Abstract

Nonlinear dynamics of ultrashort optical pulses in the vicinity of the second zero-dispersion point of a small-core photonic crystal fiber is visualized and studied using cross-correlation frequency-resolved optical gating. New spectral features observed in the experiments match well with recent theoretical predictions of the generation of new frequencies via mixing of solitons and dispersive waves. Power- as well as length-dependent dynamics is obtained showing strong interaction between solitons and dispersive waves, soliton-soliton interaction, soliton stabilization against Raman self-frequency shift and Cherenkov continuum generation.

© 2004 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |

  1. W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, F. G. Omenetto, A. Efimov, A. J. Taylor, "Transformation and control of ultra-short pulses in dispersion-engineered photonic crystal fibers,�?? Nature 424, 511-515 (2003).
    [CrossRef] [PubMed]
  2. J. M. Dudley, X. Gu, L. Xu, M. Kimmel, E. Zeek, P. O�??Shea, R. Trebino, S. Coen, R. S. Windeler, "Cross-correlation frequency resolved optical gating analysis of broadband continuum generation in photonic crystal fiber: simulations and experiments,�?? Opt. Express 10, 1215-1221 (2002), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-21-1215">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-21-1215</a>.
    [CrossRef] [PubMed]
  3. 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]
  4. D. V. Skryabin, F. Luan, J. C. Knight, P. St. J. Russell, "Soliton self-frequency shift cancellation in photonic crystal fibers,�?? Science 301, 1705-1708 (2003).
    [CrossRef] [PubMed]
  5. F. Biancalana, D. V. Skryabin, 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]
  6. A. Yulin, D. V. Skryabin, P. St. J. Russell, "Four-wave mixing of linear waves and solitons in fibers with higher-order dispersion,�?? Opt. Lett. 29, 2411-2413 (2004).
    [CrossRef] [PubMed]
  7. J. M. Harbold, F. O. Ilday, F. Wise, T. A. Birks, W. J. Wadsworth, Z. Chen, "Long-wavelength continuum generation about the second dispersion zero of a tapered fiber,�?? Opt. Lett. 27, 1558-1560 (2002).
    [CrossRef]
  8. G. Genty, M. Lehtonen, H. Ludvigsen, M. Kaivola, "Enhanced bandwidth of super-continuum generated in microstructured fibers,�?? Opt. Express 12, 3471-3480 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-15-3471">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-15-3471</a>.
    [CrossRef] [PubMed]
  9. G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, San Diego, 2001).
  10. I. Cristiani, R. Tediosi, L. Tartara, 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]
  11. P. A.Wai, H. H. Chen, 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]
  12. V. I. Karpman, "Radiation by solitons due to higher-order dispersion,�?? Phys. Rev. E 47, 2073-2082 (1993).
    [CrossRef]
  13. N. Akhmediev, M. Karlsson, "Cherenkov radiation emitted by solitons in optical fibers,�?? Phys. Rev. A 51, 2602-2607 (1995).
    [CrossRef] [PubMed]
  14. S. Linden, H. Giessen, J. Kuhl, "XFROG - A new method for amplitude and phase characterization of weak ultrashort pulses,�?? Phys. Stat. Sol. (b) 206, 119-124 (1998).
    [CrossRef]
  15. P. K. A. Wai, C. R. Menyuk, Y. C. Lee, 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. P. K. A. Wai, C. R. Menyuk, H. H. Chen, Y. C. Lee, "Soliton at the zero-group-dispersion wavelength of a single-model fiber,�?? Opt. Lett. 12, 628-630 (1987).
    [CrossRef] [PubMed]
  17. G. Genty, M. Lehtonen, H. Ludvigsen, "Effect of cross-phase modulation on supercontinuum generated in microstructured fibers with sub-30 fs pulses,�?? Opt. Express 12, 4614-4624 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-19-4614">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-19-4614</a>.
    [CrossRef] [PubMed]

Nature

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, F. G. Omenetto, A. Efimov, A. J. Taylor, "Transformation and control of ultra-short pulses in dispersion-engineered photonic crystal fibers,�?? Nature 424, 511-515 (2003).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

Phys. Rev. A

N. Akhmediev, M. Karlsson, "Cherenkov radiation emitted by solitons in optical fibers,�?? Phys. Rev. A 51, 2602-2607 (1995).
[CrossRef] [PubMed]

P. A.Wai, H. H. Chen, 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]

Phys. Rev. E

V. I. Karpman, "Radiation by solitons due to higher-order dispersion,�?? Phys. Rev. E 47, 2073-2082 (1993).
[CrossRef]

F. Biancalana, D. V. Skryabin, 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]

Phys. Rev. Lett.

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]

Phys. Stat. Sol. (b)

S. Linden, H. Giessen, J. Kuhl, "XFROG - A new method for amplitude and phase characterization of weak ultrashort pulses,�?? Phys. Stat. Sol. (b) 206, 119-124 (1998).
[CrossRef]

Science

D. V. Skryabin, F. Luan, J. C. Knight, P. St. J. Russell, "Soliton self-frequency shift cancellation in photonic crystal fibers,�?? Science 301, 1705-1708 (2003).
[CrossRef] [PubMed]

Other

G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, San Diego, 2001).

Supplementary Material (6)

» Media 1: MOV (2868 KB)     
» Media 2: MOV (2592 KB)     
» Media 3: MOV (849 KB)     
» Media 4: MOV (940 KB)     
» Media 5: MOV (1988 KB)     
» Media 6: MOV (1588 KB)     

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1.
Fig. 1.

Optical properties of the PCF used in the experiments. Blue curve—attenuation, solid red curve—group velocity dispersion with 2ZD point at 1510 nm and a negative dispersion slope. For comparison the GVD of a regular telecom fiber is shown by the dashed curve. Inset—scanning electron microscope image of the PCF; the central guiding core diameter is about 1.2µm.

Fig. 2.
Fig. 2.

Experimental power-dependent X-FROG spectrograms at the output of a 130 cm-long PCF with λ 2ZD=1510 nm. The pump wavelength is 1510 nm, i.e. at the 2ZD. Formation of a soliton-“hole” pair is observed above 10 mW input power. The onset of resonant energy transfer into the spectral band between the soliton and the dispersive wave branch occurs at 41–43 mW. At 45 mW and above the soliton begins to emit Cherenkov radiation at longer wavelengths. The vertical dashed line shows the 2ZD point of the fiber, separating regions of normal and anomalous dispersion. The color scale is logarithmic with the intensity of the SF signal. SF wavelength is related to the fundamental signal and reference pulse wavelengths as λSF =λsigλref /(λsig +λref ). The reference pulse wavelength is equal to the input pulse wavelength, 1510 nm in this case. QuickTime movie, 2.8 MB.

Fig. 3.
Fig. 3.

Modelling of Eq. (2) for the experimental conditions of Fig. 2. X-FROG traces are computed numerically from the complex field amplitude output of Eq. (2) for the parameters of the experiment. The running numbers indicate average input power. The color scale is logarithmic. QuickTime movie 2.6 Mb

Fig. 4.
Fig. 4.

Illustration of the wavevector matching condition (1) for J=1. The full (dashed) lines show the right hand-side (left hand-side) of Eq. (1) as a function of wavelength. Crossings of these lines give the of resonances. (a) illustrates the case when the group velocities of the soliton and the CW-pump are matched, so that the resonance wavelength coincides with the wavelength of theCW-pump and no new frequency is efficiently excited; (b) shows the case when the group velocities of the soliton and the CW-pump become different due to the soliton self-frequency shift. In this case the most efficiently excited and experimentally observed resonance wavelength is located between the soliton and the CW-pump. The excitation efficiency of the resonance marked by a circle in (b) and other resonances, which can be found for J=±1, is not sufficient to be observed under our experimental conditions. The thick grey arrow in (b) indicates the direction of the energy flow observed in numerical modelling.

Fig. 5.
Fig. 5.

Experimental length-dependent X-FROG spectrograms for pumping conditions similar to Fig. 2: The pump wavelength is 1510 nm and the input power is held constant at 55 mW. QuickTime movie, 0.9 MB

Fig. 6.
Fig. 6.

Modelling results of Eq. (2) corresponding to the experimental measurements in Fig. 5. The running numbers indicate propagation distance inside the fiber. QuickTime movie 960 Kb

Fig. 7.
Fig. 7.

Experimental power-dependent X-FROG spectrograms at the output of a 130 cm-long PCF with λ 2ZD =1510nm. The fiber is pumped at 1430 nm, i.e. on the anomalous dispersion side. At lower input powers formation of the primary strong soliton and its Cherenkov radiation are observed. Subsequently, a second weaker soliton is formed which interacts with the continuum emitted by the first soliton. The scattering of the Cherenkov radiation by the second soliton leads to energy transfer into a spectral band located between the solitons and the Cherenkov radiation band. QuickTime movie, 2 MB.

Fig. 8.
Fig. 8.

Numerical X-FROG traces for the power-dependent case of pumping the PCF in the anomalous dispersion region at 1430 nm; the other parameters correspond to those in Fig. 7. The running numbers indicate average input power. QuickTime movie 1.6 Mb

Equations (4)

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

J ( β CW k sol CW ) + k sol signal = β signal , J = 0 , ± 1 .
z A = i D ( i t ) A + i A + R ( t ' ) A ( t t ' , z ) 2 d t ' .
D ( δ ) = { β ( ω 0 + δ τ ) β ( ω 0 ) β 1 ( ω 0 ) δ τ } L gvd ,
R ( t ) = [ 1 θ ] Δ ( t ) + θ τ 1 2 + τ 2 2 τ 1 τ 2 2 Θ ( t ) e t τ 2 sin t τ 1

Metrics