## Enhanced Supercontinuum Generation through Dispersion-Management

Optics Express, Vol. 13, Issue 11, pp. 3989-3998 (2005)

http://dx.doi.org/10.1364/OPEX.13.003989

Acrobat PDF (1878 KB)

### Abstract

We show in theory and simulation that the supercontinuum generation from an initial continuous wave field in a highly nonlinear fiber operating near the zero-dispersion point can be significantly enhanced with the aid of dispersion management. We characterize the spectral broadening as a process initiated by modulational instability, but driven by the zero-dispersion dynamics of an *N*-soliton interacting with the asymmetric phase profile generated by the Raman effect, self-steepening effect, and/or higher-order dispersion. Higher *N*-soliton values lead to shorter pulses and a broader spectrum. This insight allows us to use dispersion management in conjunction with modulational instability to effectively increase the *N* value and greatly enhance the supercontiuum generation process.

© 2005 Optical Society of America

## 1. Introduction

1. 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]

2. G. Genty, M. Lehtonen, H. Ludvigsen, J. Broeng, and M. Kaivola, “Spectral broadening of femtosecond pulses into continuum radiation in microstructured fibers,” Opt. Express **10**, 1083–1098 (2002). [PubMed]

1. 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. A. K. Abeeluck, C. Headley, and C. G. Jørgensen, “High-power supercontinuum generation in highly nonlinear, dispersion-shifted fibers by use of a continuous-wave Raman fiber laser,” Opt. Lett. **29**, 2163–2165 (2004). [CrossRef] [PubMed]

4. A. K. Abeeluck and C. Headley, “Supercontinuum growth in a highly nonlinear fiber with a low-coherence semiconductor laser diode,” App. Phys. Lett. **85**, 4863 (2004). [CrossRef]

5. A. Mussot, E. Lantz, H. Maillotte, and T. Sylvestre, “Spectral broadening of a partially coherent CW laser beam in single-mode optical fibers,” Opt. Express **12**2838 (2004). [CrossRef] [PubMed]

6. J. D. Harvey, R. Leonhardt, S. Coen, G. Wong, J. Knight, W. J. Wadsworth, and P. St. J. Russell, “Scalar modulational instability in the normal dispersion regime by use of photonic crystal fiber,” Opt. Lett. **28**, 2225–2227 (2003). [CrossRef] [PubMed]

7. A. Demircan and U. Bandelow, “Supercontinuum generation by the modulation instability,” Opt. Comm. **244**, 181–185 (2005). [CrossRef]

8. E. Golovchenko, P. Mamyshev, A. Pilipetskii, and E. A. Dianov, “Mutual Influence of the Parametric Effects and Stimulated Raman Scattering in Optical Fibers,” IEEE J. Quant. Elec. **26**, 1815–1820 (1990). [CrossRef]

9. J. K. Ranka, R. S. Windeler, and A. J. Stentz, “Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm,” Opt. Lett. **25**, 25–27 (2000). [CrossRef]

*N*-soliton pulse which in turn creates and ejects ultra-short one-soliton pulses. The one-soliton pulse widths, which are narrower for higher

*N*values, can be controlled and shortened substantially through dispersion management, thus allowing for enhanced spectral broadening. Specifically, dispersion management allows us to control the modulational instability frequencies which initially determine the energy contained in each N-soliton pulse created. A similar idea has been used by Hori

*et al*. [10

10. T. Hori, J. Takayanagi, N. Nishizawa, and T. Goto, “Flatly broadened, wideband and low noise supercontinuum generation in highly nonlinear hybrid fiber,” Opt. Express **12**, 317–324 (2004). [CrossRef] [PubMed]

6. J. D. Harvey, R. Leonhardt, S. Coen, G. Wong, J. Knight, W. J. Wadsworth, and P. St. J. Russell, “Scalar modulational instability in the normal dispersion regime by use of photonic crystal fiber,” Opt. Lett. **28**, 2225–2227 (2003). [CrossRef] [PubMed]

3. A. K. Abeeluck, C. Headley, and C. G. Jørgensen, “High-power supercontinuum generation in highly nonlinear, dispersion-shifted fibers by use of a continuous-wave Raman fiber laser,” Opt. Lett. **29**, 2163–2165 (2004). [CrossRef] [PubMed]

4. A. K. Abeeluck and C. Headley, “Supercontinuum growth in a highly nonlinear fiber with a low-coherence semiconductor laser diode,” App. Phys. Lett. **85**, 4863 (2004). [CrossRef]

5. A. Mussot, E. Lantz, H. Maillotte, and T. Sylvestre, “Spectral broadening of a partially coherent CW laser beam in single-mode optical fibers,” Opt. Express **12**2838 (2004). [CrossRef] [PubMed]

13. J. C. Bronski, “Semiclassical eigenvalue distribution of the Zakharov-Shabat eigenvalue problem,” Physica D **97**, 376–397 (1996). [CrossRef]

14. J. C. Bronski and J. N. Kutz, “Numerical simulation of the semiclassical limit of the focusing nonlinear Schrodinger equation,” Phys. Lett. A **254**, 325 (1999). [CrossRef]

13. J. C. Bronski, “Semiclassical eigenvalue distribution of the Zakharov-Shabat eigenvalue problem,” Physica D **97**, 376–397 (1996). [CrossRef]

14. J. C. Bronski and J. N. Kutz, “Numerical simulation of the semiclassical limit of the focusing nonlinear Schrodinger equation,” Phys. Lett. A **254**, 325 (1999). [CrossRef]

15. D. Krylov, L. Leng, K. Bergman, J. C. Bronski, and J. N. Kutz, “Observation of the breakup of a pre-chirped N-soliton in an optical fiber,” Opt. Lett. **24**, 1191–1193 (1999). [CrossRef]

16. 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]

17. 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]

18. K. Tai, A. Hasegawa, and N. Bekki, “Fission of optical solitons induced by stimulated Raman effect,” Opt. Lett. **13**, 392–394 (1988). [CrossRef] [PubMed]

19. H. Kubota, K. Tamura, and M. Nakazawa, “Analyses of coherence-maintained ultrashort optical pulse trains and supercontinuum generation in the presence of soliton-amplified spontaneous-emission interaction,” J. Opt. Soc. Am. B **16**, 2223–2232 (1999). [CrossRef]

*N*-soliton fission. Of critical importance in this section is the role that asymmetric phase variations, generated, for instance, by the Raman effect, play in the fission process. Section 3 builds on the insights of Sec. 2 and makes connection between the MI observed with CW light to the

*N*-soliton fission dynamics. The key observation is made that the

*N*-soliton energy, which ultimately determines the soliton fission, can be controlled via dispersion management. A brief summary and conclusion is provided in Sec. 4.

## 2. N-soliton Fission

*N*-soliton fission. Special emphasis will be given to the

*N*-soliton dynamics under the influence of the Raman effect. However, higher-order dispersion, self-steepening or pre-chirping all have a qualitatively similar effect. Ultimately, it is the fission process that is responsible for the generated supercontiuum.

*Q*is the normalized electric field envelope, the variable

*T*represents the physical time normalized by

*T*

_{0}/1.76 where

*T*

_{0}is the full-width half-maximum (FWHM) of an intial onesoliton pulse, and the variable

*Z*is the physical distance divided by the dispersion length

*Z*

_{0}=(2

*πc*)/(

*D̄*)(

*T*

_{0}/1.76)

^{2}where

*D̄*is the average dispersion of the signal field. This gives a peak field power of a one-soliton solution of the NLS to be |

*E*

_{0}|

^{2}=(

*λ*

_{0}

*A*

_{eff})/(2

*πn2Z*

_{0}) where

*n*

_{2}=2.6×10

^{-16}cm

^{2}/W is the nonlinear coefficient in the fiber,

*A*

_{eff}=11

*μ*m

^{2}is the cross-sectional area of the HNLF fiber, and

*λ*

_{0}=1.554

*µ*m and c are the free-space wavelength and speed of light respectively. Finally,

*τ*=

*T*

_{R}

*/T*

_{0}where

*T*

_{R}=1-5 femtoseconds is the response time of the Raman effect.

*N*-soliton

*Q*(0,

*T*)=

*N*sech

*T*where

*N*≫1. Thus the nonlinear term is

*O*(

*N*

^{2}) larger than the dispersive term and dominates the dynamics, i.e. the zero-dispersion limit [12, 13

13. J. C. Bronski, “Semiclassical eigenvalue distribution of the Zakharov-Shabat eigenvalue problem,” Physica D **97**, 376–397 (1996). [CrossRef]

14. J. C. Bronski and J. N. Kutz, “Numerical simulation of the semiclassical limit of the focusing nonlinear Schrodinger equation,” Phys. Lett. A **254**, 325 (1999). [CrossRef]

15. D. Krylov, L. Leng, K. Bergman, J. C. Bronski, and J. N. Kutz, “Observation of the breakup of a pre-chirped N-soliton in an optical fiber,” Opt. Lett. **24**, 1191–1193 (1999). [CrossRef]

*N*-soliton:

*i∂Q*/

*∂Z*+[2

*N*

^{2}τsech2

*T*tanh

*T*]

*Q*=0 which has the solution

*N*

^{2}≫1, the phase profile generated is large and asymmetric. It is known that a large, symmetric phase splits the eigenvalue spectrum associated with the semi-classical NLS like a

*zipper*[13

**97**, 376–397 (1996). [CrossRef]

**254**, 325 (1999). [CrossRef]

15. D. Krylov, L. Leng, K. Bergman, J. C. Bronski, and J. N. Kutz, “Observation of the breakup of a pre-chirped N-soliton in an optical fiber,” Opt. Lett. **24**, 1191–1193 (1999). [CrossRef]

*λ*

_{n}=

*k*

_{n}+

*iη*

_{n}. The relationship between the eigenvalues and the fundamental 1-solitons contained in a given

*N*-soliton is given by [20, 21

21. S. Friberg and K. Delong, “Breakup of bound higher-order solitons,” Opt. Lett. **17**, 979–981 (1992). [CrossRef] [PubMed]

*k*

_{n}determines the ejection velocity while the imaginary part

*η*

_{n}determines the ejected soliton pulse height and width. Figure 2 demonstrates the qualitative distribution of the eigenvalue spectrum for an

*N*-soliton with and without phase chirp [13

**97**, 376–397 (1996). [CrossRef]

*k*

_{n}begins the ejection process since it determines the group velocity for the fundamental solitons of Eq. (4). Additionally, to achieve the maximal amount of supercontinuum generation, a large value of

*η*

_{n}is desired. This is strictly controlled by the

*N*-soliton considered, i.e.

*η*

_{n}scales with

*N*so that the larger the

*N*-soliton the shorter (spectrally broader) the ejected solitons. For the Raman case considered here, a large asymmetric chirp is generated for

*N*-soliton initial data which is capable of splitting the spectrum like a zipper in an asymmetric fashion. The ejected solitons are now ultra-short femtosecond solitons which are broad in the spectral domain. Soliton ejection due to asymmetric perturbations has also been observed experimentally [21

21. S. Friberg and K. Delong, “Breakup of bound higher-order solitons,” Opt. Lett. **17**, 979–981 (1992). [CrossRef] [PubMed]

*N*-soliton. A

*T*

_{0}=1 ps soliton pulse is considered with cavity dispersion

*D̄*=0.1 ps/(km-nm) and Raman response time of

*T*

_{R}=3 fs. Figures 3 illustrates the time domain evolution along with the spectral evolution over 1.4 kilometers of HNLF for an initial

*N*=5 soliton. The higher the

*N*value, the further into the semi-classical regime and the broader the spectrum. Indeed, the resulting pulse width for the narrowest one-soliton ejected is ≈600,250,100 and 40 fs for

*N*=2,4,6 and 8 respectively. Thus, the hallmark feature of the dynamics is the asymmetric ejection of ultra-short one-solitons from the inital

*N*-soliton data. Further, it shows that the larger the initial

*N*-soliton energy (∫

^{∞}

_{−∞}|

*Q*|

^{2}

*dT*=2

*N*

^{2}) the narrower the ejected pulses. This is critical in using dispersion management to enhance the supercontinuum generation. Further, since the asymmetric phase variation, such as that given by Eq. (3), drives the ultra-short one-soliton ejection process, it shows that strong pre-chirping can also be used to help enhance the spectral broadening. This may be difficult to achieve for CW light, but can be accomplished with pulses [15

**24**, 1191–1193 (1999). [CrossRef]

## 3. CWModulational Instability and N-soliton Fission

*D̄*=0.1 ps/(km-nm) and

*D̄*=1 ps/(km-nm). The resulting modulations are consistent with the theoretical predictions for the MI instability [11]. Of importance is the energy captured in each

*modulation cell*. For this specific example, the modulational cells capture energies of ≈0.2 pJ Fig. 4(top) and ≈1.6 pJ Fig. 4(bottom) respectively. In general, the modulation cell energy is simply the product of the dominant modulation period [11] (

*P*

_{0}), i.e.

*N*-soliton and some dispersive radiation [13

**97**, 376–397 (1996). [CrossRef]

**254**, 325 (1999). [CrossRef]

*N*-soliton, leading to ultra-short pulse formation and enhanced supercontinuum generation. The basic supercontinuum dynamics and experimental configuration, which includes a concatenation of high dispersion fiber followed by low dispersion fiber, is depicted in Fig. 1. Note that for pulsed femtosecond supercontinuum generation, the modulation cell is pre-determined by the launched pulse energy. For the CW case, it is the MI which is responsible for generating the pulsed structure which is then spectrally broadened.

*T*

_{R}=3 fs. Although many effects are neglected, i.e. linear attenuation, higher-order dispersion, self-steepening, and discrete signal-stokes coupling, the critical issue here is to demonstrate the fundamental phenomena illustrated in Figs. 1, 3 and 4. To observe the supercontinuumgenerated via dispersion management, we propagate again over 7 km. But in this case, the first five kilometers are a dispersion-shifted HNLF with

*D̄*=5 ps/(km-nm). Note that the launched CW light is seeded with a small amount of white-noise (≈50 dB lower than the launched signal) in order to more accurately model experiments and induce MI. Further note that dispersion tapering of a fiber may be an equivalently efficient method for performing the necessary dispersion management. Figure 5 demonstrates the evolution of the pulse over 7 km with and without dispersion management. In the case of no dispersion management the resulting FWHM pulse train is on the order of picoseconds. In contrast, the case of dispersion management results in FWHM pulses on the order of femtoseconds, demonstrating the enhanced ultra-short pulse generation. Figure 6 (light line) demonstrates the ≈60 nm supercontinuum generated in the HNLF fiber for

*D̄*=0.2 ps/(km-nm). The enhanced supercontinuum is shown in Fig. 6 (bold line). The moderate amount of dispersion-management gives more than four times the spectral width, which is a significant improvement in the supercontinuumgeneration. To further enhance the broadening, higher dispersion fiber can be used in the first segment to increase the modulation cell, further enhancing in the supercontinuum. Note that simulations of Eq. (1) operating closer to the zero-dispersion point or for much stronger dispersion maps require significant computational resources in order to avoid numerical high-frequency instabilities. In the simulations, care must also be taken to ensure that the periodic boundary conditions imposed by the pseudo-spectral split-step technique do not generate any numerical artifacts. Specifically, the computational domain is taken to be large enough so that the observed dynamics is independent of the computational window. Thus as the domain is increased the solution converges to a domain independent solution in both the time- and Fourier-domain.Note that for illustrative purposes only, Figs. 4 and 5 show a magnified view of the time-domain evolution.

*β*is the normalized third-order dispersion, G is the normalized attenuation, and σ measures the normalized self-steepening response [11]. Simulations which include the additional terms show only minor qualitative differences from the spectral broadening which occurs from the simulations of Eq. (1) alone, i.e. the qualitative predictions and spectral broadening made previously are unaltered by the inclusion of these additional terms. Indeed, numerous studies which include some or all of these terms [16

16. 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]

17. 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]

18. K. Tai, A. Hasegawa, and N. Bekki, “Fission of optical solitons induced by stimulated Raman effect,” Opt. Lett. **13**, 392–394 (1988). [CrossRef] [PubMed]

19. H. Kubota, K. Tamura, and M. Nakazawa, “Analyses of coherence-maintained ultrashort optical pulse trains and supercontinuum generation in the presence of soliton-amplified spontaneous-emission interaction,” J. Opt. Soc. Am. B **16**, 2223–2232 (1999). [CrossRef]

16. 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]

17. 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]

18. K. Tai, A. Hasegawa, and N. Bekki, “Fission of optical solitons induced by stimulated Raman effect,” Opt. Lett. **13**, 392–394 (1988). [CrossRef] [PubMed]

19. H. Kubota, K. Tamura, and M. Nakazawa, “Analyses of coherence-maintained ultrashort optical pulse trains and supercontinuum generation in the presence of soliton-amplified spontaneous-emission interaction,” J. Opt. Soc. Am. B **16**, 2223–2232 (1999). [CrossRef]

## 4. Conclusions

**97**, 376–397 (1996). [CrossRef]

**254**, 325 (1999). [CrossRef]

**24**, 1191–1193 (1999). [CrossRef]

21. S. Friberg and K. Delong, “Breakup of bound higher-order solitons,” Opt. Lett. **17**, 979–981 (1992). [CrossRef] [PubMed]

## Acknowledgments

## References and links

1. | 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 |

2. | G. Genty, M. Lehtonen, H. Ludvigsen, J. Broeng, and M. Kaivola, “Spectral broadening of femtosecond pulses into continuum radiation in microstructured fibers,” Opt. Express |

3. | A. K. Abeeluck, C. Headley, and C. G. Jørgensen, “High-power supercontinuum generation in highly nonlinear, dispersion-shifted fibers by use of a continuous-wave Raman fiber laser,” Opt. Lett. |

4. | A. K. Abeeluck and C. Headley, “Supercontinuum growth in a highly nonlinear fiber with a low-coherence semiconductor laser diode,” App. Phys. Lett. |

5. | A. Mussot, E. Lantz, H. Maillotte, and T. Sylvestre, “Spectral broadening of a partially coherent CW laser beam in single-mode optical fibers,” Opt. Express |

6. | J. D. Harvey, R. Leonhardt, S. Coen, G. Wong, J. Knight, W. J. Wadsworth, and P. St. J. Russell, “Scalar modulational instability in the normal dispersion regime by use of photonic crystal fiber,” Opt. Lett. |

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

8. | E. Golovchenko, P. Mamyshev, A. Pilipetskii, and E. A. Dianov, “Mutual Influence of the Parametric Effects and Stimulated Raman Scattering in Optical Fibers,” IEEE J. Quant. Elec. |

9. | J. K. Ranka, R. S. Windeler, and A. J. Stentz, “Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm,” Opt. Lett. |

10. | T. Hori, J. Takayanagi, N. Nishizawa, and T. Goto, “Flatly broadened, wideband and low noise supercontinuum generation in highly nonlinear hybrid fiber,” Opt. Express |

11. | G. P. Agrawal, |

12. | A. Hasegawa and Y. Kodama, |

13. | J. C. Bronski, “Semiclassical eigenvalue distribution of the Zakharov-Shabat eigenvalue problem,” Physica D |

14. | J. C. Bronski and J. N. Kutz, “Numerical simulation of the semiclassical limit of the focusing nonlinear Schrodinger equation,” Phys. Lett. A |

15. | D. Krylov, L. Leng, K. Bergman, J. C. Bronski, and J. N. Kutz, “Observation of the breakup of a pre-chirped N-soliton in an optical fiber,” Opt. Lett. |

16. | A. V. Husakou and J. Herrmann, “Supercontinuum Generation of Higher-Order Solitons by Fission in Photonic Crystal Fibers,” Phys. Rev. Lett. |

17. | 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. |

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

19. | H. Kubota, K. Tamura, and M. Nakazawa, “Analyses of coherence-maintained ultrashort optical pulse trains and supercontinuum generation in the presence of soliton-amplified spontaneous-emission interaction,” J. Opt. Soc. Am. B |

20. | V. E. Zakharov and A. B. Shabat, “Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media,” Sov. Phys. JETP |

21. | S. Friberg and K. Delong, “Breakup of bound higher-order solitons,” Opt. Lett. |

**OCIS Codes**

(060.7140) Fiber optics and optical communications : Ultrafast processes in fibers

(190.5650) Nonlinear optics : Raman effect

**ToC Category:**

Research Papers

**History**

Original Manuscript: April 5, 2005

Revised Manuscript: May 13, 2005

Published: May 30, 2005

**Citation**

J. Nathan Kutz, C Lyngå, and B. Eggleton, "Enhanced Supercontinuum Generation through Dispersion-Management," Opt. Express **13**, 3989-3998 (2005)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-11-3989

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### References

- 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]
- G. Genty, M. Lehtonen, H. Ludvigsen, J. Broeng, and M. Kaivola, �??Spectral broadening of femtosecond pulses into continuum radiation in microstructured fibers,�?? Opt. Express 10, 1083-1098 (2002). [PubMed]
- A. K. Abeeluck, C. Headley, and C. G. Jørgensen, �??High-power supercontinuum generation in highly nonlinear, dispersion-shifted fibers by use of a continuous-wave Raman fiber laser,�?? Opt. Lett. 29, 2163-2165 (2004). [CrossRef] [PubMed]
- A. K. Abeeluck and C. Headley, �??Supercontinuum growth in a highly nonlinear fiber with a low-coherence semiconductor laser diode,�?? App. Phys. Lett. 85, 4863 (2004). [CrossRef]
- A. Mussot, E. Lantz, H. Maillotte, and T. Sylvestre, �??Spectral broadening of a partially coherent CW laser beam in single-mode optical fibers,�?? Opt. Express 12 2838 (2004). [CrossRef] [PubMed]
- J. D. Harvey, R. Leonhardt, S. Coen, G.Wong, J. Knight, W. J.Wadsworth, P. St. J. Russell, �??Scalar modulational instability in the normal dispersion regime by use of photonic crystal fiber,�?? Opt. Lett. 28, 2225-2227 (2003). [CrossRef] [PubMed]
- A. Demircan and U. Bandelow, �??Supercontinuum generation by the modulation instability,�?? Opt. Comm. 244, 244-185 (2005). [CrossRef]
- E. Golovchenko, P. Mamyshev, A. Pilipetskii, E. A. Dianov, �??Mutual Influence of the Parametric Effects and Stimulated Raman Scattering in Optical Fibers,�?? IEEE J. Quant. Elec. 26, 1815-1820 (1990). [CrossRef]
- J. K. Ranka, R. S. Windeler, and A. J. Stentz, �??Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm,�?? Opt. Lett. 25, 25-27 (2000). [CrossRef]
- T. Hori, J. Takayanagi, N. Nishizawa, and T. Goto, �??Flatly broadened, wideband and low noise supercontinuum generation in highly nonlinear hybrid fiber,�?? Opt. Express 12, 317-324 (2004). [CrossRef] [PubMed]
- G. P. Agrawal, Nonlinear Fiber Optics, 3rd Ed., Academic Press, San Diego, 2001.
- A. Hasegawa and Y. Kodama, Solitons in Optical Communications, Oxford University Press, 1995.
- J. C. Bronski, �??Semiclassical eigenvalue distribution of the Zakharov-Shabat eigenvalue problem,�?? Physica D 97, 376-397 (1996) [CrossRef]
- J. C. Bronski and J. N. Kutz, �??Numerical simulation of the semiclassical limit of the focusing nonlinear Schrodinger equation ,�?? Phys. Lett. A 254, 325 (1999). [CrossRef]
- D. Krylov, L. Leng, K. Bergman, J. C. Bronski, and J. N. Kutz, �??Observation of the breakup of a pre-chirped N-soliton in an optical fiber,�?? Opt. Lett. 24, 1191-1193 (1999). [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. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P St. J. Russell, G. Korn, �??Experimental Evidence for Supercontinuum Generation by Fission of Higher-Order Solitons in Photonic Fibers,�?? Phys. Rev. Lett. 88, 173901 (2002) [CrossRef] [PubMed]
- K. Tai, A. Hasegawa, and N. Bekki, �??Fission of optical solitons induced by stimulated Raman effect,�?? Opt. Lett. 13, 392-394 (1988). [CrossRef] [PubMed]
- H. Kubota, K. Tamura, M. Nakazawa, �??Analyses of coherence-maintained ultrashort optical pulse trains and supercontinuum generation in the presence of soliton-amplified spontaneous-emission interaction,�?? J. Opt. Soc. Am. B 16, 2223-2232 (1999). [CrossRef]
- V. E. Zakharov and A. B. Shabat, �??Exact theory of two-dimensional self-focusing and one-dimensional selfmodulation of waves in nonlinear media,�?? Sov. Phys. JETP 34, 62-69 (1972).
- S. Friberg and K. Delong, �??Breakup of bound higher-order solitons,�?? Opt. Lett. 17, 979-981 (1992). [CrossRef] [PubMed]

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