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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 24 — Nov. 22, 2010
  • pp: 25449–25460

Limitations of the linear Raman gain approximation in modeling broadband nonlinear propagation in optical fibers

Miro Erkintalo, Goëry Genty, Benjamin Wetzel, and John M. Dudley  »View Author Affiliations

Optics Express, Vol. 18, Issue 24, pp. 25449-25460 (2010)

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We consider the accuracy of modeling ultrashort pulse propagation and supercontinuum generation in optical fibers based on the assumption of a material Raman response that varies linearly with frequency. Numerical simulations in silica fiber using the linear Raman gain approximation are compared with simulations using the full Raman response, and differences in the spectral, temporal and stability characteristics are considered. A major finding is that for conditions typical of many experiments, although the input pulses may satisfy the criteria where the linear gain approximation is valid, the subsequent evolution and breakup of the input pulse can rapidly lead to a situation where the linear model leads to severe inaccuracies. Numerical artifacts within the linear model inducing unphysical pulse collapse are also identified.

© 2010 OSA

OCIS Codes
(190.4370) Nonlinear optics : Nonlinear optics, fibers
(190.5530) Nonlinear optics : Pulse propagation and temporal solitons
(190.5650) Nonlinear optics : Raman effect
(320.6629) Ultrafast optics : Supercontinuum generation

ToC Category:
Nonlinear Optics

Original Manuscript: September 24, 2010
Revised Manuscript: November 4, 2010
Manuscript Accepted: November 4, 2010
Published: November 19, 2010

Miro Erkintalo, Goëry Genty, Benjamin Wetzel, and John M. Dudley, "Limitations of the linear Raman gain approximation in modeling broadband nonlinear propagation in optical fibers," Opt. Express 18, 25449-25460 (2010)

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  1. E. P. Ippen, “Low-power quasi-cw Raman oscillator,” Appl. Phys. Lett. 16(8), 303–305 (1970). [CrossRef]
  2. R. H. Stolen, E. P. Ippen, and A. R. Tynes, “Raman oscillation in glass optical waveguides,” Appl. Phys. Lett. 20(2), 62–64 (1972). [CrossRef]
  3. R. G. Smith, “Optical power handling capacity of low loss optical fibers as determined by stimulated Raman and brillouin scattering,” Appl. Opt. 11(11), 2489–2494 (1972). [CrossRef] [PubMed]
  4. F. M. Mitschke and L. F. Mollenauer, “Discovery of the soliton self-frequency shift,” Opt. Lett. 11(10), 659–661 (1986). [CrossRef] [PubMed]
  5. J. P. Gordon, “Theory of the soliton self-frequency shift,” Opt. Lett. 11(10), 662–664 (1986). [CrossRef] [PubMed]
  6. Y. Kodama and A. Hasegawa, “Nonlinear pulse propagation in a monomode dielectric guide,” IEEE J. Quantum Electron. 23(5), 510–524 (1987). [CrossRef]
  7. K. Tai, A. Hasegawa, and N. Bekki, “Fission of optical solitons induced by stimulated Raman effect,” Opt. Lett. 13(5), 392–394 (1988). [CrossRef] [PubMed]
  8. G. P. Agrawal, Nonlinear Fiber Optics, 4th Edition, (Academic Press, Boston, 2007)
  9. K. J. Blow and D. Wood, “Theoretical description of transient stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. 25(12), 2665–2673 (1989). [CrossRef]
  10. P. V. Mamyshev and S. V. Chernikov, “Ultrashort-pulse propagation in optical fibers,” Opt. Lett. 15(19), 1076–1078 (1990). [CrossRef] [PubMed]
  11. J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006). [CrossRef]
  12. S. V. Smirnov, J. D. Ania-Castanon, T. J. Ellingham, S. M. Kobtsev, S. V. Kukarin, and S. K. Turitsyn, “Optical spectral broadening and supercontinuum generation in telecom applications,” Opt. Fiber Technol. 12(2), 122–147 (2006). [CrossRef]
  13. R. H. Stolen, J. P. Gordon, W. J. Tomlinson, and H. A. Haus, “Raman response function of silica-core fibers,” J. Opt. Soc. Am. B 6(6), 1159–1166 (1989). [CrossRef]
  14. Q. Lin and G. P. Agrawal, “Raman response function for silica fibers,” Opt. Lett. 31(21), 3086–3088 (2006). [CrossRef] [PubMed]
  15. D. Hollenbeck and C. D. Cantrell, “Multiple-vibrational-mode model for fiber-optic Raman gain spectrum and response function,” J. Opt. Soc. Am. B 19(12), 2886–2892 (2002). [CrossRef]
  16. N. Akhmediev, W. Krolikowski, and A. J. Lowery, “Influence of the Raman-effect on solitons in optical fibers,” Opt. Commun. 131(4-6), 260–266 (1996). [CrossRef]
  17. A. V. Gorbach and D. V. Skryabin, “Light trapping in gravity-like potentials and expansion of supercontinuum spectra in photonic-crystal fibres,” Nat. Photonics 1(11), 653–657 (2007). [CrossRef]
  18. M. Facão, M. I. Carvalho, and D. F. Parker, “Soliton self-frequency shift: Self-similar solutions and their stability,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 81(4 ), 046604 (2010). [CrossRef] [PubMed]
  19. C. Conti, S. Stark, P. S. Russell, and F. Biancalana, “Multiple hydrodynamical shocks induced by Raman effect in photonic crystal fibres,” Phys. Rev. A 82(1), 013838 (2010). [CrossRef]
  20. W. Hodel and H. P. Weber, “Decay of femtosecond higher-order solitons in an optical fiber induced by Raman self-pumping,” Opt. Lett. 12(11), 924–926 (1987). [CrossRef] [PubMed]
  21. M. N. Islam, G. Sucha, I. Bar-Joseph, M. Wegener, J. P. Gordon, and D. S. Chemla, “Broad bandwidths from frequency-shifting solitons in fibers,” Opt. Lett. 14(7), 370–372 (1989). [CrossRef] [PubMed]
  22. J. M. Harbold, F. Ö. Ilday, F. W. Wise, T. A. Birks, W. J. Wadsworth, and Z. Chen, “Long-wavelength continuum generation about the second dispersion zero of a tapered fiber,” Opt. Lett. 27(17), 1558–1560 (2002). [CrossRef]
  23. K. Saitoh and M. Koshiba, “Highly nonlinear dispersion-flattened photonic crystal fibers for supercontinuum generation in a telecommunication window,” Opt. Express 12(10), 2027–2032 (2004), http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-10-2027 . [CrossRef] [PubMed]
  24. Y. Nan, J. Wang, C. Lou, and Y. Gao, “Performance analysis for a supercontinuum continuous-wave optical source for dense wavelength division multiplexed transmission,” J. Opt. A, Pure Appl. Opt. 7(3), 129–134 (2005). [CrossRef]
  25. J. N. Kutz, C. Lyngå, and B. Eggleton, “Enhanced Supercontinuum Generation through Dispersion-Management,” Opt. Express 13(11), 3989–3998 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-11-3989 . [CrossRef] [PubMed]
  26. A. Demircan and U. Bandelow, “Supercontinuum generation by the modulation instability,” Opt. Commun. 244(1-6), 181–185 (2005). [CrossRef]
  27. D. R. Solli, C. Ropers, and B. Jalali, “Active control of optical rogue waves for stimulated supercontinuum generation,” Phys. Rev. Lett. 101(23), 233902 (2008). [CrossRef] [PubMed]
  28. H. Lu, X. Liu, Y. Gong, X. Hu, and X. Li, “Optimization of supercontinuum generation in air-silica nanowires,” J. Opt. Soc. Am. B 27(5), 904–908 (2010). [CrossRef]
  29. D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450(7172), 1054–1057 (2007). [CrossRef] [PubMed]
  30. G. Genty, J. M. Dudley, and B. J. Eggleton, “Modulation control and spectral shaping of optical fiber supercontinuum generation in the picosecond regime,” Appl. Phys. B 94(2), 187–194 (2009). [CrossRef]
  31. M. Erkintalo, G. Genty, and J. M. Dudley, “On the statistical interpretation of optical rogue waves,” Eur. Phys. J. Spec. Top. 185(1), 135–144 (2010). [CrossRef]
  32. Z. Chen, A. J. Taylor, and A. Efimov, “Soliton dynamics in non-uniform fiber tapers: analytical description through an improved moment method,” J. Opt. Soc. Am. B 27(5), 1022–1030 (2010). [CrossRef]
  33. D. J. Dougherty, F. X. Kärtner, H. A. Haus, and E. P. Ippen, “Measurement of the Raman gain spectrum of optical fibers,” Opt. Lett. 20(1), 31–33 (1995). [CrossRef] [PubMed]
  34. A. K. Atieh, P. Myslinski, J. Chrostowski, and P. Galko, “Measuring the Raman Time Constant for Soliton Pulses in Standard Single-Mode Fiber,” J. Lightwave Technol. 17(2), 216–221 (1999). [CrossRef]
  35. There is considerable uncertainty about the slope of the Raman gain slope at zero frequencies. Some measurements of Raman gain for small wavelength shifts suggest that a value of TR = 3 fs when fitting to the gain peak (Fig. 1) is also consistent with a good fit to the slope near ω = 0. See e.g. A. Dogariu and D. Hagan, “Low frequency Raman gain measurements using chirped pulses,” Opt. Express 1, 73–76 (1997). G. Shaulov, V. J. Mazurczyk, and E. A. Golovchenko, “Measurement of Raman gain coefficient for small wavelength shifts,” in Optical Fiber Communication Conference, Paper TuA4 (2000).
  36. J. M. Dudley and S. Coen, “Coherence properties of supercontinuum spectra generated in photonic crystal and tapered optical fibers,” Opt. Lett. 27(13), 1180–1182 (2002). [CrossRef]
  37. M. H. Frosz, “Validation of input-noise model for simulations of supercontinuum generation and rogue waves,” Opt. Express 18(14), 14778–14787 (2010), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-14-14778 . [CrossRef] [PubMed]
  38. 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(19), 4614–4624 (2004), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-19-4614 . [CrossRef] [PubMed]
  39. J. M. Dudley, G. Genty, F. Dias, B. Kibler, and N. Akhmediev, “Modulation instability, Akhmediev Breathers and continuous wave supercontinuum generation,” Opt. Express 17(24), 21497–21508 (2009), http://www.opticsinfobase.org/abstract.cfm?URI=oe-17-24-21497 . [CrossRef] [PubMed]
  40. K. Hammani, B. Kibler, C. Finot, and A. Picozzi, “Emergence of rogue waves from optical turbulence,” Phys. Lett. A 374(34), 3585–3589 (2010). [CrossRef]

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