Abstract

Supercontinuum generation with femtosecond pulses in photonic crystal fibers with two zero-dispersion wavelengths (ZDWs) is investigated numerically. The role of the higher ZDW is examined for 5 fiber designs with a nearly constant lower ZDW. It is found that the resulting spectrum is mainly determined by self-phase modulation in the first few mm of fiber, followed by soliton self-frequency shift and amplification of dispersive waves. It is demonstrated how femtosecond soliton pulses can be generated with any desired center wavelength in the 1020–1200 nm range by adjusting the fiber length. Further, the generation of a bright-bright soliton-pair from an initial single red-shifted soliton is found. The soliton-pair has one color in the anomalous dispersion region and the other color in the normal dispersion region, which has not previously been described for bright-bright soliton-pairs.

© 2005 Optical Society of America

Full Article  |  PDF Article

Corrections

Michael H. Frosz, Peter Falk, and Ole Bang, "The role of the second zero-dispersion wavelength in generation of supercontinua and bright-bright soliton-pairs across the zero-dispersion wavelength: erratum," Opt. Express 15, 5262-5263 (2007)
https://www.osapublishing.org/oe/abstract.cfm?uri=oe-15-8-5262

References

  • View by:
  • |

  1. G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic Press, San Diego, CA, USA, 2001).
  2. 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]
  3. N. I. Nikolov, T. Sørensen, O. Bang, and A. Bjarklev, �??Improving efficiency of supercontinuum generation in photonic crystal fibers by direct degenerate four-wave mixing,�?? J. Opt. Soc. Am. B 20, 2329�??2337 (2003).
    [CrossRef]
  4. N. Akhmediev and M. Karlsson, �??Cherenkov radiation emitted by solitons in optical fibers,�?? Phys. Rev. A 51, 2602�??2607 (1995).
    [CrossRef] [PubMed]
  5. G. Genty, M. Lehtonen, H. Ludvigsen, and M. Kaivola, �??Enhanced bandwidth of supercontinuum 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]
  6. A. Efimov, A. J. Taylor, F. G. Omenetto, A. V. Yulin, N. Y. Joly, F. Biancalana, D. V. Skryabin, J. C. Knight, and P. S. J. Russell, �??Time-spectrally-resolved ultrafast nonlinear dynamics in small-core photonic crystal fibers: Experiment and modelling,�?? Opt. Express 12, 6498�??6507 (2004).
    [CrossRef] [PubMed]
  7. K. M. Hilligsøe, T. V. Andersen, H. N. Paulsen, C. K. Nielsen, K. Mølmer, S. Keiding, R. Kristiansen, K. P. Hansen, and J. J. Larsen, �??Supercontinuum generation in a photonic crystal fiber with two zero dispersion wavelengths,�?? Opt. Express 12, 1045�??1054 (2004). <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-6-1045.">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-6-1045.</a>
    [CrossRef] [PubMed]
  8. D. V. Skryabin, F. Luan, J. C. Knight, and P. S. J. Russel, �??Soliton self-frequency shift cancellation in photonic crystal fibers,�?? Science 301, 1705�??1708 (2003).
    [CrossRef] [PubMed]
  9. 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, 016 615 (2004). <a href="http://dx.doi.org/10.1103/PhysRevE.70.016615">http://dx.doi.org/10.1103/PhysRevE.70.016615.</a>
    [CrossRef]
  10. J. M. Schmitt, S. H. Xiang, and K. M. Yung, �??Differential absorption imaging with optical coherence tomography,�?? J. Opt. Soc. Am. A 15, 2288�??2296 (1998).
    [CrossRef]
  11. M. H. Frosz, O. Bang, A. Bjarklev, P. E. Andersen, and J. Broeng, �??Supercontinuum Generation in Photonic Crystal Fibers: The Role of the Second Zero Dispersion Wavelength,�?? presented May 25th 2005, CWC1, at CLEO/QELS 2005, Baltimore, Maryland, USA, 22-27 May 2005.
  12. M. H. Frosz, P. Falk, L. T. Pedersen, O. Bang, and A. Bjarklev, �??Supercontinuum generation in untapered and tapered photonic crystal fibers with two zero dispersion wavelengths,�?? talk #5733-36 presented at SPIE Photonics West, San Jose, California, USA, 22-27 January 2005.
  13. S.G. Johnson and J.D. Joannopoulos, �??Block-Iterative Frequency-Domain Methods for Maxwell�??s Equations in a Planewave Basis,�?? Opt. Express 8, 173�??190 (2001). <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-3-173.">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-3-173</a>
    [CrossRef] [PubMed]
  14. 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]
  15. J. Lægsgaard, N. A. Mortensen, and A. Bjarklev, �??Mode areas and field-energy distribution in honeycomb photonic bandgap fibers,�?? J. Opt. Soc. Am. B 20, 2037�??2045 (2003).
    [CrossRef]
  16. O. V. Sinkin, R. Holzl¨ohner, J. Zweck, and C. R. Menyuk, �??Optimization of the Split-Step Fourier Method in Modeling Optical-Fiber Communications Systems,�?? J. Lightwave Technol. 21(1), 61�??68 (2003).
    [CrossRef]
  17. A. Efimov and A. J. Taylor, �??Spectral-temporal dynamics of ultrashort Raman solitons and their role in third-harmonic generation in photonic crystal fibers,�?? Appl. Phys. B 80, 721�??725 (2005). <a href="http://dx.doi.org/10.1007/s00340-005-1789-2">http://dx.doi.org/10.1007/s00340-005-1789-2</a>
    [CrossRef]
  18. J. K. Lucek and K. J. Blow, �??Soliton self-frequency shift in telecommunications fiber,�?? Phys. Rev. A 45, 6666�??6674 (1992).
    [CrossRef] [PubMed]
  19. J. Herrmann and A. Nazarkin, �??Soliton self-frequency shift for pulses with a duration less than the period of molecular oscillations,�?? Opt. Lett. 19, 2065�??2067 (1994).
    [CrossRef] [PubMed]
  20. 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). <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]
  21. C. S. Aparna, S. Kumar, and A. Selvarajan, �??Suppression of the soliton frequency shifts by nonlinear pairing of pulses,�?? Opt. Commun. 131, 267�??273 (1996). <a href="http://dx.doi.org/10.1016/0030-4018(96)00350-1">http://dx.doi.org/10.1016/0030-4018(96)00350-1</a>
    [CrossRef]
  22. V. V. Afansyev, Y. S. Kivshar, V. V. Konotop, and V. N. Serkin, �??Dynamics of coupled dark and bright optical solitons,�?? Opt. Lett. 14, 805�??807 (1989).
    [CrossRef]
  23. F. K. Abdullaev, S. A. Darmanyan, S. Bischoff, P. L. Christiansen, and M. P. Sørensen, �??Modulational instability in optical fibers near the zero dispersion point,�?? Opt. Commun. 108, 60�??64 (1994). <a href="http://dx.doi.org/10.1016/0030-4018(94)90216-X">http://dx.doi.org/10.1016/0030-4018(94)90216-X</a>.
    [CrossRef]
  24. J. D. Harvey, R. Leonhardt, S. Coen, G. K. L. Wong, J. C. Knight, W. J. Wadsworth, and P. S. Russell, �??Scalar modulation instability in the normal dispersion regime by use of a photonic crystal fiber,�?? Opt. Lett. 28, 2225�??2227 (2003).
    [CrossRef] [PubMed]
  25. X. Liu, C. Xu, W. H. Knox, J. K. Chandalia, B. J. Eggleton, S. G. Kosinski, and R. S. Windeler, �??Soliton selffrequency shift in a short tapered air-silica microstructure fiber,�?? Opt. Lett. 26, 358�??360 (2001).
    [CrossRef]

Appl. Phys. B (1)

A. Efimov and A. J. Taylor, �??Spectral-temporal dynamics of ultrashort Raman solitons and their role in third-harmonic generation in photonic crystal fibers,�?? Appl. Phys. B 80, 721�??725 (2005). <a href="http://dx.doi.org/10.1007/s00340-005-1789-2">http://dx.doi.org/10.1007/s00340-005-1789-2</a>
[CrossRef]

IEEE J. Quantum Electron (1)

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]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (3)

Opt. Commun. (2)

C. S. Aparna, S. Kumar, and A. Selvarajan, �??Suppression of the soliton frequency shifts by nonlinear pairing of pulses,�?? Opt. Commun. 131, 267�??273 (1996). <a href="http://dx.doi.org/10.1016/0030-4018(96)00350-1">http://dx.doi.org/10.1016/0030-4018(96)00350-1</a>
[CrossRef]

F. K. Abdullaev, S. A. Darmanyan, S. Bischoff, P. L. Christiansen, and M. P. Sørensen, �??Modulational instability in optical fibers near the zero dispersion point,�?? Opt. Commun. 108, 60�??64 (1994). <a href="http://dx.doi.org/10.1016/0030-4018(94)90216-X">http://dx.doi.org/10.1016/0030-4018(94)90216-X</a>.
[CrossRef]

Opt. Express (5)

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). <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]

G. Genty, M. Lehtonen, H. Ludvigsen, and M. Kaivola, �??Enhanced bandwidth of supercontinuum 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]

A. Efimov, A. J. Taylor, F. G. Omenetto, A. V. Yulin, N. Y. Joly, F. Biancalana, D. V. Skryabin, J. C. Knight, and P. S. J. Russell, �??Time-spectrally-resolved ultrafast nonlinear dynamics in small-core photonic crystal fibers: Experiment and modelling,�?? Opt. Express 12, 6498�??6507 (2004).
[CrossRef] [PubMed]

K. M. Hilligsøe, T. V. Andersen, H. N. Paulsen, C. K. Nielsen, K. Mølmer, S. Keiding, R. Kristiansen, K. P. Hansen, and J. J. Larsen, �??Supercontinuum generation in a photonic crystal fiber with two zero dispersion wavelengths,�?? Opt. Express 12, 1045�??1054 (2004). <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-6-1045.">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-6-1045.</a>
[CrossRef] [PubMed]

S.G. Johnson and J.D. Joannopoulos, �??Block-Iterative Frequency-Domain Methods for Maxwell�??s Equations in a Planewave Basis,�?? Opt. Express 8, 173�??190 (2001). <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-3-173.">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-3-173</a>
[CrossRef] [PubMed]

Opt. Lett. (4)

Phys. Rev. A (2)

J. K. Lucek and K. J. Blow, �??Soliton self-frequency shift in telecommunications fiber,�?? Phys. Rev. A 45, 6666�??6674 (1992).
[CrossRef] [PubMed]

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

Phys. Rev. E (1)

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, 016 615 (2004). <a href="http://dx.doi.org/10.1103/PhysRevE.70.016615">http://dx.doi.org/10.1103/PhysRevE.70.016615.</a>
[CrossRef]

Science (1)

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

Other (3)

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

M. H. Frosz, O. Bang, A. Bjarklev, P. E. Andersen, and J. Broeng, �??Supercontinuum Generation in Photonic Crystal Fibers: The Role of the Second Zero Dispersion Wavelength,�?? presented May 25th 2005, CWC1, at CLEO/QELS 2005, Baltimore, Maryland, USA, 22-27 May 2005.

M. H. Frosz, P. Falk, L. T. Pedersen, O. Bang, and A. Bjarklev, �??Supercontinuum generation in untapered and tapered photonic crystal fibers with two zero dispersion wavelengths,�?? talk #5733-36 presented at SPIE Photonics West, San Jose, California, USA, 22-27 January 2005.

Supplementary Material (4)

» Media 1: AVI (247 KB)     
» Media 2: AVI (298 KB)     
» Media 3: AVI (944 KB)     
» Media 4: AVI (865 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 (7)

Fig. 1.
Fig. 1.

Left: Calculated dispersion profiles for 5 triangular PCFs with pitch ʌ and relative air-hole size d/ʌ given in the inset. Right: Wavelength λ DW of dispersive waves vs. the soliton center wavelength λ S. The color labelling is the same in both figures.

Fig. 2.
Fig. 2.

Calculated spectrograms up to z = 6 mm in the ʌ = 1.0 μm (left) and the ʌ = 1.1 μm fiber (right). The white horizontal lines indicate the ZDWs. pitch1p0_6mm_dB.avi (0.2 MB), pitch1p1_6mm_dB.avi (0.3 MB). 210 computation points were used.

Fig. 3.
Fig. 3.

Left: power spectra after 6 mm of propagation in the ʌ = 1.0 μm fiber. Blue, solid: full simulation; green, dotted: no delayed Raman response; red, dashed: only dispersion terms are β¯2 and β¯3. Right: phase mismatch κ for degenerate FWM at a peak power P 0 = 15 kW and λ 0 = 804 nm, when β¯2 ,β¯4,…, β¯4 are included (blue, solid) and when only β¯2 is included (red, dashed) in Eq. (9).

Fig. 4.
Fig. 4.

Power spectra after 6 mm (left) and 6 cm (right) of propagation. The input spectrum is indicated as a thin black line.

Fig. 5.
Fig. 5.

Left: spectrogram for the 1.2 μm PCF up to z = 60 cm (pitch1p2_60cm_dB.avi, 0.9 MB). Right: spectrogram for the 1.3 μm PCF up to z = 52 cm (pitch1p3_52cm.avi, 0.9 MB). The white horizontal lines indicate the ZDWs.

Fig. 6.
Fig. 6.

A close-up of the spectrogram for the 1.2 μm PCF at z = 60 cm. It is seen that the pulse generated in the normal dispersion region has not changed its width significantly over several centimeters. The white horizontal lines indicate the ZDWs.

Fig. 7.
Fig. 7.

(a) The red-infrared part of the pulse spectrum output from the ʌ = 1.3 μm PCF at various fiber lengths.

Equations (11)

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

A z = i m 2 i m β ¯ m m ! m A t m + [ 1 + i ω 0 t ] [ A ( z , t ) t R ( t′ ) A ( z , t t′ ) 2 d t′ ] ,
β 2 ( ω ) = β ¯ 2 + β ¯ 3 [ ω ω 0 ] + 1 2 β ¯ 4 [ ω ω 0 ] 2 + 1 6 β ¯ 5 [ ω ω 0 ] 3 +
β ¯ m = β m ( ω 0 ) = ( d m β d ω m ) ω = ω 0 ,
S ( z , t , ω ) = e iωt′ e [ t′ t ] 2 α 2 A ( z , t′ ) d t′ 2 ,
A z = i β 2 ( ω sol ) 2 2 A t 2 + iγA A 2 ,
A z = i m 2 i m β m ( ω sol ) m ! m A t m .
β 2 ( ω sol ) 2 T sol 2 = m 2 β m ( ω sol ) m ! [ ω DW ω sol ] m ,
T sol = T 0 2 N 1 = T 0 2 ( γ P 0 T 0 2 β 2 ( ω sol ) | ) 1 ,
κ = 2 γ P 0 + Ω 2 β ¯ 2 + 2 4 ! Ω 4 β ¯ 4 + 2 6 ! Ω 6 β ¯ 6 +
β 1 ( ω ) = β 1 ( ω A ) + β 2 ( ω A ) [ ω ω A ] + β 3 ( ω A ) 2 [ ω ω A ] 2 ,
Δ ω = 2 β 2 ( ω A ) β 3 ( ω A ) ,

Metrics