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

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

http://dx.doi.org/10.1364/OE.18.025449

Acrobat PDF (1260 KB)

### Abstract

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

## 1. Introduction

1. E. P. Ippen, “Low-power quasi-cw Raman oscillator,” Appl. Phys. Lett. **16**(8), 303–305 (1970). [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]

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]

6. Y. Kodama and A. Hasegawa, “Nonlinear pulse propagation in a monomode dielectric guide,” IEEE J. Quantum Electron. **23**(5), 510–524 (1987). [CrossRef]

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]

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]

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]

5. J. P. Gordon, “Theory of the soliton self-frequency shift,” Opt. Lett. **11**(10), 662–664 (1986). [CrossRef] [PubMed]

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]

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]

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]

## 2. Numerical modeling

*A*(

*z*,

*t*) represents the envelope of the electric field, the

*β*'s and

_{k}*γ*are the usual dispersion and nonlinear coefficients respectively, and the shock timescale

*τ*describes the dispersion of the nonlinearity. The nonlinear response

_{shock}*R*(t) = (1 –

*f*)

_{R}*δ*(t) +

*f*(

_{R}h_{R}*t*) includes instantaneous and delayed Raman contributions, with

*h*(

_{R}*t*) normalized such that its integral evaluated with respect to the time variable

*t*is unity. The fractional contribution of the Raman response is

*f*, typically taken as

_{R}*f*= 0.18 in fused silica.

_{R}*h*(

_{R}*t*)]. Here FT denotes Fourier transform. For fused silica, this experimental data (adapted from Ref. 13

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]

*ω*/2π = 13.2 THz, with the response becoming negligible at frequencies greater than 30 THz. In what follows we refer to this for convenience as “the full model”. Note that in our simulations, we use the experimental form of the response curve taken from Ref. 13

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]

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]

*ωΒ*, where

*B*is a slope parameter used to fit the measured Raman gain. Subject to this approximation and also assuming that the effect of shock term on the Raman response is negligible [32

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]

*T*is derived from the Raman gain slope using

_{R}*T*=

_{R}*f*, and can be determined from the slope at

_{R}B*ω*= 0 such that

*T*assumes the interpretation as the first moment of

_{R}*h*(

_{R}*t*) [8]. However, the linear approximation can be used to fit the experimental curve in other ways [33

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]

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).

*T*= 3.0 fs and this is the value used in all subsequent simulations. In what follows we refer to this approach described by Eq. (2) as “the linear model”.

_{R}## 3. Soliton propagation and coherent supercontinuum generation

*N*= 1 soliton in a fiber with only a constant dispersion coefficient

*β*

_{2}= −4.10 ´ 10

^{−1}ps

^{2}km

^{−1}and nonlinearity

*γ*= 0.01066 W

^{−1}m

^{−1}, neglecting higher order dispersion and shock terms. These dispersion and nonlinearity parameters are typical of highly nonlinear photonic crystal fibers with zero dispersion wavelength around 1 μm (see below for further details of the fiber considered). For this case, Fig. 1(b) plots the rate of self frequency shift |d

*ν*/d

*z|*as a function of the initial pulse spectral bandwidth. Note that the bandwidth of the soliton actually evolves negligibly in the absence of higher order dispersion, remaining constant with propagation distance. From this figure, we see how the rate of soliton self-frequency shift predicted by the linear model with

*T*= 3 fs is in good agreement with that obtained from the full model only when the pulse bandwidth is less that ~5 THz (corresponding to a pulse duration FWHM τ > 60 fs). As the bandwidth increases above 5 THz, it is clear that the deviation between the two models start increasing, with the linear model significantly overestimating the rate of self-frequency shift. As we shall see in what follows, it is this fundamental difference in the way in which the two models predict the soliton dynamics that imposes the main restriction on the use of the linear Raman model for SC simulations.

_{R}11. J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. **78**(4), 1135–1184 (2006). [CrossRef]

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]

*γ*= 0.01066 W

^{−1}m

^{−1}and

*τ*= 0.55 fs. The fiber dispersion curve was included directly in the numerical simulations in the frequency domain, but near-identical results can be obtained using dispersion coefficients (at 1035 nm):

_{shock}*β*

_{2}= −7.10 ´ 10

^{−1}ps

^{2}km

^{−1},

*β*

_{3}= 6.90 ´ 10

^{−2}ps

^{3}km

^{−1},

*β*

_{4}= −1.02 ´ 10

^{−4}ps

^{4}km

^{−1},

*β*

_{5}= 2.7 ´ 10

^{−7}ps

^{5}km

^{−1},

*β*

_{6}= −8.3 ´ 10

^{−10}ps

^{6}km

^{−1},

*β*

_{7}= 3.0 ´ 10

^{−12}ps

^{7}km

^{−1},

*β*

_{8}= −1.2´10

^{−14}ps

^{8}km

^{−1},

*β*

_{9}= 6.5′10

^{−17}ps

^{9}km

^{−1},

*β*

_{10}= −3.2´ 10

^{−20}ps

^{10}km

^{−1}.

*τ*= 50 fs – 1 ps. As the pulse duration is varied, we adjust peak power to keep constant soliton number

*N*= (

*γP*

_{0}

*T*

_{0}

^{2}/|

*β*

_{2}|)

^{1/2}with

*T*

_{0}=

*τ*/1.763. For a meaningful comparison between results using different input pulses, we compare spectral characteristics after a propagation distance of

*z*= 10

*L*

_{fiss}where the characteristic soliton fission distance is

*L*

_{fiss}=

*L*

_{D}/

*N*with

*L*

_{D}=

*T*

_{0}

^{2}/|

*β*

_{2}| [11

11. J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. **78**(4), 1135–1184 (2006). [CrossRef]

*N*= 5 input pulses, there is good qualitative agreement between the spectra predicted by both models, and for the 1 ps case in particular, there is also very good quantitative agreement. On the other hand, as the soliton number increases to

*N*= 10, the degree of quantitative agreement decreases for the 1 ps case, and for the shorter pulse durations of 200 fs and 50 fs we see significant qualitative differences between the spectra predicted by the two models.

*τ*~60 fs. Moreover, since the duration of the first ejected soliton can be predicted from the FWHM of the input pulse and soliton number

*N*using

*τ*

_{1}~

*τ*/ (2

*N*−1) fs [6

6. Y. Kodama and A. Hasegawa, “Nonlinear pulse propagation in a monomode dielectric guide,” IEEE J. Quantum Electron. **23**(5), 510–524 (1987). [CrossRef]

*τ*/ (2

*N*−1) > 60 fs. Thus, for large input pulse durations and/or small input soliton numbers SC generation may be modeled accurately by a linear Raman gain model. In this regard, we note that the soliton number-dependence of this validity condition allows the potential accuracy or inaccuracy of the linear approximation to be conveniently tested for different combinations of peak power and/or duration of the input pulses.

*N*= 10 input pulse [as in Fig. 2 (vi)], and we follow the dynamical evolution of the spectrum over a distance of 20

*L*

_{fiss}. The figure shows also corresponding output temporal profiles and temporal spectrograms. There are clear physical differences between the field characteristics predicted using the different models: besides the significantly larger bandwidth predicted by the linear model, the most notable difference is that whilst the full Raman gain model predicts significant spectral content on both sides of the ZDW for the output spectrum, the corresponding spectrum predicted by the linear Raman model lies almost entirely in the anomalous dispersion regime.

## 4. Incoherent supercontinuum generation

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]

29. D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature **450**(7172), 1054–1057 (2007). [CrossRef] [PubMed]

*N*~107, and propagation would be expected to be highly incoherent with significant shot-to-shot spectral and temporal fluctuations. Figure 4 compares results from simulations using the linear Raman gain and full Raman gain models. The two models predict very different results, with the absence of gain bandwidth limitation in the linear model leading to significantly greater spectral broadening at the same propagation distance as shown in Fig. 4(a) for a distance of 15 m. In Fig. 4(b) we plot the outputs at two different distances such that there is comparable mean spectral broadening on the long wavelength side of ~200 nm at the −20 dB level relative to the residual pump. This level of broadening is reached after only 11 m of propagation with the linear model compared to the much greater propagation distance of 25 m when using the full model.

**78**(4), 1135–1184 (2006). [CrossRef]

29. D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature **450**(7172), 1054–1057 (2007). [CrossRef] [PubMed]

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]

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]

^{(1)}

_{12}|> [31

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]

**78**(4), 1135–1184 (2006). [CrossRef]

^{(1)}

_{12}|> ~1). On the other hand, for higher soliton numbers when noise plays an increasingly important role in the dynamics, we see that the linear model predicts increased decoherence (lower <|g

^{(1)}

_{12}|>) when compared to the full model. This behavior can be readily understood because the coupling between the Raman and MI gain leads to an essentially unlimited bandwidth for noise amplification in the linear model that greatly overestimates the degree of decoherence compared to the full model.

## 5. Pulse collapse in the linear Raman gain model

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]

**78**(4), 1135–1184 (2006). [CrossRef]

## 6. Conclusion

## Acknowledgements

## References and links

1. | E. P. Ippen, “Low-power quasi-cw Raman oscillator,” Appl. Phys. Lett. |

2. | R. H. Stolen, E. P. Ippen, and A. R. Tynes, “Raman oscillation in glass optical waveguides,” Appl. Phys. Lett. |

3. | R. G. Smith, “Optical power handling capacity of low loss optical fibers as determined by stimulated Raman and brillouin scattering,” Appl. Opt. |

4. | F. M. Mitschke and L. F. Mollenauer, “Discovery of the soliton self-frequency shift,” Opt. Lett. |

5. | J. P. Gordon, “Theory of the soliton self-frequency shift,” Opt. Lett. |

6. | Y. Kodama and A. Hasegawa, “Nonlinear pulse propagation in a monomode dielectric guide,” IEEE J. Quantum Electron. |

7. | K. Tai, A. Hasegawa, and N. Bekki, “Fission of optical solitons induced by stimulated Raman effect,” Opt. Lett. |

8. | G. P. Agrawal, |

9. | K. J. Blow and D. Wood, “Theoretical description of transient stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. |

10. | P. V. Mamyshev and S. V. Chernikov, “Ultrashort-pulse propagation in optical fibers,” Opt. Lett. |

11. | J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. |

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. |

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 |

14. | Q. Lin and G. P. Agrawal, “Raman response function for silica fibers,” Opt. Lett. |

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 |

16. | N. Akhmediev, W. Krolikowski, and A. J. Lowery, “Influence of the Raman-effect on solitons in optical fibers,” Opt. Commun. |

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 |

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. |

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 |

20. | W. Hodel and H. P. Weber, “Decay of femtosecond higher-order solitons in an optical fiber induced by Raman self-pumping,” Opt. Lett. |

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. |

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. |

23. | K. Saitoh and M. Koshiba, “Highly nonlinear dispersion-flattened photonic crystal fibers for supercontinuum generation in a telecommunication window,” Opt. Express |

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. |

25. | J. N. Kutz, C. Lyngå, and B. Eggleton, “Enhanced Supercontinuum Generation through Dispersion-Management,” Opt. Express |

26. | A. Demircan and U. Bandelow, “Supercontinuum generation by the modulation instability,” Opt. Commun. |

27. | D. R. Solli, C. Ropers, and B. Jalali, “Active control of optical rogue waves for stimulated supercontinuum generation,” Phys. Rev. Lett. |

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 |

29. | D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature |

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 |

31. | M. Erkintalo, G. Genty, and J. M. Dudley, “On the statistical interpretation of optical rogue waves,” Eur. Phys. J. Spec. Top. |

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 |

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. |

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. |

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. |

37. | M. H. Frosz, “Validation of input-noise model for simulations of supercontinuum generation and rogue waves,” Opt. Express |

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 |

39. | J. M. Dudley, G. Genty, F. Dias, B. Kibler, and N. Akhmediev, “Modulation instability, Akhmediev Breathers and continuous wave supercontinuum generation,” Opt. Express |

40. | K. Hammani, B. Kibler, C. Finot, and A. Picozzi, “Emergence of rogue waves from optical turbulence,” Phys. Lett. A |

**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

**History**

Original Manuscript: September 24, 2010

Revised Manuscript: November 4, 2010

Manuscript Accepted: November 4, 2010

Published: November 19, 2010

**Citation**

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)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-24-25449

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### References

- E. P. Ippen, “Low-power quasi-cw Raman oscillator,” Appl. Phys. Lett. 16(8), 303–305 (1970). [CrossRef]
- 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]
- 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]
- F. M. Mitschke and L. F. Mollenauer, “Discovery of the soliton self-frequency shift,” Opt. Lett. 11(10), 659–661 (1986). [CrossRef] [PubMed]
- J. P. Gordon, “Theory of the soliton self-frequency shift,” Opt. Lett. 11(10), 662–664 (1986). [CrossRef] [PubMed]
- Y. Kodama and A. Hasegawa, “Nonlinear pulse propagation in a monomode dielectric guide,” IEEE J. Quantum Electron. 23(5), 510–524 (1987). [CrossRef]
- 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]
- G. P. Agrawal, Nonlinear Fiber Optics, 4th Edition, (Academic Press, Boston, 2007)
- 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]
- P. V. Mamyshev and S. V. Chernikov, “Ultrashort-pulse propagation in optical fibers,” Opt. Lett. 15(19), 1076–1078 (1990). [CrossRef] [PubMed]
- J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006). [CrossRef]
- 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]
- 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]
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