## Dynamics of ultrashort pulses near zero dispersion wavelength

JOSA B, Vol. 23, Issue 11, pp. 2425-2433 (2006)

http://dx.doi.org/10.1364/JOSAB.23.002425

Enhanced HTML Acrobat PDF (144 KB)

### Abstract

The adiabatic dynamics of solitons under the action of third-order dispersion (TOD), the Raman effect, and self-steepening is studied. Using equations that describe the evolution of the pulse parameters, it is shown that the interplay between these effects results in nontrivial pulse dynamics. It is found that positive TOD slows down the self-frequency shift. The theory also describes the eventual suppression of the self-frequency shift in fibers with negative TOD that was recently observed in experiments and described theoretically. The relations of our results to supercontinuum generation are discussed.

© 2006 Optical Society of America

**OCIS Codes**

(060.5530) Fiber optics and optical communications : Pulse propagation and temporal solitons

(190.4370) Nonlinear optics : Nonlinear optics, fibers

(190.5530) Nonlinear optics : Pulse propagation and temporal solitons

(190.7110) Nonlinear optics : Ultrafast nonlinear optics

**ToC Category:**

Ultrafast Optics

**History**

Original Manuscript: May 18, 2006

Revised Manuscript: July 24, 2006

Manuscript Accepted: July 25, 2006

**Citation**

Eduard N. Tsoy and C. Martijn de Sterke, "Dynamics of ultrashort pulses near zero dispersion wavelength," J. Opt. Soc. Am. B **23**, 2425-2433 (2006)

http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-23-11-2425

Sort: Year | Journal | Reset

### References

- G. P. Agrawal, Nonlinear Fiber Optics (Academic, 1995).
- N. Akhmediev and A. Ankiewicz, Solitons: Nonlinear Pulses and Beams (Chapman & Hall, 1997).
- A. I. Maimistov and A. M. Basharov, Nonlinear Optical Waves (Kluwer, 1999).
- See, for example, R.R.Alfano, ed., The Supercontinuum Laser Source (Springer-Verlag, 1989).
- See, for example, the special issue on supercontinuum generation, Appl. Phys. B 77, A. Zheltikov, ed. (2003).
- J. K. Ranka, R. S. Windeler, and A. J. Stentz, "Visible continuum generation in air silica microstructure optical fibers with anomalous dispersion at 800nm," Opt. Lett. 25, 25-27 (2000). [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]
- 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]
- A. Fuerbach, P. Steinvurzel, J. A. Bolger, and B. J. Eggleton, "Nonlinear pulse propagation at zero dispersion wavelength in anti-resonant photonic crystal fibers," Opt. Express 13, 2977-2987 (2005). [CrossRef] [PubMed]
- R. K. A. Wai, C. R. Menyuk, Y. C. Lee, and 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]
- F. M. Mitschke and L. F. Mollenauer, "Discovery of the soliton self-frequency shift," Opt. Lett. 11, 659-661 (1986). [CrossRef] [PubMed]
- J. P. Gordon, "Theory of the soliton self-frequency shift," Opt. Lett. 11, 662-664 (1986). [CrossRef] [PubMed]
- Yu. Kodama and A. Hasegawa, "Nonlinear pulse-propagation in a monomode dielectric guide," IEEE J. Quantum Electron. 23, 510-524 (1987). [CrossRef]
- 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. N. Elgin, T. Brabec, and S. M. J. Kelly, "A perturbative theory of soliton propagation in the presence of third-order dispersion," Opt. Commun. 114, 321-328 (1995). [CrossRef]
- T. P. Horikis and J. N. Elgin, "Soliton radiation in an optical fiber," J. Opt. Soc. Am. B 18, 913-918 (2001). [CrossRef]
- W. Zhao and E. Bourkoff, "Femtosecond pulse-propagation in optical fibers: higher-order effects," IEEE J. Quantum Electron. 24, 365-372 (1987). [CrossRef]
- D. J. Frantzeskakis, K Hizanidis, G. S. Tombras, and I. Bella, "Nonlinear dynamics of femtosecond optical solitary wave-propagation at the zero dispersion point," IEEE J. Quantum Electron. 31, 183-189 (1995). [CrossRef]
- A. Ankiewicz, "Simplified description of soliton perturbation and interaction using averaged complex potentials," J. Nonlinear Opt. Phys. Mater. 4, 857-870 (1995). [CrossRef]
- M. Golles, I. M. Uzunov, and F. Lederer, "Break up of N-soliton bound states due to intrapulse Raman scattering and third order dispersion--an eigenvalue analysis," Phys. Lett. A 231, 195-200 (1997). [CrossRef]
- V. I. Karpman, "Radiation of solitons described by a high-order cubic nonlinear Schrödinger equation," Phys. Rev. E 62, 5678-5687 (2000). [CrossRef]
- D. V. Skryabin, F. Luan, J. C. Knight, and P. St. J. Russell, "Soliton self-frequency shift cancelation in photonic crystal fibers," Science 301, 1705-1708 (2003). [CrossRef] [PubMed]
- 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]
- A. I. Maimistov, "Evolution of single waves close to solitons of Schrödinger nonlinear equation," J. Exp. Theor. Phys. 77, 727 (1993) A. I. Maimistov,[Zh. Eksp. Teor. Fiz. 104, 3620-3629 (1993)].
- E. N. Tsoy, A. Ankiewicz, and N. Akhmediev, "Dynamical models for dissipative localized waves of the complex Ginzburg-Landau equation," Phys. Rev. E 73, 036621 (2006). [CrossRef]
- W. L. Kath and N. F. Smith, "Soliton evolution and radiation loss for the nonlinear Schrödinger equation," Phys. Rev. E 51, 1484-1492 (1995). [CrossRef]
- D. J. Kaup and A. C. Newell, "Exact solution for a derivative non-linear Schrödinger equation," J. Math. Phys. 19, 798-801 (1978). [CrossRef]
- See, for example, B. A. Malomed, "Variational methods in nonlinear fiber optics and related fields," Prog. Opt. Vol. 43, (Elsevier, 2002), pp. 71-193, and references therein. [CrossRef]
- F. Kh. Abdullaev and J. G. Caputo, "Validation of the variational approach for chirped pulses in fibers with periodic dispersion," Phys. Rev. E 58, 6637-6648 (1998). [CrossRef]
- H. Goldstein, Classical Mechanics (Addison-Wesley, 1980).
- J. Satsuma and N. Yajima, "Initial value-problems of one-dimensional self-modulation of nonlinear waves in dispersive media," Prog. Theor. Phys. Suppl. 55, 284-306 (1974). [CrossRef]
- 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). [CrossRef] [PubMed]
- M. H. Frosz, P. Falk, and O. Bang, "The role of the second zero-dispersion wavelength in generation of supercontinua and bright-bright soliton-pairs across the zero-dispersion wavelength," Opt. Express 13, 6181-6192 (2005). [CrossRef] [PubMed]

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.