Abstract

We investigate the effects of cross-phase modulation between the solitons and dispersive waves present in a supercontinuum generated in microstructured fibers by sub-30 fs pulses. Cross-phase modulation is shown to have a crucial importance as it extends the supercontinuum towards shorter wavelengths. The experimental observations are confirmed through numerical simulations.

© 2004 Optical Society of America

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References

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  4. A. Ortigosa-Blanch, J. C. Knight, and P. S. 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]
  5. M. Lehtonen, G. Genty, M. Kaivola, and H. Ludvigsen, �??Supercontinuum generation in a highly birefringent microstructured fiber,�?? Appl. Phys. Let. 82, 2197-2199 (2003).
    [CrossRef]
  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. Proulx, J. Ménard, N. Hô, J. M. Laniel, R. Vallée, and C. Paré, �??Intensity and polarization dependences of the supercontinuum generation in birefringent and highly nonlinear microstructured fibers,�?? Opt. Express 11, 3338-3345 (2003), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-25-3338">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-25-3338</a>
    [CrossRef] [PubMed]
  8. Z. Zhu and T. G. Brown, �??Experimental studies of polarization properties of supercontinua generated in a birefringent photonic crystal fiber,�?? Opt. Express 12, 791-796 (2004), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-5-791">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-5-791</a>
    [CrossRef] [PubMed]
  9. N. Nishizawa and T. Goto, �??Experimental analysis of ultrashort pulse propagation in optical fibers around zero-dispersion region using cross-correlation frequency resolved optical gating,�?? Opt. Express 8, 328-334 (2001), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-6-328">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-6-328</a>
    [CrossRef] [PubMed]
  10. N. Nishizawa and T. Goto, �??Characteristics of pulse trapping by ultrashort soliton pulse in optical fibers across zerodispersion wavelength,�?? Opt. Express 10, 1151-1160 (2002), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-21-1151">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-21-1151</a>
    [CrossRef] [PubMed]
  11. L. Tartara, I. Cristiani, and V. Degiorgio, �??Blue light and infrared continuum generation by soliton fission in a microstructured fiber,�?? Appl. Phys. B 77, 307-311 (2003).
    [CrossRef]
  12. 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]
  13. A. V. Husakou and J. Herrmann, �??Supercontinuum generation in photonic crystal fibers made from highly nonlinear glasses,�?? Appl. Phys. B. 77, 227-234 (2003).
    [CrossRef]
  14. 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).
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  15. G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic Press, New York, 2001).
  16. P. Beaud, W. Hodel, B. Zysset, and H. P. Weber, �??Ultrashort pulse propagation, pulse breakup, and fundamental soliton formation in a single-mode optical fiber,�?? IEEE J. Quantum Electron. 23, 1938-1946 (1987).
    [CrossRef]
  17. H. A. Haus and E. P. Ippen, �??Group velocity of solitons,�?? Opt. Lett. 26, 1654-1656 (2001).
    [CrossRef]
  18. N. Nishizawa and T. Goto, �??Widely broadened super continuum generation using highly nonlinear dispersion shifted fibers and femtosecond fiber laser,�?? Jpn. J. Appl. Phys. 40, L365-L367 (2001).
    [CrossRef]
  19. I. Cristiani, R. Tediosi, L. Tartara, and V. Degiorgio, "Dispersive wave generation by solitons in microstructured optical fibers," Opt. Express 12, 124-135 (2004), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-1-124">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-1-124</a>
    [CrossRef] [PubMed]

Appl. Phys. B (1)

L. Tartara, I. Cristiani, and V. Degiorgio, �??Blue light and infrared continuum generation by soliton fission in a microstructured fiber,�?? Appl. Phys. B 77, 307-311 (2003).
[CrossRef]

Appl. Phys. B. (1)

A. V. Husakou and J. Herrmann, �??Supercontinuum generation in photonic crystal fibers made from highly nonlinear glasses,�?? Appl. Phys. B. 77, 227-234 (2003).
[CrossRef]

Appl. Phys. Let. (1)

M. Lehtonen, G. Genty, M. Kaivola, and H. Ludvigsen, �??Supercontinuum generation in a highly birefringent microstructured fiber,�?? Appl. Phys. Let. 82, 2197-2199 (2003).
[CrossRef]

IEEE J. Quantum Electron. (1)

P. Beaud, W. Hodel, B. Zysset, and H. P. Weber, �??Ultrashort pulse propagation, pulse breakup, and fundamental soliton formation in a single-mode optical fiber,�?? IEEE J. Quantum Electron. 23, 1938-1946 (1987).
[CrossRef]

J. Opt. Soc. Am. B (2)

J. Opt. Soc. Am. B. (2)

A. Ortigosa-Blanch, J. C. Knight, and P. S. 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]

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]

Jpn. J. Appl. Phys. (1)

N. Nishizawa and T. Goto, �??Widely broadened super continuum generation using highly nonlinear dispersion shifted fibers and femtosecond fiber laser,�?? Jpn. J. Appl. Phys. 40, L365-L367 (2001).
[CrossRef]

Opt. Express (6)

N. Nishizawa and T. Goto, �??Experimental analysis of ultrashort pulse propagation in optical fibers around zero-dispersion region using cross-correlation frequency resolved optical gating,�?? Opt. Express 8, 328-334 (2001), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-6-328">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-6-328</a>
[CrossRef] [PubMed]

G. Genty, M. Lehtonen, H. Ludvigsen, J. Broeng, and M. Kaivola, �??Spectral broadening of femtosecond pulses into continuum radiation in microstructured fibers,�?? Opt. Express 10, 1083-1098 (2002), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-20-1083">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-20-1083</a>
[CrossRef] [PubMed]

N. Nishizawa and T. Goto, �??Characteristics of pulse trapping by ultrashort soliton pulse in optical fibers across zerodispersion wavelength,�?? Opt. Express 10, 1151-1160 (2002), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-21-1151">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-21-1151</a>
[CrossRef] [PubMed]

A. Proulx, J. Ménard, N. Hô, J. M. Laniel, R. Vallée, and C. Paré, �??Intensity and polarization dependences of the supercontinuum generation in birefringent and highly nonlinear microstructured fibers,�?? Opt. Express 11, 3338-3345 (2003), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-25-3338">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-25-3338</a>
[CrossRef] [PubMed]

I. Cristiani, R. Tediosi, L. Tartara, and V. Degiorgio, "Dispersive wave generation by solitons in microstructured optical fibers," Opt. Express 12, 124-135 (2004), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-1-124">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-1-124</a>
[CrossRef] [PubMed]

Z. Zhu and T. G. Brown, �??Experimental studies of polarization properties of supercontinua generated in a birefringent photonic crystal fiber,�?? Opt. Express 12, 791-796 (2004), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-5-791">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-5-791</a>
[CrossRef] [PubMed]

Opt. Lett. (2)

Phys. Rev. Lett. (1)

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]

Other (1)

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic Press, New York, 2001).

Supplementary Material (1)

» Media 1: MOV (1390 KB)     

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Figures (10)

Fig. 1.
Fig. 1.

Dispersion profile of the microstructured fiber. λ ZD : zero-dispersion wavelength.

Fig. 2.
Fig. 2.

Supercontinuum spectra recorded at the output of the MF for increasing average input power. Pav : average power, XPM: cross-phase modulation, and DW: dispersive wave. λP =790 nm and Δ τ=27 fs.

Fig. 3.
Fig. 3.

Phase-matching condition for the generation of the dispersive wave (blue line). The SC spectrum is displayed as a black line. Pav =118 mW, λP =790 nm, and Δτ=27 fs. λDW denotes the wavelength of the dispersive wave calculated from Eq. (1).

Fig. 4.
Fig. 4.

Simulated SC spectrum. The parameters of the input pulse are the same as in the experiment shown in Fig. 3. For better comparison, the simulated spectrum was averaged over the same spectral window as is the resolution bandwidth of the optical spectrum analyzer applied in the experiments, i.e., 10 nm.

Fig. 5.
Fig. 5.

Simulated spectrogram of the continuum after a) 2 cm, b) 5cm, d) 15 cm and d) 50 cm of propagation along the MF. DW: dispersive wave. Pav =118 mW, λP =790 nm, and Δτ=27 fs.

Fig. 6.
Fig. 6.

Spectrogram and corresponding spectrum of the blue dispersive wave after a) 2 cm, b) 5 cm, c) 10 cm, d) 20 cm, e) 30 cm and f) 50 cm of propagation in the fiber.

Fig. 7.
Fig. 7.

Spectrogram animation of the soliton and dispersive wave. [Media 1]

Fig. 8.
Fig. 8.

Simulated spectrum of the dispersive wave for increasing propagation length using Eq. (3). a) z = 5 cm, b) z = 10 cm, and c) z = 20 cm.

Fig. 9.
Fig. 9.

Experimental spectra as a function of input power recorded at the output of 1 m of the same MF as in Fig. 2. λP =800 nm, and Δτ=140 fs. The dashed line represents the spectrum of the input pulse.

Fig. 10.
Fig. 10.

Simulated spectrogram of the continuum after 50 cm of propagation. λP =800 nm, Pav =50 mW and Δτ=140 fs. The parameters of the fiber are the same as the ones of Fig. 5.

Equations (3)

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Δβ = β ( ω P ) β ( ω DW ) = ( 1 f R ) γ ( ω P ) P P n 2 ( ω DW ω P ) n n ! β n ( ω P ) = 0 ,
δ φ XPM ( T ) = 2 γ ( ω DW ) A ( T Δ β 1 z ) 2 δz = 2 γ ( ω DW ) P S ( z ) sech ( T Δ β 1 z T S ( z ) ) 2 δz ,
B z + Δ β 1 B T + i β 2 ( ω DW ) 2 2 B T 2 = i φ XPM .

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