## Narrowband supercontinuum control using phase shaping

Optics Express, Vol. 14, Issue 26, pp. 13142-13150 (2006)

http://dx.doi.org/10.1364/OE.14.013142

Acrobat PDF (128 KB)

### Abstract

We study theoretically, numerically and experimentally the effect of self-phase modulation of ultrashort pulses with spectrally narrow phase features. We show that spectral enhancement and depletion is caused by changing the relative phase between the initial field and the nonlinearly generated components. Our theoretical results explain observations of supercontinuum enhancement by fiber Bragg gratings, and predict similar enhancements for spectrally shaped pulses in uniform fiber. As proof of principle, we demonstrate this effect in the laboratory using a femtosecond pulse shaper.

© 2006 Optical Society of America

## 1. Introduction

2. I. Hartl, X. D. Li, C. Chudoba, R. K. Ghanta, T. H. Ko, J. G. Fujimoto, J. K. Ranka, and R. S. Windeler, “Ultrahigh-resolution optical coherence tomography using continuum generation in an air silica microstructure optical fiber,” Opt. Lett. **26**, 608–610 (2001). [CrossRef]

3. A. S. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T.W. Hansch, “Direct Link between Microwave and Optical Frequencies with a 300 THz Femtosecond Laser Comb,” Phys. Rev. Lett. **84**, 5102–5105 (2000). [CrossRef] [PubMed]

4. K. Mori, T. Morioka, and M. Saruwatari, “Group-velocity dispersion measurement using supercontinuum picosecond pulses generated in an optical-fiber,” Electron. Lett. **29**, 987–989 (1993). [CrossRef]

5. 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]

6. D. Türke, W. Wohlleben, J. Teipel, M. Motzkus, B. Kibler, J. Dudley, and H. Giessen, “Chirp-controlled soliton fission in tapered optical fibers,” Appl. Phys. B **83**, 37–42 (2006). [CrossRef]

7. S. Xu, D. Reitze, and R. Windeler, “Controlling nonlinear processes in microstructured fibers using shaped pulses,” Opt. Express **12**, 4731–4741 (2004). [CrossRef] [PubMed]

8. M. Tianprateep, J. Tada, T. Yamazaki, and F. Kannari, “Spectral-Shape-Controllable Supercontinuum Generation in Microstructured Fibers Using Adaptive Pulse Shaping Technique,” Japanese J. of Appl. Phys. **43**, 8059–8063 (2004). [CrossRef]

9. P. S. Westbrook, J. W. Nicholson, K. S. Feder, and A. D. Yablon, “Improved supercontinuum generation through UV processing of highly nonlinear fibers,” J. Lightwave Technol. **23**, 13–18 (2005). [CrossRef]

10. J. C. Travers, R. E. Kennedy, S. V. Popov, J. R. Taylor, H. Sabert, and B. Mangan, “Extended continuous-wave supercontinuum generation in a low-water-loss holey fiber,” Opt. Lett. **30**, 1938–1940 (2005). [CrossRef] [PubMed]

11. F. Lu, Y. Deng, and W. Knox, “Generation of broadband femtosecond visible pulses in dispersion-micromanaged holey fibers,” Opt. Lett. **30**, 1566–1568 (2005). [CrossRef] [PubMed]

12. P. S. Westbrook, J. W. Nicholson, K. S. Feder, Y. Li, and T. Brown, “Supercontinuum generation in a fibre grating,” Appl. Phys. Lett. **85**, 4600–4602 (2004). [CrossRef]

13. K. Kim, S. A. Diddams, P. S. Westbrook, J. W. Nicholson, and K. S. Feder, “Improved stabilization of a 1.3 *µm* femtosecond optical frequency comb by use of a spectrally tailored continuum from a nonlinear fiber grating,” Opt. Lett. **31**, 277–279 (2006). [CrossRef] [PubMed]

14. Y. Li, F. C. Salisbury, Z. Zhu, T. G. Brown, P. S. Westbrook, K. S. Feder, and R. S. Windeler, “Interaction of supercontinuum and Raman solitons with microstructure fiber gratings,” Opt. Express **13**, 998–1007 (2005). [CrossRef] [PubMed]

15. P. S. Russell, “Bloch Wave Analysis of Dispersion and Pulse-Propagation in Pure Distributed Feedback Structures,” J. Mod. Opt. **38**, 1599–1619 (1991). [CrossRef]

## 2. Nonlinear pulse propagation in Bragg grating

16. P. Westbrook and J. Nicholson, “Perturbative approach to continuum generation in a fiber Bragg grating,” Opt. Express **14**, 7610–7616 (2006). [CrossRef] [PubMed]

16. P. Westbrook and J. Nicholson, “Perturbative approach to continuum generation in a fiber Bragg grating,” Opt. Express **14**, 7610–7616 (2006). [CrossRef] [PubMed]

16. P. Westbrook and J. Nicholson, “Perturbative approach to continuum generation in a fiber Bragg grating,” Opt. Express **14**, 7610–7616 (2006). [CrossRef] [PubMed]

**14**, 7610–7616 (2006). [CrossRef] [PubMed]

17. C.-M. Chen and P. L. Kelley, “Nonlinear pulse compression in optical fibers: scaling laws and numerical analysis,” J. Opt. Soc. Am. B **19**, 1961–1967 (2002). [CrossRef]

12. P. S. Westbrook, J. W. Nicholson, K. S. Feder, Y. Li, and T. Brown, “Supercontinuum generation in a fibre grating,” Appl. Phys. Lett. **85**, 4600–4602 (2004). [CrossRef]

13. K. Kim, S. A. Diddams, P. S. Westbrook, J. W. Nicholson, and K. S. Feder, “Improved stabilization of a 1.3 *µm* femtosecond optical frequency comb by use of a spectrally tailored continuum from a nonlinear fiber grating,” Opt. Lett. **31**, 277–279 (2006). [CrossRef] [PubMed]

15. P. S. Russell, “Bloch Wave Analysis of Dispersion and Pulse-Propagation in Pure Distributed Feedback Structures,” J. Mod. Opt. **38**, 1599–1619 (1991). [CrossRef]

18. B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, “Bragg Grating Solitons,” Phys. Rev. Lett. **76**, 1627–1630 (1996). [CrossRef] [PubMed]

*A*(

*ω*′,

*z*) is the Fourier transform of the field envelope,

*β*

_{T}(

*ω*) the transformed wavenumber,

*γ*=80W

^{-1}km

^{-1}is the fiber’s nonlinear coefficient and

*B*(

*ω*′,

*z*)=FT[|

*A*(

*T*,

*z*)|

^{2}

*A*(

*T*,

*z*)] is the Fourier transform of the usual self-phase modulation term, where

*T*is retarded time. Bandgap reflection is ignored for reasons discussed below. In this frame,

*ω*′=

*ω*-

*ω*

_{0}is the frequency relative to the carrier

*ω*

_{0}. The transformed wavenumber is

*β*(

*ω*) and

*β*

_{F}(

*ω*) are the wavenumbers with and without the grating. Equation (2) transforms

*β*(

*ω*) from the laboratory frame to a comoving frame with the phase and group velocity of the uniform fibre at

*ω*

_{0}- we do not wish to “transform away” the grating dispersion. The grating is modeled as a 1-D photonic bandgap [15

15. P. S. Russell, “Bloch Wave Analysis of Dispersion and Pulse-Propagation in Pure Distributed Feedback Structures,” J. Mod. Opt. **38**, 1599–1619 (1991). [CrossRef]

*λ*

_{B}. In the chosen frame,

*β*

_{T}=0 away from the bandgap,

*β*

_{T}<0 for

*λ*<

*λ*

_{B}, since

*β*<

*β*

_{F}, and

*β*

_{T}>0 for

*λ*>

*λ*

_{B}since

*β*>

*β*

_{F}. We ignore background fiber dispersion because of the short propagation lengths under consideration.

*et al.*[14

14. Y. Li, F. C. Salisbury, Z. Zhu, T. G. Brown, P. S. Westbrook, K. S. Feder, and R. S. Windeler, “Interaction of supercontinuum and Raman solitons with microstructure fiber gratings,” Opt. Express **13**, 998–1007 (2005). [CrossRef] [PubMed]

*λ*

_{B}=950 nm and coupling strength κ=600 m

^{-1}, and pulse duration

*T*

_{FWHM}=150 fs and centre wavelength

*λ*

_{0}=945 nm. The pulse bandwidth (6.3 nm) considerably exceeds that of the grating (0.7 nm), so only a small fraction of the pulse energy is affected, justifying the absence of the bandgap reflection in Eq. (1). At the bandgap edges the transformed wavenumber is ±

*κ*, so the typical grating length scale

*L*

_{G}=1/

*κ*=1.67 mm is much smaller than the nonlinear length

*L*

_{NL}=1/(

*γP*

_{0})=25 mm where

*P*

_{0}=0.5 kW is the pulse peak power.

*z*/

*L*

_{NL}; equivalently we assume

*z*≪

*L*

_{NL}. Whilst this may seem overly restrictive, we show that much of the essential physics can be explained by this simple model. We then write

*A*

_{NL}(

*ω*′,

*z*) the nonlinear contribution correct to first order in

*z*/

*L*

_{NL}. Without the grating, the nonlinearity causes self-phase modulation (SPM). The equivalent frequency domain description of SPM is intrapulse four-wave mixing (FWM) between all energy conserving frequency combinations in the pulse spectrum

*A*

_{L}(

*ω*′,

*z*). Hence the second simplification: since the FWM contribution at frequency

*ω*′ results from the many mixing processes just described, the spectrally narrow effect of the grating on

*A*

_{NL}(

*ω*′,

*z*) is small. Alternatively the spectrally narrow feature is broad and weak in time, lacking nonlinear effect. By ignoring the grating’s effect on the FWM, the nonlinear term

*B*(

*ω*,

*z*), which drives

*A*

_{NL}(

*ω*′,

*z*), can be evaluated at

*z*=0.

*A*

_{L}(

*ω*′,

*z*) terms remain in the nonlinear driving term, which by the second assumption can be evaluated at

*z*=0. We obtain

*A*

_{NL}(

*ω*′,

*z*) in the initial stages of propagation i.e.

*z*≪

*L*

_{G}; equivalently we ignore grating dispersion of the nonlinear terms. This additional assumption is not intrinsic to our formalism and is only required for the simple argument which follows. In this limit, Eq. (6) reduces to

*T*=0, so ∠

*A*(

*ω*′, 0)=∠B(

*ω*′, 0)=0. Thus ∠

*A*

_{L}(

*ω*′,

*z*)=

*β*

_{T}(

*ω*)

*z*and from Eq. (7), ∠

*A*

_{NL}(

*ω*′,

*z*)=

*π*/2, leading to the simple vector construction in Fig. 2. For

*λ*<

*λ*

_{B},

*β*

_{T}(

*ω*)<0 and the resultant vector is shortened, corresponding to a depletion of the spectrum, whereas for

*λ*>

*λ*

_{B},

*β*

_{T}(

*ω*)>0 leading to an enhancement. By rotating the spectral phase for a narrow wavelength range without changing the nonlinear processes, therefore, the grating alters the phase angle between the original field at a frequency, and the nonlinearly generated field at that same frequency, thereby changing the vector sum.

**14**, 7610–7616 (2006). [CrossRef] [PubMed]

*z*≪

*L*

_{G}, the analogous result in Ref. [16

**14**, 7610–7616 (2006). [CrossRef] [PubMed]

**14**, 7610–7616 (2006). [CrossRef] [PubMed]

*z*≪

*L*

_{NL}, and transform limited pulses. In return, however, we provide the simple physical interpretation described above, and show that the sign of the interference depends only on the sign of the transformed wavenumber.

*z*>

*L*

_{G}. Combining Eqs (3), (4) and (6) we obtain

*β*outside the bandgap is shown in Fig. 3(a). The sign of the

_{T}*β*

_{T}(

*ω*) term in the numerator determines whether Eq. (8) corresponds to enhancement or depletion. We shall “approach” the bandgap from the long wavelength side, where

*β*

_{T}(

*ω*)>0 and enhancement occurs. As expected, well away from the bandgap there is no spectral modulation owing to the rapid falloff of the transformed wavenumber. Moving closer,

*β*

_{T}(

*ω*) begins to increase monotically and hence the sin

^{2}argument in Eq. (8) increases. For small

*β*

_{T}(

*ω*)

*z*(e.g. at 950.5 nm), an enhancement proportional to

*z*

^{2}is observed. Closer to the bandgap, however,

*β*

_{T}(

*ω*)

*z*>1 and the oscillatory behaviour of the sine term in Eq. (8) becomes important. The enhancement goes through a maximum where

*β*

_{T}(

*ω*)

*z*≈

*π*. (The relation is not exact because of the

*β*

_{T}(

*ω*) term in the denominator of Eq. (8)). The enhancement peak therefore moves to longer wavelengths with increasing

*z*. Even closer to the bandedge, fine spectral fringes appear since

*β*

_{T}(

*ω*)

*z*>2

*π*. However, because of the large

*β*

_{T}(

*ω*) term in the numerator of Eq. (8), the amplitude of these fringes is very small. Published experimental spectra have suggested the presence of fine fringes [12

12. P. S. Westbrook, J. W. Nicholson, K. S. Feder, Y. Li, and T. Brown, “Supercontinuum generation in a fibre grating,” Appl. Phys. Lett. **85**, 4600–4602 (2004). [CrossRef]

14. Y. Li, F. C. Salisbury, Z. Zhu, T. G. Brown, P. S. Westbrook, K. S. Feder, and R. S. Windeler, “Interaction of supercontinuum and Raman solitons with microstructure fiber gratings,” Opt. Express **13**, 998–1007 (2005). [CrossRef] [PubMed]

*L*=30 mm. The approximation begins to break down for

*z*>

*L*

_{NL}as second-order nonlinear effects begin to dominate.

**14**, 7610–7616 (2006). [CrossRef] [PubMed]

**14**, 7610–7616 (2006). [CrossRef] [PubMed]

**14**, 7610–7616 (2006). [CrossRef] [PubMed]

## 3. Nonlinear pulse propagation with arbitrary narrow phase feature

*ϕ*(

*ω*)=

*β*

_{T}(

*ω*)

*L*at

*z*=0 mm. This means that the two roles played by the grating in the process, namely the inscription of a phase feature, and providing the medium for nonlinear propagation, can be separated. In other words, the process is equivalent to inscribing a spectral feature, by whatever means, followed by self-phase modulation in a fiber. Since this insight allows the two elements to be selected and optimized independently, it broadens the possible application of this process.

*A*(

*ω*′, 0

^{-}) is the transform limited pulse before the phase discontinuity. Since we are ignoring fibre dispersion and the phase feature has been incorporated into the initial condition, we solve Eq. (1) with

*β*

_{T}(

*ω*)=0. As with the previous section, we work to first order in

*z*/

*L*

_{NL}. However, whereas before we ignored the grating’s influence on the nonlinear contribution, here we ignore the effect of the phase filter instead. This enables us to evaluate the nonlinear driving term at

*z*=0- i.e. with a transform limited pulse, and we obtain

*L*=30 mm. Compared with Eq. (8), the fringes are larger close to the bandgap because Eq. (11) does not have the large phase term in the denominator. Also, the sign of the effect (enhancement or depletion) is now determined by the sign of sin Δ

*ϕ*(

*ω*) rather than simply

*β*

_{T}(

*ω*) as in Eq. (8). Physically, both of these differences correspond to the entire grating phase

*β*

_{T}(

*ω*)

*L*being pre-applied at

*z*=0 mm, before any nonlinear components are generated, rather than continuously throughout the propagation. Besides this, the two curves are qualitatively similar.

*prior to*propagation through a nonlinear medium. The experiment described in the following section tests such a scenario. We note that the application of spectrally narrow amplitude features, followed by self-phase modulation was earlier considered by Präkelt

*et al.*[19

19. A. Präkelt, M. Wollenhaupt, C. Sarpe-Tudoran, A. Assion, and T. Baumerta, “Filling a spectral hole via self-phase modulation,” Appl. Phys. Lett. **87**, 121113 (2005). [CrossRef]

## 4. Experiment

*λ*

_{0}=778 nm from a modelocked Ti:Sapph laser using a 4-

*f*femtosecond pulse shaper [20

20. A. M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum. **71**, 1929 (2000). [CrossRef]

*D*=50 mm,

*f*=200 mm) onto the Fourier plane. A transparent phase mask in the Fourier plane imparts a phase profile Δ

*ϕ*(

*ω*), then a second lens and grating pair recollimate the beam which is coupled into 4.5 m of small core PCF (Crystal Fibre NL-1.8-750) with measured zero dispersion wavelength

*λ*

_{ZD}=760 nm and manufacturer specified nonlinearity

*γ*=99 W

^{-1}km

^{-1}. The output is spectrally resolved on an optical spectrum analyser. Our phase mask was a

*d*=92

*µ*m thick piece of polished BK7 glass, which was rotated to adjust the effective thickness and hence phase delay within a range equivalent to 74–80 wavelengths at a wavelength

*λ*

_{D}=778 nm.

*L*

_{NL}=0.7 m.Without the phase mask, SPM has only a small effect. With a phase delay such that sin Δ

*ϕ*=1, a 5 dB enhancement is observed as predicted by Eq. (11), whilst a corresponding depletion is seen for sin Δ

*ϕ*=-1. Across the width of the feature Δ

*λ*=1.7 nm, the enhancement is not uniform; because of the wavelength dependent phase delay (

*ϕ*∝2

*π*/

*λ*) the relatively large thickness produces a perceptible change in phase over the spectral feature. Material dispersion also plays a small role in the asymmetry. Figure 6(b) shows the spectral intensity at

*λ*

_{D}from a series of spectra taken with varying delay. As predicted in Eq. (11), sinusoidal dependence on Δ

*ϕ*with period 2

*π*is observed.

## 5. Discussion

*et al.*[14

**13**, 998–1007 (2005). [CrossRef] [PubMed]

**14**, 7610–7616 (2006). [CrossRef] [PubMed]

*et al.*[19

19. A. Präkelt, M. Wollenhaupt, C. Sarpe-Tudoran, A. Assion, and T. Baumerta, “Filling a spectral hole via self-phase modulation,” Appl. Phys. Lett. **87**, 121113 (2005). [CrossRef]

*et al.*[14

**13**, 998–1007 (2005). [CrossRef] [PubMed]

20. A. M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum. **71**, 1929 (2000). [CrossRef]

*et al.*However, their work, in which the self-phase modulation occurs in a water jet, was not conducted in the context of fiber supercontinuum generation.

## References and links

1. | R. R. Alfano, |

2. | I. Hartl, X. D. Li, C. Chudoba, R. K. Ghanta, T. H. Ko, J. G. Fujimoto, J. K. Ranka, and R. S. Windeler, “Ultrahigh-resolution optical coherence tomography using continuum generation in an air silica microstructure optical fiber,” Opt. Lett. |

3. | A. S. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T.W. Hansch, “Direct Link between Microwave and Optical Frequencies with a 300 THz Femtosecond Laser Comb,” Phys. Rev. Lett. |

4. | K. Mori, T. Morioka, and M. Saruwatari, “Group-velocity dispersion measurement using supercontinuum picosecond pulses generated in an optical-fiber,” Electron. Lett. |

5. | A. V. Husakou and J. Herrmann, “Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers,” Phys. Rev. Lett. |

6. | D. Türke, W. Wohlleben, J. Teipel, M. Motzkus, B. Kibler, J. Dudley, and H. Giessen, “Chirp-controlled soliton fission in tapered optical fibers,” Appl. Phys. B |

7. | S. Xu, D. Reitze, and R. Windeler, “Controlling nonlinear processes in microstructured fibers using shaped pulses,” Opt. Express |

8. | M. Tianprateep, J. Tada, T. Yamazaki, and F. Kannari, “Spectral-Shape-Controllable Supercontinuum Generation in Microstructured Fibers Using Adaptive Pulse Shaping Technique,” Japanese J. of Appl. Phys. |

9. | P. S. Westbrook, J. W. Nicholson, K. S. Feder, and A. D. Yablon, “Improved supercontinuum generation through UV processing of highly nonlinear fibers,” J. Lightwave Technol. |

10. | J. C. Travers, R. E. Kennedy, S. V. Popov, J. R. Taylor, H. Sabert, and B. Mangan, “Extended continuous-wave supercontinuum generation in a low-water-loss holey fiber,” Opt. Lett. |

11. | F. Lu, Y. Deng, and W. Knox, “Generation of broadband femtosecond visible pulses in dispersion-micromanaged holey fibers,” Opt. Lett. |

12. | P. S. Westbrook, J. W. Nicholson, K. S. Feder, Y. Li, and T. Brown, “Supercontinuum generation in a fibre grating,” Appl. Phys. Lett. |

13. | K. Kim, S. A. Diddams, P. S. Westbrook, J. W. Nicholson, and K. S. Feder, “Improved stabilization of a 1.3 |

14. | Y. Li, F. C. Salisbury, Z. Zhu, T. G. Brown, P. S. Westbrook, K. S. Feder, and R. S. Windeler, “Interaction of supercontinuum and Raman solitons with microstructure fiber gratings,” Opt. Express |

15. | P. S. Russell, “Bloch Wave Analysis of Dispersion and Pulse-Propagation in Pure Distributed Feedback Structures,” J. Mod. Opt. |

16. | P. Westbrook and J. Nicholson, “Perturbative approach to continuum generation in a fiber Bragg grating,” Opt. Express |

17. | C.-M. Chen and P. L. Kelley, “Nonlinear pulse compression in optical fibers: scaling laws and numerical analysis,” J. Opt. Soc. Am. B |

18. | B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, “Bragg Grating Solitons,” Phys. Rev. Lett. |

19. | A. Präkelt, M. Wollenhaupt, C. Sarpe-Tudoran, A. Assion, and T. Baumerta, “Filling a spectral hole via self-phase modulation,” Appl. Phys. Lett. |

20. | A. M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum. |

**OCIS Codes**

(190.4370) Nonlinear optics : Nonlinear optics, fibers

(190.4380) Nonlinear optics : Nonlinear optics, four-wave mixing

(230.1480) Optical devices : Bragg reflectors

(320.7140) Ultrafast optics : Ultrafast processes in fibers

**ToC Category:**

Ultrafast Optics

**History**

Original Manuscript: November 1, 2006

Revised Manuscript: December 8, 2006

Manuscript Accepted: December 8, 2006

Published: December 22, 2006

**Citation**

Dane R. Austin, Jeremy A. Bolger, C. Martijn de Sterke, Benjamin J. Eggleton, and Thomas G. Brown, "Narrowband supercontinuum control
using phase shaping," Opt. Express **14**, 13142-13150 (2006)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-26-13142

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### References

- R. R. Alfano, The supercontinuum laser source: fundamentals with updated references, 2nd ed. (Springer, New York, 2006).
- I. Hartl, X. D. Li, C. Chudoba, R. K. Ghanta, T. H. Ko, J. G. Fujimoto, J. K. Ranka, and R. S. Windeler, "Ultrahigh-resolution optical coherence tomography using continuum generation in an air silica microstructure optical fiber," Opt. Lett. 26, 608-610 (2001). [CrossRef]
- A. S. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T.W. Hansch, "Direct Link between Microwave and Optical Frequencies with a 300 THz Femtosecond Laser Comb," Phys. Rev. Lett. 84, 5102-5105 (2000). [CrossRef] [PubMed]
- K. Mori, T. Morioka, and M. Saruwatari, "Group-velocity dispersion measurement using supercontinuum picosecond pulses generated in an optical-fiber," Electron. Lett. 29, 987-989 (1993). [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]
- D. Türke, W. Wohlleben, J. Teipel, M. Motzkus, B. Kibler, J. Dudley, and H. Giessen, "Chirp-controlled soliton fission in tapered optical fibers," Appl. Phys. B 83, 37-42 (2006). [CrossRef]
- S. Xu, D. Reitze, and R. Windeler, "Controlling nonlinear processes in microstructured fibers using shaped pulses," Opt. Express 12, 4731-4741 (2004). [CrossRef] [PubMed]
- M. Tianprateep, J. Tada, T. Yamazaki, and F. Kannari, "Spectral-Shape-Controllable Supercontinuum Generation in Microstructured Fibers Using Adaptive Pulse Shaping Technique," Japanese J. of Appl. Phys. 43, 8059-8063 (2004). [CrossRef]
- P. S. Westbrook, J.W. Nicholson, K. S. Feder, and A. D. Yablon, "Improved supercontinuum generation through UV processing of highly nonlinear fibers," J. Lightwave Technol. 23, 13-18 (2005). [CrossRef]
- J. C. Travers, R. E. Kennedy, S. V. Popov, J. R. Taylor, H. Sabert, and B. Mangan, "Extended continuous-wave supercontinuum generation in a low-water-loss holey fiber," Opt. Lett. 30, 1938-1940 (2005). [CrossRef] [PubMed]
- F. Lu, Y. Deng, and W. Knox, "Generation of broadband femtosecond visible pulses in dispersion-micromanaged holey fibers," Opt. Lett. 30, 1566-1568 (2005). [CrossRef] [PubMed]
- P. S. Westbrook, J. W. Nicholson, K. S. Feder, Y. Li, and T. Brown, "Supercontinuum generation in a fibre grating," Appl. Phys. Lett. 85, 4600-4602 (2004). [CrossRef]
- K. Kim, S. A. Diddams, P. S. Westbrook, J. W. Nicholson, and K. S. Feder, "Improved stabilization of a 1.3 μm femtosecond optical frequency comb by use of a spectrally tailored continuum from a nonlinear fiber grating," Opt. Lett. 31, 277-279 (2006). [CrossRef] [PubMed]
- Y. Li, F. C. Salisbury, Z. Zhu, T. G. Brown, P. S. Westbrook, K. S. Feder, and R. S. Windeler, "Interaction of supercontinuum and Raman solitons with microstructure fiber gratings," Opt. Express 13, 998-1007 (2005). [CrossRef] [PubMed]
- P. S. Russell, "Bloch Wave Analysis of Dispersion and Pulse-Propagation in Pure Distributed Feedback Structures," J. Mod. Opt. 38, 1599-1619 (1991). [CrossRef]
- P. Westbrook and J. Nicholson, "Perturbative approach to continuum generation in a fiber Bragg grating," Opt. Express 14, 7610-7616 (2006). [CrossRef] [PubMed]
- C.-M. Chen and P. L. Kelley, "Nonlinear pulse compression in optical fibers: scaling laws and numerical analysis," J. Opt. Soc. Am. B 19, 1961-1967 (2002). [CrossRef]
- B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, "Bragg Grating Solitons," Phys. Rev. Lett. 76, 1627-1630 (1996). [CrossRef] [PubMed]
- A. Präkelt, M. Wollenhaupt, C. Sarpe-Tudoran, A. Assion, and T. Baumerta, "Filling a spectral hole via self-phase modulation," Appl. Phys. Lett. 87, 121113 (2005). [CrossRef]
- A. M. Weiner, "Femtosecond pulse shaping using spatial light modulators," Rev. Sci. Instrum. 71, 1929 (2000). [CrossRef]

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