supercontinuum in a cobweb photonic-crystal fiber with sub-20-fs pulses,” J. Opt. Soc. Am. B 19, 2165–2170 (2002).
[CrossRef]

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 gen-eration by fission of higher-order solitons in photonic fibers,” Phys. Rev. Lett. 88, 173901 (2002).
[CrossRef]

S. Coen, A. H. L. 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]

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]

W. J. Wadsworth, A. Ortigosa-Blanch, J. C. Knight, T. A. Birks, T. P. M. Man, and P. St. J. Russell, “Supercontinuum generation in photonic crystal fibers and optical fiber tapers: a novel light source,” J. Opt. Soc. Am. B 19, 2148–2155 (2002).
[CrossRef]

S. Coen, A. H. L. Chan, R. Leonhardt, J. D. Harvey, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “White-light supercontinuum generation with 60-ps pump pulses in a photonic crystal fiber,” Opt. Lett. 26, 1356–1358 (2001).
[CrossRef]

T. A. Birks, W. J. Wadsworth, and P. St. J. Russell, “Supercontinuum generation in tapered fibers,” Opt. Lett. 25, 1415–1417 (2000).
[CrossRef]

R. Holzwarth, T. Udem, T. W. Hänsch, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “Optical frequency synthesizer for precision spectroscopy,” Phys. Rev. Lett. 85, 2264–2267 (2000).
[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 Photon. Technol. Lett. 12, 807–809 (2000).
[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]

J. C. Knight, T. A. Birks, P. St. J. Russell, and D. M. Atkin, “All-silica single mode optical fiber with photonic crystal cladding,” Opt. Lett. 21, 1547–1549 (1996).
[CrossRef] [PubMed]

Silvestre, E.

Simonsen, H.

T. P. Hansen, J. Broeng, S. E. B. Libori, E. Knudsen, A. Bjarklev, J. R. Jensen, and H. Simonsen, “Highly birefringent index-guiding photonic crystal fibers,” IEEE Photon. Technol. Lett. 13, 588–590 (2001).
[CrossRef]

Stentz, A. J.

Udem, T.

R. Holzwarth, T. Udem, T. W. Hänsch, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “Optical frequency synthesizer for precision spectroscopy,” Phys. Rev. Lett. 85, 2264–2267 (2000).
[CrossRef] [PubMed]

Unterhuber, A.

Wadsworth, W. J.

A. Apolonski, B. Povazay, A. Unterhuber, W. Drexler, W. J. Wadsworth, J. C. Knight, and P. St. J. Russell, “Spectral shaping of supercontinuum in a cobweb photonic-crystal fiber with sub-20-fs pulses,” J. Opt. Soc. Am. B 19, 2165–2170 (2002).
[CrossRef]

S. Coen, A. H. L. 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]

W. J. Wadsworth, A. Ortigosa-Blanch, J. C. Knight, T. A. Birks, T. P. M. Man, and P. St. J. Russell, “Supercontinuum generation in photonic crystal fibers and optical fiber tapers: a novel light source,” J. Opt. Soc. Am. B 19, 2148–2155 (2002).
[CrossRef]

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 gen-eration by fission of higher-order solitons in photonic fibers,” Phys. Rev. Lett. 88, 173901 (2002).
[CrossRef]

S. Coen, A. H. L. Chan, R. Leonhardt, J. D. Harvey, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “White-light supercontinuum generation with 60-ps pump pulses in a photonic crystal fiber,” Opt. Lett. 26, 1356–1358 (2001).
[CrossRef]

R. Holzwarth, T. Udem, T. W. Hänsch, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “Optical frequency synthesizer for precision spectroscopy,” Phys. Rev. Lett. 85, 2264–2267 (2000).
[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 Photon. Technol. Lett. 12, 807–809 (2000).
[CrossRef]

T. A. Birks, W. J. Wadsworth, and P. St. J. Russell, “Supercontinuum generation in tapered fibers,” Opt. Lett. 25, 1415–1417 (2000).
[CrossRef]

Washburn, B. R.

Windeler, R. S.

Wood, D.

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

Zhavoronkov, N.

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 gen-eration by fission of higher-order solitons in photonic fibers,” Phys. Rev. Lett. 88, 173901 (2002).
[CrossRef]

Appl. Phys. Lett.

M. Lehtonen, G. Genty, H. Ludvigsen, and M. Kaivola, “Supercontinuum generation in a highly birefringent microstructured fiber,” Appl. Phys. Lett. 82, 2197–2199 (2003).
[CrossRef]

Electron. Lett.

T. M. Monro, D. J. Richardson, and P. J. Bennett, “Developing holey fibres for evanescent field devices,” Electron. Lett. 35, 1188–1189 (1999).
[CrossRef]

IEEE J. Quantum Electron.

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

IEEE J. Sel. Top. Quantum Electron.

J. M. Dudley and S. Coen, “Numerical simulations and coherence properties of supercontinuum generation in photonic crystal and tapered optical fibers,” IEEE J. Sel. Top. Quantum Electron. 8, 651–659 (2002).
[CrossRef]

IEEE Photon. Technol. Lett.

T. P. Hansen, J. Broeng, S. E. B. Libori, E. Knudsen, A. Bjarklev, J. R. Jensen, and H. Simonsen, “Highly birefringent index-guiding photonic crystal fibers,” IEEE Photon. Technol. Lett. 13, 588–590 (2001).
[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 Photon. Technol. Lett. 12, 807–809 (2000).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Express

Opt. Lett.

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]

N. G. R. Broderick, T. M. Monro, P. J. Bennett, and D. J. Richardson, “Nonlinearity in holey optical fibers: measurement and future opportunities,” Opt. Lett. 24, 1395–1397 (1999).
[CrossRef]

S. Coen, A. H. L. Chan, R. Leonhardt, J. D. Harvey, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “White-light supercontinuum generation with 60-ps pump pulses in a photonic crystal fiber,” Opt. Lett. 26, 1356–1358 (2001).
[CrossRef]

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

A. Ferrando, E. Silvestre, J. J. Miret, and P. Andres, “Nearly zero ultraflattened dispersion in photonic crystal fibers,” Opt. Lett. 25, 790–792 (2000).
[CrossRef]

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

T. A. Birks, W. J. Wadsworth, and P. St. J. Russell, “Supercontinuum generation in tapered fibers,” Opt. Lett. 25, 1415–1417 (2000).
[CrossRef]

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]

J. C. Knight, T. A. Birks, P. St. J. Russell, and D. M. Atkin, “All-silica single mode optical fiber with photonic crystal cladding,” Opt. Lett. 21, 1547–1549 (1996).
[CrossRef] [PubMed]

J. M. Dudley and S. Coen, “Coherence properties of supercontinuum spectra generated in photonic crystal and tapered optical fibers,” Opt. Lett. 27, 1180–1182 (2002).
[CrossRef]

Phys. Rev. Lett.

R. Holzwarth, T. Udem, T. W. Hänsch, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “Optical frequency synthesizer for precision spectroscopy,” Phys. Rev. Lett. 85, 2264–2267 (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 (2001).
[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 gen-eration by fission of higher-order solitons in photonic fibers,” Phys. Rev. Lett. 88, 173901 (2002).
[CrossRef]

Other

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, San Diego, Calif., 2002).

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Figures (10)

Fig. 1
Fig. 1

Dispersion and effective mode area of the fiber considered in this paper. The parameters were obtained from a circular silica rod of 2.2-µm diameter.

Fig. 2
Fig. 2

Evolution of a SC along the propagation distance: (a) temporal intensity, (b) spectrum, (c) ellipticity. B=1×10-5, λ0=800 nm, P0=10 kW, TFWHM=100 fs, θ=45°. Solid (dashed) curves, the x- (y-) polarization component.

Fig. 3
Fig. 3

SC obtained with input pulses polarized at different angles with respect to the x axis: (a) temporal intensity, (b) spectrum, (c) ellipticity. Fiber length, L=5 cm; other parameters are the same as in Fig. 2. Solid (dashed) curves, x- (y-) polarization component.

Fig. 4
Fig. 4

Gain spectra of VMI at input powers of (a) 10 and (b) 1.5 kW for a cw beam polarized along the fast axis (both solid and dashed curves) and the slow axis (solid curves only) of a birefringent PCF. B=1×10-5, λ0=800 nm.

Fig. 5
Fig. 5

Evolution of a SC along the propagation distance: (a) mean temporal intensity, (b) mean spectrum, (c) polarization correlation, (d) mean ellipticity. B=1×10-5, λ0=800 nm, TFWHM=100 fs, P0=10 kW, θ=45°. Solid (dashed) curves, x- (y-) polarization component.

Fig. 6
Fig. 6

SC obtained with input pulses of different peak powers: (a) mean spectrum, (b) polarization correlation, (c) mean ellipticity. B=1×10-5, L=10 cm, λ0=800 nm, TFWHM=100 fs, θ=45°. Solid (dashed) curves, x- (y-) polarization component.

Fig. 7
Fig. 7

SC obtained with input pulses of different widths TFWHM: (a) mean spectrum, (b) polarization correlation, (c) mean ellipticity. B=1×10-5, L=5 cm, λ0=800 nm, P0=10 kW, θ=45°. Solid (dashed) curves, x- (y-) polarization component.

Fig. 8
Fig. 8

SC obtained with input pulses of different center wavelengths: (a) mean spectrum, (b) polarization correlation, (c) mean ellipticity. B=1×10-5, L=5 cm, P0=10 kW, TFWHM=100 fs, θ=45°. Solid (dashed) curves, x- (y-) polarization component.

Fig. 9
Fig. 9

Dependence of a SC on input polarization orientation: (a) mean spectrum, (b) polarization correlation, (c) mean ellipticity. B=1×10-5, L=5 cm, λ0=800 nm, P0=10 kW, TFWHM=100 fs. Solid (dashed) curves, x- (y-) polarization component.

Fig. 10
Fig. 10

SC generated in PCFs with different values of birefringence: (a) mean spectrum, (b) polarization correlation, (c) mean ellipticity. The input is polarized at 2° to the x axis. Other parameters are same as for Fig. 9. Solid (dashed) curves, x- (y-) polarization component.

Equations (4)

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ujz=i Δβ02-Δβ12 τu3-j-iβ22! 2τ2+i β33! 3τ3-β44! 4τ4+uj-α2uj+iγ1+iω0 τ×(1-fR)23|uj|2+43|u3-j|2uj+fRuj-τdτhR(τ-τ)[|uj(τ)|2+|u3-j(τ)|2](j=1, 2),
hR(τ)=τ12+τ22τ1τ22 exp(-τ/τ2)sin(τ/τ1),
ep=2 Im[A˜x*(λ)A˜y(λ)]|A˜x(λ)|2+|A˜y(λ)|2.
ρ(λ)=|A˜x(λ)A˜y*(λ)|[|A˜x(λ)|2|A˜y(λ)|2]1/2,

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