## Tailoring the soliton and supercontinuum dynamics by engineering the profile of tapered fibers |

Optics Express, Vol. 18, Issue 19, pp. 20151-20163 (2010)

http://dx.doi.org/10.1364/OE.18.020151

Acrobat PDF (3905 KB)

### Abstract

We demonstrate by means of numerical simulations of the generalized Nonlinear Schrödinger Equation that the variation of the diameter of a tapered fiber along the fiber axis can be used as a new degree of freedom to tailor the spectrum generated by ultrashort laser pulses. We show that, apart from the cross-section geometry of the fiber and the materials used for the core, cladding, and surrounding medium, the diameter profile along the fiber axis crucially influences the soliton dynamics, the temporal and spectral evolution as well as the generation of a supercontinuum. As an example, we have investigated a few centimeters long conical waists, which reveal large differences of the output spectra depending on the incoupling direction. For a decreasing fiber diameter, we find that, keeping the pulse energy constant, a lower input peak power may generate a broader supercontinuum. We attribute this result to the dynamics of higher-order solitons. A comparison of the simulated spectra to experimentally measured ones shows excellent agreement.

© 2010 Optical Society of America

## 1. Introduction

1. T. A. Birks, W. J. Wadsworth, and P. St. J. Russell, “Supercontinuum generation in tapered fibers,” Opt. Lett. **25**, 1415–1417 (2000). [CrossRef]

*A*

_{eff}yielding a high nonlinearity described by the nonlinear parameter

*γ*, which is inversely proportional to

*A*

_{eff}. On the other hand, the dispersion of the fiber can be shifted such that the commonly used pump wavelengths lie in the anomalous dispersion regime [9

9. D. Mogilevtsev, T. A. Birks, and P. St. J. Russell, “Group-velocity dispersion in photonic crystal fibers,” Opt. Lett. **23**, 1662–1664 (1998). [CrossRef]

11. L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental Observation of Picosecond Pulse Narrowing and Solitons in Optical Fibers,” Phys. Rev. Lett. **45**, 1095–1098 (1980). [CrossRef]

12. A. Husakou and J. Herrmann, “Supercontinuum Generation of Higher-Order Solitons by Fission in Photonic Crystal Fibers,” Phys. Rev. Lett. **87**, 203901 (2001). [CrossRef] [PubMed]

13. G. Genty, S. Coen, and J. M. Dudley, “Fiber supercontinuum sources (Invited),” J. Opt. Soc. Am. B **24**, 1771–1785 (2007). [CrossRef]

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

15. P. St. J. Russell, “Photonic Crystal Fibers,” Science **17**, 358–362 (2003). [CrossRef]

16. S. Pricking and H. Giessen, “Tapering fibers with complex shape,” Opt. Express **18**, 3426–3437 (2010). [CrossRef] [PubMed]

17. R. Zhang, X. Zhang, D. Meiser, and H. Giessen, “Mode and group velocity dispersion evolution in the tapered region of a single-mode tapered fiber,” Opt. Express **12**, 5840–5849 (2004). [CrossRef] [PubMed]

18. S. V. Chernikov, E. M. Dianov, D. J. Richardson, and D. N. Payne, “Soliton pulse compression in dispersion-decreasing fiber,” Opt. Lett. **18**, 476–478 (1993). [CrossRef] [PubMed]

23. J. C. Travers, S. V. Popov, and J. R. Taylor, “Extended blue supercontinuum generation in cascaded holey fibers,” Opt. Lett. **30**, 3132–3134 (2005). [CrossRef] [PubMed]

## 2. Simulation method

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

24. E. C. Mӓgi, P. Steinvurzel, and B. J. Eggleton, “Tapered photonic crystal fibers,” Opt. Express **12**, 776–784 (2004). [CrossRef]

25. W. J. Wadsworth, A. Witkowska, S. G. Leon-Saval, and T. A. Birks, “Hole inflation and tapering of stock photonic crystal fibres,” Opt. Express **13**, 6541–6549 (2005). [CrossRef] [PubMed]

*A*is the envelope of the electric field,

*z*the propagation distance, and

*T*the time in the co-moving reference frame.

*D̂*denotes the dispersion operator as discussed later.

*γ*=

*n*

_{2}

*ω*

_{0}/(

*cA*

_{eff}) stands for the nonlinear parameter with

*n*

_{2}being the nonlinear index of refraction,

*ω*

_{0}the central frequency of the pulse,

*c*the vacuum speed of light and

*A*

_{eff}the effective mode area, which is also discussed below. The delayed response of the fiber material mainly due to the Raman effect is included by

*R*(

*t*). This response function is well known for fused silica [10] and can be parametrized as

*f*= 0.18 being the Raman fraction,

_{R}*τ*

_{1}= 12.2 fs, and

*τ*

_{2}= 32 fs. As a simplification, we neglect the influence of noise.

*µ*m and a cladding diameter of 125

*µ*m; the refractive index difference is 0.36%. As the surrounding medium we assume air. For an untapered fiber the light is guided as a core mode, and the influence of the cladding-air interface is negligible. This changes dramatically when the fiber is tapered down to cladding diameters of a few micrometers. Now the cladding mode is dominant and the cladding-air interface becomes important, whereas the impact of the core-cladding interface almost vanishes. To take this change into account, we derive the propagation constant

*β*, which is strongly connected to the dispersion coefficients

*β*via

_{k}17. R. Zhang, X. Zhang, D. Meiser, and H. Giessen, “Mode and group velocity dispersion evolution in the tapered region of a single-mode tapered fiber,” Opt. Express **12**, 5840–5849 (2004). [CrossRef] [PubMed]

*β*, which is solved numerically. The largest root corresponds to the propagation constant of the fundamental mode, which we use for the further calculations. This procedure delivers

*β*in dependence of the cladding diameter

*d*and the frequency

*ω*. Knowing

*β*, we can calculate the effective mode area, also in dependence of

*d*and

*ω*, using an equation similar to the one given in [17

17. R. Zhang, X. Zhang, D. Meiser, and H. Giessen, “Mode and group velocity dispersion evolution in the tapered region of a single-mode tapered fiber,” Opt. Express **12**, 5840–5849 (2004). [CrossRef] [PubMed]

*z*is small enough to warrant a quasicontinuous change of the simulation parameters. For the fibers we investigate, ∆

*z*is chosen to be smaller than 10

*µ*m.

*D̃*can be written as

*ω*=

*ω*−

*ω*

_{0}. Since the calculation of

*β*described above yields the full functional dependence

*β*(

*ω*,

*d*), we are able to circumvent the commonly used Taylor expansion for

*β*(

*ω*) with its problematic choice of the highest order.

*β*

_{0}and

*β*

_{1}necessary for our ansatz can easily be derived from

*β*(

*ω*) with a high precision. For the treatment of the nonlinear operator in the time domain, we apply the convolution theorem and the 4th-order Runge-Kutta algorithm. As the initial pulse we choose a sech-pulse given by

*P*

_{0}denotes the peak power,

*T*

_{0}the pulse width and

*C*the chirp parameter, which imposes a linear chirp if not set to 0. As the central wavelength we set

*λ*

_{0}= 773 nm for the following simulations. In the following section the given values for the diameter refer to the cladding diameter.

## 3. Simulation results

### 3.1. General considerations

*z*first exhibits a strong temporal compression with a simultaneous increase of the peak power up to a maximum value. Propagating further, the peak power decreases again, and the soliton undergoes its well-known ‘breathing’ behavior [29]. For us in particular the propagation distance

_{s}*z*

_{MPC}, which we define as the propagation distance at which the first local maximum of the peak power is achieved, is of importance, because in the presence of disturbing effects the break-up of the soliton occurs at this very position. This distance is closely connected to the so-called fission length

*L*

_{fis}[14

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

*L*

_{fis}≈ √2

*z*(

_{s}*πN*)

^{−1}with

*N*being the soliton order [26

26. 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]

*z*

_{MPC}relative to the soliton period

*N*, defined by

*E*is the pulse energy, which is connected to the peak power and pulse width by

_{p}*E*= 2

_{p}*P*

_{0}

*T*

_{0}for a sech

^{2}-pulse. If we translate the results of this plot to the longitudinal position of maximum pulse compression

*z*

_{MPC}, we find that for an increasing peak power of the input pulse

*z*

_{MPC}decreases, regardless if

*T*

_{0}or

*E*is kept constant. Notably, this holds not only for an ideal soliton (blue line) but also for the pulses launched into conical fibers, although in these cases the curves change slightly for different input and fiber parameters (red and black lines, parameters are given later). The results are in good agreement with the theoretical approximation

_{p}*L*

_{fis}/

*z*as defined in Ref. [26

_{s}26. 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]

*z*

_{MPC}determines the important optical parameters, i.e., dispersion and nonlinearity, which in turn define main features of the generated supercontinuum such as the wavelength of the non-solitonic radiation (NSR). Figure 2(b) shows the dependence of the nonlinear parameter

*γ*on the diameter. In the inset, we plot

*γ*for a constant

*λ*= 773 nm, our pump wavelength. We note that

*γ*increases significantly for smaller diameters, since the effective area is reduced.

*z*

_{MPC}the profile of the fiber just fits that diameter. In other words, scanning the input peak power while

*E*is kept constant translates to a scanning of the diameter profile. For a quantitative analysis we assume a conically shaped fiber with a diameter changing linearly from 0.9

_{p}*µ*m to 2.7

*µ*m over a distance of 60 mm. The input peak power

*P*

_{0}is varied while

*E*is fixed to 1 nJ. Figure 3 shows the corresponding results, which we are going to discuss in detail in the following paragraph.

_{p}*z*

_{MPC}. This implies that also the diameter at this position becomes smaller [Fig. 3(c)], which leads to a higher nonlinearity as seen above [Fig. 3(e)]. The opposite is true for the decreasing cone: Here again a higher input peak power yields a smaller

*z*

_{MPC}, but now the diameter corresponding to a smaller

*z*

_{MPC}rises (middle right of Fig. 3), leading to a lower

*γ*at this position (bottom right of Fig. 3). We unexpectedly obtain narrower output spectra beyond

*P*

_{0}= 5 kW, although the input peak power still is increased. For a more detailed analysis we therefore compare the pulse evolution of the increasing cone with the decreasing one at this particular input peak power of 5 kW in the following.

### 3.2. Increasing cone

*z*

_{MPC}≈ 5.5 mm the break-up of the launched higher-order soliton occurs and the supercontinuum formation is triggered. During the decay NSR is generated at a wavelength according to the phasematching condition [27

27. N. Akhmediev and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fibers,” Phys. Rev. A **51**, 2602–2607 (1995). [CrossRef] [PubMed]

28. A. V. Yulin, D. V. Skryabin, and P. St. J. Russell, “Four-wave mixing of linear waves and solitons in fibers with higher-order dispersion,” Opt. Lett. **29**, 2411–2413 (2004). [CrossRef] [PubMed]

*ω*is the central frequency of the soliton,

_{s}*P*its peak power, and

_{s}*ω*

_{NSR}the central frequency of the generated NSR. Figure 4(f) visualizes this phasematching condition. With the diameter of ≈ 1.1

*µ*m corresponding to

*z*

_{MPC}≈ 5.5 mm and

*P*= √2

_{s}*NP*

_{0}≈ 163 kW [26

26. 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]

*λ*

_{NSR}≈ 350 nm, which fits well to the simulated spectrum.

*λ*

_{NSR}, which means that the soliton and the NSR do not co-propagate and hence not interact. This leads to the isolation of the NSR in the temporal as well as in the spectral domain. This finding is supported by the XFROG trace [31

31. S. Linden, H. Giessen, and J. Kuhl, “XFROG - A New Method for Amplitude and Phase Characterization of Weak Ultrashort Pulses,” Phys. Status Solidi B **206**, 119–124 (1999). [CrossRef]

*γ*decreases for longer propagation distances, the phasematching condition does not allow the generation of components with even smaller wavelengths. Hence, this isolation of the NSR leads to sharp edges at the short wavelength side of the output spectrum, whereas the long-wavelength solitons keep redshifting during the propagation due to intra-pulse Raman scattering.

*λ*

_{NSR}leading to broader output spectra, since the diameter where the NSR is generated becomes smaller for higher input peak powers.

### 3.3. Decreasing cone

*z*

_{MPC}≈ 30.5 mm corresponding to a diameter of 1.75

*µ*m. With

*P*≈ 64 kW the phasematching condition [Eq. (6)] leads to

_{s}*λ*

_{NSR}≈ 480 nm, which again is in good agreement to the initially generated NSR shown in the spectral evolution [Fig. 5(b)].

30. 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**, 653–657 (2007). [CrossRef]

*λ*

_{NSR}increases from 400 nm to 500 nm when increasing the input peak power in the given interval.

*λ*

_{NSR}, the output spectra becomes narrower again.

### 3.4. Subsequent soliton fission

*d*= 2

*µ*m) and decays into two fundamental solitons while emitting NSR. After a propagation length of 200 mm, which allows the two solitons to separate temporarily and spectrally, we increase the diameter of the fiber over a small distance linearly to 3

*µ*m such that the soliton number of the dominant soliton with the larger wavelength rises again to 2. This is possible since according to Eq. (5) N is not only dependent on the pulse parameters but also on the diameter-determined

*β*

_{2}and

*γ*. This new second-order soliton decays again into two fundamental solitons and a new dispersive wave, which shows a different central wavelength when compared to the one generated by the first decay in agreement with Eq. (6). As a second effect of the increased diameter, the wavelength of the short-wavelength soliton of the first decay shifts from the anomalous to the normal dispersion regime, turning the soliton into a dispersive wave. The temporal and spectral evolution of this process as well as a simulated XFROG trace [31

31. S. Linden, H. Giessen, and J. Kuhl, “XFROG - A New Method for Amplitude and Phase Characterization of Weak Ultrashort Pulses,” Phys. Status Solidi B **206**, 119–124 (1999). [CrossRef]

*P*

_{0}and

*T*

_{0}have been extracted by fitting a sech

^{2}-function to the solitonic part of |

*A*(

*z*,

*T*)|

^{2}for the given propagation distances.

## 4. Experimental results and conclusion

32. A. Konyukhov, L. Melnikov, and Y. Mazhirina, “Dispersive wave generation in microstructured fiber with periodically modulated diameter,” Proc. SPIE **6165**, 616508 (2006). [CrossRef]

*C*in Eq. (4) to −3.

## Acknowledgement

## References and links

1. | T. A. Birks, W. J. Wadsworth, and P. St. J. Russell, “Supercontinuum generation in tapered fibers,” Opt. Lett. |

2. | S. Coen, A. H. L. Chau, R. Leonhardt, J. D. Harvey, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “Supercontinuum generation via stimulated Raman scattering and parametric four-wave-mixing in photonic crystal fibers,” J. Opt. Soc. Am. B |

3. | J. Teipel, K. Franke, D. Türke, F. Warken, D. Meiser, M. Leuschner, and H. Giessen, “Characteristics of supercontinuum generation in tapered fibers using femtosecond laser pulses,” Appl. Phys. B |

4. | G. Genty, M. Lehtonen, M. Kaivola, and H. Ludvigsen, “Enhanced bandwidth of supercontinuum generated in microstructured fibers,” Opt. Express |

5. | J. N. Kutz, C. Lynga, and B. J. Eggleton, “Enhanced supercontinuum generation through dispersion-management,” Opt. Express |

6. | F. Hoos, S. Pricking, and H. Giessen, “Compact portable 20 MHz solid-state femtosecond whitelight-laser,” Opt. Express |

7. | D.-I. Yeom, J. A. Bolger, G. D. Marshall, D. R. Austin, B. T. Kuhlmey, M. J. Withford, C. Martijn de Sterke, and B. J. Eggleton, “Tunable spectral enhancement of fiber supercontinuum,” Opt. Lett. |

8. | G. Genty, P. Kinsler, B. Kibler, and J. M. Dudley, “Nonlinear envelope equation modeling of sub-cycle dynamics and harmonic generation in nonlinear waveguides,” Opt. Express |

9. | D. Mogilevtsev, T. A. Birks, and P. St. J. Russell, “Group-velocity dispersion in photonic crystal fibers,” Opt. Lett. |

10. | G. P. Agrawal, |

11. | L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental Observation of Picosecond Pulse Narrowing and Solitons in Optical Fibers,” Phys. Rev. Lett. |

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

13. | G. Genty, S. Coen, and J. M. Dudley, “Fiber supercontinuum sources (Invited),” J. Opt. Soc. Am. B |

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

15. | P. St. J. Russell, “Photonic Crystal Fibers,” Science |

16. | S. Pricking and H. Giessen, “Tapering fibers with complex shape,” Opt. Express |

17. | R. Zhang, X. Zhang, D. Meiser, and H. Giessen, “Mode and group velocity dispersion evolution in the tapered region of a single-mode tapered fiber,” Opt. Express |

18. | S. V. Chernikov, E. M. Dianov, D. J. Richardson, and D. N. Payne, “Soliton pulse compression in dispersion-decreasing fiber,” Opt. Lett. |

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

20. | A. Kudlinski, A. K. George, J. C. Knight, J. C. Travers, A. B. Rulkov, S. V. Popov, and J. R. Taylor “Zero-dispersion wavelength decreasing photonic crystal fibers for ultraviolet-extended supercontinuum generation,” Opt. Express |

21. | J. C. Travers, J. M. Stone, A. B. Rulkov, B. A. Cumberland, A. K. George, S. V. Popov, J. C. Knight, and J. R. Taylor “Optical pulse compression in dispersion decreasing photonic crystal fiber,” Opt. Express |

22. | A. Kudlinski and A. Mussot, “Visible cw-pumped supercontinuum,” Opt. Lett. |

23. | J. C. Travers, S. V. Popov, and J. R. Taylor, “Extended blue supercontinuum generation in cascaded holey fibers,” Opt. Lett. |

24. | E. C. Mӓgi, P. Steinvurzel, and B. J. Eggleton, “Tapered photonic crystal fibers,” Opt. Express |

25. | W. J. Wadsworth, A. Witkowska, S. G. Leon-Saval, and T. A. Birks, “Hole inflation and tapering of stock photonic crystal fibres,” Opt. Express |

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

27. | N. Akhmediev and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fibers,” Phys. Rev. A |

28. | A. V. Yulin, D. V. Skryabin, and P. St. J. Russell, “Four-wave mixing of linear waves and solitons in fibers with higher-order dispersion,” Opt. Lett. |

29. | J. R. Taylor, |

30. | A. V. Gorbach and D. V. Skryabin, “Light trapping in gravity-like potentials and expansion of supercontinuum spectra in photonic-crystal fibres,” Nat. Photonics |

31. | S. Linden, H. Giessen, and J. Kuhl, “XFROG - A New Method for Amplitude and Phase Characterization of Weak Ultrashort Pulses,” Phys. Status Solidi B |

32. | A. Konyukhov, L. Melnikov, and Y. Mazhirina, “Dispersive wave generation in microstructured fiber with periodically modulated diameter,” Proc. SPIE |

**OCIS Codes**

(060.0060) Fiber optics and optical communications : Fiber optics and optical communications

(060.4370) Fiber optics and optical communications : Nonlinear optics, fibers

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

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: July 23, 2010

Revised Manuscript: September 1, 2010

Manuscript Accepted: September 3, 2010

Published: September 7, 2010

**Citation**

Sebastian Pricking and Harald Giessen, "Tailoring the soliton and supercontinuum dynamics by engineering the profile of tapered fibers," Opt. Express **18**, 20151-20163 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-19-20151

Sort: Year | Journal | Reset

### References

- T. A. Birks, W. J. Wadsworth, and P. St. J. Russell, "Supercontinuum generation in tapered fibers," Opt. Lett. 25, 1415-1417 (2000). [CrossRef]
- S. Coen, A. H. L. Chau, R. Leonhardt, J. D. Harvey, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, "Supercontinuum generation via stimulated Raman scattering and parametric four-wave-mixing in photonic crystal fibers," J. Opt. Soc. Am. B 19, 753-764 (2002). [CrossRef]
- J. Teipel, K. Franke, D. T¨urke, F. Warken, D. Meiser, M. Leuschner, and H. Giessen, "Characteristics of supercontinuum generation in tapered fibers using femtosecond laser pulses," Appl. Phys. B 77, 245-251 (2003). [CrossRef]
- G. Genty, M. Lehtonen, M. Kaivola, and H. Ludvigsen, "Enhanced bandwidth of supercontinuum generated in microstructured fibers," Opt. Express 12, 3471-3480 (2004). [CrossRef] [PubMed]
- J. N. Kutz, C. Lynga, and B. J. Eggleton, "Enhanced supercontinuum generation through dispersion nmanagement," Opt. Express 13, 3989-3998 (2005). [CrossRef] [PubMed]
- F. Hoos, S. Pricking, and H. Giessen, "Compact portable 20 MHz solid-state femtosecond white light-laser," Opt. Express 14, 10913-10920 (2006). [CrossRef] [PubMed]
- D.-I. Yeom, J. A. Bolger, G. D. Marshall, D. R. Austin, B. T. Kuhlmey, M. J. Withford, C. Martijn de Sterke, and B. J. Eggleton, "Tunable spectral enhancement of fiber supercontinuum," Opt. Lett. 32, 1644-1646 (2007). [CrossRef] [PubMed]
- G. Genty, P. Kinsler, B. Kibler, and J. M. Dudley, "Nonlinear envelope equation modeling of sub-cycle dynamics and harmonic generation in nonlinear waveguides," Opt. Express 15, 5382-5387 (2007). [CrossRef] [PubMed]
- D. Mogilevtsev, T. A. Birks, and P. St. J. Russell, "Group-velocity dispersion in photonic crystal fibers," Opt. Lett. 23, 1662-1664 (1998). [CrossRef]
- G. P. Agrawal, Nonlinear fiber optics (Academic Press, San Diego, 1995).
- L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, "Experimental Observation of Picosecond Pulse Narrowing and Solitons in Optical Fibers," Phys. Rev. Lett. 45, 1095-1098 (1980). [CrossRef]
- A. Husakou, and J. Herrmann, "Supercontinuum Generation of Higher-Order Solitons by Fission in Photonic Crystal Fibers," Phys. Rev. Lett. 87, 203901 (2001). [CrossRef] [PubMed]
- G. Genty, S. Coen, and J. M. Dudley, "Fiber supercontinuum sources (Invited)," J. Opt. Soc. Am. B 24, 1771-1785 (2007). [CrossRef]
- J. M. Dudley, G. Genty, and S. Coen, "Supercontinuum generation in photonic crystal fiber," Rev. Mod. Phys. 78, 1135-1184 (2006). [CrossRef]
- P. St. J. Russell, "Photonic Crystal Fibers," Science 17, 358-362 (2003). [CrossRef]
- S. Pricking, and H. Giessen, "Tapering fibers with complex shape," Opt. Express 18, 3426-3437 (2010). [CrossRef] [PubMed]
- R. Zhang, X. Zhang, D. Meiser, and H. Giessen, "Mode and group velocity dispersion evolution in the tapered region of a single-mode tapered fiber," Opt. Express 12, 5840-5849 (2004). [CrossRef] [PubMed]
- S. V. Chernikov, E. M. Dianov, D. J. Richardson, and D. N. Payne, "Soliton pulse compression in dispersion decreasing fiber," Opt. Lett. 18, 476-478 (1993). [CrossRef] [PubMed]
- F. Lu, Y. Deng, and W. H. Knox, "Generation of broadband femtosecond visible pulses in dispersion micromanaged holey fibers," Opt. Lett. 30, 1566-1568 (2005). [CrossRef] [PubMed]
- A. Kudlinski, A. K. George, J. C. Knight, J. C. Travers, A. B. Rulkov, S. V. Popov, and J. R. Taylor, "Zero dispersion wavelength decreasing photonic crystal fibers for ultraviolet-extended supercontinuum generation," Opt. Express 14, 5715-5722 (2006). [CrossRef] [PubMed]
- J. C. Travers, J. M. Stone, A. B. Rulkov, B. A. Cumberland, A. K. George, S. V. Popov, J. C. Knight, and J. R. Taylor, "Optical pulse compression in dispersion decreasing photonic crystal fiber," Opt. Express 15, 13203-13211 (2007). [CrossRef] [PubMed]
- A. Kudlinski and A. Mussot, "Visible cw-pumped supercontinuum," Opt. Lett. 33, 2407-2409 (2008). [CrossRef] [PubMed]
- J. C. Travers, S. V. Popov, and J. R. Taylor, "Extended blue supercontinuum generation in cascaded holey fibers," Opt. Lett. 30, 3132-3134 (2005). [CrossRef] [PubMed]
- E. C. Magi, P. Steinvurzel, and B. J. Eggleton, "Tapered photonic crystal fibers," Opt. Express 12, 776-784 (2004). [CrossRef]
- W. J. Wadsworth, A. Witkowska, S. G. Leon-Saval, and T. A. Birks, "Hole inflation and tapering of stock photonic crystal fibres," Opt. Express 13, 6541-6549 (2005). [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]
- N. Akhmediev and M. Karlsson, "Cherenkov radiation emitted by solitons in optical fibers," Phys. Rev. A 51, 2602-2607 (1995). [CrossRef] [PubMed]
- A. V. Yulin, D. V. Skryabin, and P. St. J. Russell, "Four-wave mixing of linear waves and solitons in fibers with higher-order dispersion," Opt. Lett. 29, 2411-2413 (2004). [CrossRef] [PubMed]
- J. R. Taylor, Optical solitons: Theory and Experiment (Cambridge University Press, Cambridge, 2005).
- 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, 653-657 (2007). [CrossRef]
- S. Linden, H. Giessen, and J. Kuhl, "XFROG - A New Method for Amplitude and Phase Characterization of Weak Ultrashort Pulses," Phys. Status Solidi B 206, 119-124 (1999). [CrossRef]
- A. Konyukhov, L. Melnikov, and Y. Mazhirina, "Dispersive wave generation in microstructured fiber with periodically modulated diameter," Proc. SPIE 6165, 616508 (2006). [CrossRef]

## 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.