## Coherent mid-infrared broadband continuum generation in non-uniform ZBLAN fiber taper

Optics Express, Vol. 17, Issue 7, pp. 5852-5860 (2009)

http://dx.doi.org/10.1364/OE.17.005852

Acrobat PDF (744 KB)

### Abstract

A simple method is described for efficient, asymmetric and coherent continuum generation in the mid-infrared region based on the dynamics of a stabilized soliton in the vicinity of a second dispersion zero of a nonlinear fiber. The mechanism involves nonlinear soliton compression, Raman self-frequency shift and resonant emission of a dispersive (Cherenkov) wave in a non-uniformly tapered ZBLAN fluoride fiber pumped by a low-power compact femtosecond laser at 1.55 *μ*m. The fiber taper features a continuous shift of the second zero dispersion wavelength, which facilitates the progressive shift in the wavelength of the dispersive wave generated by the stabilized soliton. Numerical solution of the generalized nonlinear Schrödinger equation, which accounts for the exact wavelength dependence of dispersion and nonlinear coefficients, shows robust generation of near-octave continuum spanning 1.5–3 *μ*m wavelength range.

© 2009 Optical Society of America

## 1. Introduction

1. I. T. Sorokina and K. L. Vodopyanov, eds., *Solid-State Mid-Infrared Laser Sources*, (Springer-Verlag, 2003). [CrossRef]

2. C. Xia, M. Kumar, O. P. Kulkarni, M. N. Islam, F. L. Terry, M. J. Freeman, M. Poulain, and G. Mazé, “Mid-infrared supercontinuum generation to 4.5 mm in ZBLAN fluoride fibers by nanosecond diode pumping,” Opt. Lett. **31**, 2553–2555 (2006). [CrossRef] [PubMed]

3. C. L. Hagen, J. W. Walewski, and S. T. Sanders, “Generation of a continuum extending to midinfrared by pumping ZBLAN fiber with an ultrafast 1550-nm source,” IEEE Photon. Technol. Lett. **18**, 91–93 (2006). [CrossRef]

*L*=

_{MI}*L*/2 [4], or deterministic soliton fission with an empirical characteristic length

_{NL}*L*≈

_{fiss}*L*/

_{D}*N*[5

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

*L*and

_{NL}*L*are the nonlinear and dispersion lengths, respectively, and

_{D}*N*= √

*L*/

_{D}*L*is the soliton number. The ratio of the soliton fission and MI characteristic lengths, which is proportional to

_{NL}*N*, determines the degree of coherence. Therefore, a critical value of the soliton number exists (

*N*≈ 10) above which soliton fission will be overcome by MI thus changing the nature of the continuum from coherent to incoherent [5

_{crit}5. J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. **78**, 1135–1184 (2006). [CrossRef]

*dD*/

*dλ*< 0. Importantly, we use realistic parameters in our design for the pump pulse based on commercially available compact femtosecond fiber lasers at 1.55

*μ*m central wavelength. Also, the low input soliton number (

*N*≪

*N*) used in our design ensures high level of continuum spectral coherence as opposed to continuum generated in the multiple soliton regime.

_{crit}*dD*/

*dλ*> 0), as is usually done [6

6. 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]

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

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

8. A. Efimov, A. J. Taylor, F. G. Omenetto, A. V. Yulin, N. Y. Joly, F. Biancalana, D. V. Skryabin, J. C. Knight, and P. St. J. Russell, “Time-spectrally-resolved ultrafast nonlinear dynamics in small-core photonic crystal fibers: Experiment and modeling,” Opt. Express **12**, 6498–6507 (2004). [CrossRef] [PubMed]

9. D. V. Skryabin and A. V. Yulin, “Theory of generation of new frequencies by mixing of solitons and dispersive waves in optical fibers,” Phys. Rev. E **72**, 016619 (2005). [CrossRef]

10. D. V. Skryabin, F. Luan, J. C. Knight, and P. St. J. Russell, “Soliton self-frequency shift cancellation in photonic crystal fibers,” Science **301**, 1705–1708 (2003). [CrossRef] [PubMed]

**78**, 1135–1184 (2006). [CrossRef]

## 2. Non-uniform fiber taper concept and design

*N*is greater than 2), followed by the Raman self-frequency shift toward longer wavelengths. Because the Raman shift of a fundamental soliton is inversely proportional to the fourth power of its duration [4], the initial soliton compression is very important to achieve rapid Raman shifts. In the second stage the soliton approaches the second ZDW of the fiber with a negative dispersion slope and begins to emit a DW at longer wavelengths, which in turn stabilizes the soliton in the vicinity of the second ZDW halting further Raman shift [10

10. D. V. Skryabin, F. Luan, J. C. Knight, and P. St. J. Russell, “Soliton self-frequency shift cancellation in photonic crystal fibers,” Science **301**, 1705–1708 (2003). [CrossRef] [PubMed]

*N*= 1 soliton is

*E*= 2|

*β*

_{2}|/

*γT*

_{0}, where

*β*

_{2}and

*γ*are the dispersion and nonlinear parameters, and

*T*

_{0}is the soliton duration. Typical energies for realistic fibers would thus be in a sub-nanojoule range. Appropriate selection of the specific fiber structure allows certain degree of flexibility in selection of the input pulse duration and energy to either maximize the continuum power or to use a compact low-energy pump source. Another important implication of the controlled nature of the continuum generation via phase-matched DW emission by a soliton is that nearly 100% of the pump power can be transferred to the continuum and only into the wavelength range determined by the design of the ZDW wavelength as a function of propagation distance. Although only one simple profile

*λ*(

_{ZDW}*z*) is studied below, more complex dependences may yield spectral shapes unachievable by other means.

*μ*m and relatively flat dispersion profile

*D*(

*λ*), thus requiring only mild (e.g. compared to silica or IRG2) waveguide contribution to the total dispersion in order to form a second ZDW at a longer wavelength. A core-cladding index difference of Δ

*n*= 0.09 is chosen for the fiber. A Δ

*n*value much smaller is not able to provide the required second ZDW because contribution from the waveguide dispersion becomes too small. While the choice of such a large core-cladding index difference is hardly realistic for a conventional step-index fiber, it is certainly attainable through PCF designs. The GVD

*β*

_{2}as a function of wavelength for various core radii is plotted in Fig. 2(a). Wavelength-dependent values for

*β*

_{2}(and the mode-propagation constant

*β*) are obtained by numerically solving the eigenvalue equation for the fundamental HE

_{11}mode of a step-index fiber, with material dispersion of ZBLAN included in the calculation. As shown in Fig. 2(a), the second ZDW shifts to shorter wavelengths with decreasing core radius, although no second ZDW is available for core radius larger than ~ 2.4

*μm*. Fig. 2(b) shows the nonlinear coefficient

*γ*for various core radii, which is numerically calculated using [11

11. M. A. Foster, K. D. Moll, and A. L. Gaeta, “Optimal waveguide dimensions for nonlinear interactions,” Opt. Express **12**, 2880–2887 (2004). [CrossRef] [PubMed]

*n*

_{2}= 2.2×10

^{-20}m

^{2}/W is the nonlinear index of refraction for ZBLAN, and

*S*is the longitudinal component of the Poynting vector, numerically calculated from the field distribution. For the same wavelength

_{z}*γ*increases with decreasing core size because of a reduced effective mode area.

*μ*m to 1.5

*μ*m,

*r*(

*z*) =

*r*

_{0}exp(-

*z*/611.73), where

*r*

_{0}=

*r*(

*z*= 0) = 4

*μm*is the initial core radius and

*z*is the propagation distance in cm. We note that similar lengths of silica PCFs tapers have been recently drawn for different applications [12

12. 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]

13. 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]

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

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

*r*(

*z*) dependencies may be used. Additionally, one may also consider tapers in which other parameters vary along the length, such as Δ

*n*, material composition, hole size and shape in PCFs, etc. as control parameters for achieving ZDW and thus DW phase-matching wavelength variation along the fiber.

## 3. Numerical simulation

*A*(

*z*,

*T*) is the complex envelope of the electric field in the reference frame moving with the group velocity of the input pulse. The left-hand side of Eq. (2) represents linear propagation, where a is the fiber linear loss, and

*β*

_{m}is the

*m*th order dispersion coefficient in a Taylor series for the mode-propagation constant

*β*(

*ω*). The right-hand side describes the nonlinear effects, with

*γ*=

_{m}*∂*/

^{m}γ*∂*

*ω*the

^{m}*m*th order derivative of the nonlinear coefficient

*γ*(

*ω*), and the response function

*R*(

*T*) = (1 -

*f*)

_{R}*δ*(

*T*) +

*f*

_{R}*h*(

_{R}*T*) describing both the instantaneous electronic and delayed Raman contributions.

*μm*and a full-width-half-maximum (FWHM) duration of 100 fs. With the numerical values of

*β*(

*ω*) available over the frequency range involved, we include all orders of dispersion in the calculation by replacing the dispersion operator in the frequency domain with

*β*(

*ω*) -

*β*

_{0}-

*ω*

*β*

_{1}[4]. Such approximation-free approach is necessary due to the broad spectral range and complex wavelength dependence of dispersion involved. Similarly, nonlinear coefficient

*γ*(

*ω*) to all orders is also included numerically, although we find that inclusion of only the zeroth and first order derivative of

*γ*(

*ω*) is sufficient to yield similar results, as

*γ*is approximately linear to frequency for the chosen taper parameters. It is, however, essential to include spectral dependence of

*γ*(resulting from variation of the modal effective area with wavelength, in addition to the self-steepening term) in the calculation in order to correctly describe the nonlinear propagation, with the continuum spectrum generated in mid-infrared largely affected by such spectral dependence [16]. We also include in the calculation the experimentally measured Raman gain spectrum for ZrF

_{4}-BaF

_{2}fiber [17], and choose the fractional contribution of Raman response

*f*to be 0.2 (similar to fused-silica glass). The numerical calculation is carried out with a symmetrized split-step Fourier method [4], in which the linear propagation part of Eq. (2) is solved completely in the frequency domain, while the nonlinear part is solved partially in the time domain and partially in the frequency domain. The convolution product between Raman response and field intensity in Eq. (2) is calculated as a product in the frequency domain. The nonlinear and dispersion characteristics at each step are determined based on the taper core radius at that step. To cover both the temporal and spectral spans of the generated continuum, a temporal window of 60 ps and spectral window of 270 THz are chosen, which corresponds to 2

_{R}^{14}sampling points.

## 4. Results and discussion

*μ*m, with a 10 dB spectral width of ~ 1.5

*μ*m (an octave). The spectrum shown in Fig. 3 is obtained for an input pulse energy of 1.0 nJ (a peak power of 8.8 kW), a realistic parameter for a compact femtosecond laser source.

*N*= √γ

*P*

_{0}

*T*

_{0}

^{2}/|

*β*

_{2}|, at the fiber input equals to 2.3. Because

*N*> 1, the input pulse undergoes initial spectral broadening and temporal compression, followed by soli-ton fission process. A fundamental soliton, taking most of the input pulse energy and having a shorter duration, is ejected from the input pulse, and starts to Raman self-frequency shift toward longer wavelengths. As shown in Fig. 3, the fundamental soliton propagates for a distance of 480 cm before DW generation begins at the long wavelength end. A long fiber taper is required for sufficient soliton self-frequency shift because of the small soliton number involved. The non-uniform fiber taper helps further compress the fundamental soliton and achieve rapid soliton self-frequency shift. Unlike in a dispersion decreasing fiber, such soliton compression results from a combination of enhancement of nonlinearity and decrease of the absolute value of the GVD (because soliton is approaching the second ZDW) during propagation.

*λ*

_{zdw}= 2.4

*μm*for a taper core radius of 1.83

*μm*) with a center wavelength of 2.2

*μm*and a FWHM duration of 25 fs and begins to emit the DW at ~ 3.0

*μ*m. This is in good agreement with the DW wavelength calculated through the phase-matching condition between soliton and DW [4]. For a uniform fiber taper, the soliton wavelength would have stabilized near the second ZDW when the Raman self-frequency shift is canceled by the spectral recoil effect. However, in our core-reducing fiber taper, because of the continuous shift of the second ZDW the soliton center wavelength is also “pushed” toward shorter wavelength, while the wavelength of the emitted DW becomes progressively shorter as well. This process lasts until the energy transfer from the soliton to DW is nearly complete. The rate at which the second ZDW shifts determines the bandwidth of the DW generated. Shifting the ZDW too fast will result in a non-adiabatic process in which ZDW passes through the soliton and the DW generation seizes prematurely. On the other hand, an overly slow shift will create a rather narrow-band DW as soliton loses most of its energy during the initial stage of ZDW shifting. We note that fringes between 1.5 and 2.3

*μ*m in the spectrum is a result of spectral interference between DW’s generated from the first fundamental soliton and the second fundamental soliton, which has less energy and smaller Raman shift. This is confirmed by spectral filtering in the numerical simulation.

*N*< 10 will ensure high level of spectral coherence [5

**78**, 1135–1184 (2006). [CrossRef]

*N*[18

18. A. Efimov and A. J. Taylor, “Supercontinuum generation and soliton timing jitter in SF6 soft glass photonic crystal fibers,” Opt. Express **16**, 5942–5953 (2008). [CrossRef] [PubMed]

**78**, 1135–1184 (2006). [CrossRef]

*E*

_{1}(

*λ*) and

*E*

_{2}(

*λ*) are continuum spectra generated by successive input pulses, or, as in our simulation, spectra generated independently from input pulses with random noise seeds. The angular brackets denote an ensemble average over a large number of such continuum spectra. In our calculation, we consider only the input pulse quantum noise, and ignore pump laser intensity fluctuations and noise that is associated with spontaneous Raman scattering. The input pulse shot noise is semiclassically modeled by adding a stochastic variation in the magnitude of the input electrical field whose standard deviation equals to the square root of the number of photons in small temporal steps [5

**78**, 1135–1184 (2006). [CrossRef]

*g*

^{(1)}

_{12}(

*λ*)| is calculated from an ensemble average on the results of 20 simulations from input pulses that have different random quantum noise. The result for a 1.0 nJ input pulse energy is plotted in Fig. 4(b). The continuum possesses nearly perfect spectral coherence over the whole continuum spectral range.

*N*= 3.3) is plotted. The overall shape of the resulting spectrum is, however, determined mostly by the tapering design, rather than by pump pulse energy. This observation suggests stability of the continuum spectrum with respect to fluctuations in pump pulse parameters, however in high-power regime multiple solitons will form, each generating its own DW rendering the continuum incompressible.

## 5. Conclusion

*n*is numerically modeled by solving a generalized nonlinear Schrödinger equation where the dispersion, nonlinear coefficient and Raman contribution are included to all orders. One-octave coherent, compressible and stable continuum is generated asymmetrically with near 100% efficient energy transfer from the pump pulse to the desired spectral region. Importantly, compact femtosecond fiber lasers delivering ~1 nJ, 100 fs pulses can be used to generate such broad spectra in the mid-infrared extending to ~ 3

*μm*and possibly beyond with further optimized taper structures.

## Acknowledgments

## References and links

1. | I. T. Sorokina and K. L. Vodopyanov, eds., |

2. | C. Xia, M. Kumar, O. P. Kulkarni, M. N. Islam, F. L. Terry, M. J. Freeman, M. Poulain, and G. Mazé, “Mid-infrared supercontinuum generation to 4.5 mm in ZBLAN fluoride fibers by nanosecond diode pumping,” Opt. Lett. |

3. | C. L. Hagen, J. W. Walewski, and S. T. Sanders, “Generation of a continuum extending to midinfrared by pumping ZBLAN fiber with an ultrafast 1550-nm source,” IEEE Photon. Technol. Lett. |

4. | G. P. Agrawal, |

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

6. | 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. |

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

8. | A. Efimov, A. J. Taylor, F. G. Omenetto, A. V. Yulin, N. Y. Joly, F. Biancalana, D. V. Skryabin, J. C. Knight, and P. St. J. Russell, “Time-spectrally-resolved ultrafast nonlinear dynamics in small-core photonic crystal fibers: Experiment and modeling,” Opt. Express |

9. | D. V. Skryabin and A. V. Yulin, “Theory of generation of new frequencies by mixing of solitons and dispersive waves in optical fibers,” Phys. Rev. E |

10. | D. V. Skryabin, F. Luan, J. C. Knight, and P. St. J. Russell, “Soliton self-frequency shift cancellation in photonic crystal fibers,” Science |

11. | M. A. Foster, K. D. Moll, and A. L. Gaeta, “Optimal waveguide dimensions for nonlinear interactions,” Opt. Express |

12. | 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 |

13. | 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 |

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

15. | S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, |

16. | G. Canat, T. Laverre, L. Lombard, V. Jolivet, and P. Bourdon, “Influence of the wavelength dependence of the effective area on infrared supercontinuum generation,” in |

17. | A. Saissy, J. Botineau, L. Macon, and G. Maze, “Raman scattering in a fluorozirconate glass optical fiber,” J. De Physicque Lettres , |

18. | A. Efimov and A. J. Taylor, “Supercontinuum generation and soliton timing jitter in SF6 soft glass photonic crystal fibers,” Opt. Express |

**OCIS Codes**

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

(320.6629) Ultrafast optics : Supercontinuum generation

**ToC Category:**

Ultrafast Optics

**History**

Original Manuscript: February 6, 2009

Revised Manuscript: March 23, 2009

Manuscript Accepted: March 23, 2009

Published: March 26, 2009

**Citation**

Zhigang Chen, Antoinette J. Taylor, and Anatoly Efimov, "Coherent mid-infrared broadband continuum generation in non-uniform ZBLAN fiber taper," Opt. Express **17**, 5852-5860 (2009)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-7-5852

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### References

- I. T. Sorokina and K. L. Vodopyanov, eds., Solid-State Mid-Infrared Laser Sources, (Springer-Verlag, 2003). [CrossRef]
- C. Xia, M. Kumar, O. P. Kulkarni, M. N. Islam, F. L. Terry, M. J. Freeman, M. Poulain, and G . Maze, "Mid infrared supercontinuum generation to 4.5 μm in ZBLAN fluoride fibers by nanosecond diode pumping," Opt. Lett. 31, 2553-2555 (2006). [CrossRef] [PubMed]
- C. L. Hagen, J. W. Walewski, and S. T. Sanders, "Generation of a continuum extending to midinfrared by pumping ZBLAN fiber with an ultrafast 1550-nm source," IEEE Photon. Technol. Lett. 18, 91-93 (2006). [CrossRef]
- G. P. Agrawal, Nonlinear Fiber Optics, 4th edition, (Academic Press, 2007).
- J. M. Dudley, G. Genty, and S. Coen, "Supercontinuum generation in photonic crystal fiber," Rev. Mod. Phys. 78, 1135-1184 (2006). [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. A. Birks, W. J. Wadsworth, and P. St. J. Russell, "Supercontinuum generation in tapered fibers," Opt. Lett. 25, 1415-1417 (2000). [CrossRef]
- A. Efimov, A. J. Taylor, F. G. Omenetto, A. V. Yulin, N. Y. Joly, F. Biancalana, D. V. Skryabin, J. C. Knight, and P. St. J. Russell,"Time-spectrally-resolved ultrafast nonlinear dynamics in small-core photonic crystal fibers: Experiment and modeling," Opt. Express 12, 6498-6507 (2004). [CrossRef] [PubMed]
- D. V. Skryabin and A. V. Yulin, "Theory of generation of new frequencies by mixing of solitons and dispersive waves in optical fibers," Phys. Rev. E 72, 016619 (2005). [CrossRef]
- D. V. Skryabin, F. Luan, J. C. Knight, and P. St. J. Russell, "Soliton self-frequency shift cancellation in photonic crystal fibers," Science 301,1705-1708 (2003). [CrossRef] [PubMed]
- M. A. Foster, K. D. Moll, and A. L. Gaeta, "Optimal waveguide dimensions for nonlinear interactions," Opt. Express 12, 2880-2887 (2004). [CrossRef] [PubMed]
- A. Kudlinski, A. K. George, J. C. Knight, J. C. Travers, A. B. Rulkov, S. V. Popov, and J. R. Taylor, "Zerodispersion 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]
- D. Mogilevtsev, T. A. Birks, and P. St. J. Russell, "Group-velocity dispersion in photonic crystal fibers," Opt. Lett. 23, 1662-1664 (1998). [CrossRef]
- S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, Optics of Femtosecond Laser Pulses, (American Institue of Physics, 1992).
- G. Canat, T. Laverre, L. Lombard, V. Jolivet, and P. Bourdon, "Influence of the wavelength dependence of the effective area on infrared supercontinuum generation," in Conference on Lasers and Electro-Optics, p. CMT4 (Optical Society of America, San Jose, CA, 2008).
- A. Saissy, J. Botineau, L. Macon, and G. Maze, "Raman scattering in a fluorozirconate glass optical fiber," J. De Physicque Lettres 46, 289-294 (1985).
- A. Efimov and A. J. Taylor, "Supercontinuum generation and soliton timing jitter in SF6 soft glass photonic crystal fibers," Opt. Express 16, 5942-5953 (2008). [CrossRef] [PubMed]

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