## Pulse quality analysis on soliton pulse compression and soliton self-frequency shift in a hollow-core photonic bandgap fiber |

Optics Express, Vol. 21, Issue 7, pp. 9132-9143 (2013)

http://dx.doi.org/10.1364/OE.21.009132

Acrobat PDF (7775 KB)

### Abstract

A numerical investigation of low-order soliton evolution in a proposed seven-cell hollow-core photonic bandgap fiber is reported. In the numerical simulation, we analyze the pulse quality evolution in soliton pulse compression and soliton self-frequency shift in three fiber structures with different cross-section sizes. In the simulation, we consider unchirped soliton pulses (of 400 fs) at the wavelength of 1060 nm. Our numerical results show that the seven-cell hollow-core photonic crystal fiber, with a cross-section size reduction of 2%, promotes the pulse quality on the soliton pulse compression and soliton self-frequency shift. For an input soliton pulse of order 3 (which corresponds to an energy of 1.69 *μ*J), the pulse gets compressed with a factor of up to 5.5 and a quality factor of 0.73, in a distance of 12 cm. It also experiences a soliton-self frequency shift of up to 28 nm, in a propagation length of 6 m, with a pulse shape quality of ≈ 0.80.

© 2013 OSA

## 1. Introduction

1. J. C. Knight, “Photonic crystal fibres,” Nature **424**, 847–851 (2003) [CrossRef] [PubMed] .

3. F. Gérôme, K. Cook, A. K. George, W. Wadsworth, and J. C. Knight, “Delivery of sub-100fs pulses through 8m of hollow-core fiber using soliton compression,” Opt. Express **15**, 7126–7131 (2007) [CrossRef] [PubMed] .

4. D. G. Ouzounov, F. R. Ahmad, D. Müller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, “Generation of megawatt optical solitons in hollow-Core photonic band-gap fibers,” Science **301**, 1702–1704 (2003) [CrossRef] [PubMed] .

6. D. V. Skryabin, “Coupled core-surface solitons in photonics crystal fibers,” Opt. Express **12**, 4841–4846 (2004) [CrossRef] [PubMed] .

2. D. G. Ouzounov, C. J. Hensley, A. L. Gaeta, N. Venkataraman, M. T. Gallagher, and K. W. Koch, “Soliton pulse compression in photonic band-gap fibers,” Opt. Express **13**, 6153–6159 (2005) [CrossRef] [PubMed] .

3. F. Gérôme, K. Cook, A. K. George, W. Wadsworth, and J. C. Knight, “Delivery of sub-100fs pulses through 8m of hollow-core fiber using soliton compression,” Opt. Express **15**, 7126–7131 (2007) [CrossRef] [PubMed] .

7. J. C. Knight, F. Gérôme, and W. J. Wadsworth, “Hollow-core photonic crystal fibres for delivery and compression of ultrashort optical pulses,” IEEE J. Quantum Electron. **39**, 1047–1056 (2007) [CrossRef] .

8. J. Lægsgaard and P. J. Roberts, “Dispersive pulse compression in hollow-core photonic band gap fibers,” Opt. Express **16**, 9268–9644 (2008) [CrossRef] .

9. J. Lægsgaard, “Soliton formation in hollow-core photonic bandgap fibers,” Appl. Phys. B **95**, 2093–3000 (2009) [CrossRef] .

10. M. G. Welch, K. Cook, R. A. Correa, F. Gerome, W. J. Wadsworth, A. V. Gorbach, D. V. Skryabin, and J. C. Knight, “Solitons in hollow core photonic crystal fiber: engineering nonlinearity and compressing pulses,” J. Lightwave Technol. **27**, 1644–1652 (2009) [CrossRef] .

11. A. A. Ivanov, A. A. Podshivalov, and A. M. Zheltikov, “Frequency-shifted megawatt soliton output of a hollow photonic-crystal fiber for time-resolved coherent anti-Stokes Raman scattering microspectroscopy,” Opt. Lett. **31**, 3318–3320 (2006) [CrossRef] [PubMed] .

12. B-W. Liu, M-L. Hu, X-H. Fang, Y-F. Li, L. Chai, C-Y. Wang, W. Tong, J. Luo, A. A. Voronin, and A. M. Zheltikov, “Stabilized soliton self-frequency shift and 0.1-PHz sideband generation in a photonic-crystal fiber with an air-hole-modified core,” Opt. Express **16**, 14987–14996 (2008) [CrossRef] [PubMed] .

4. D. G. Ouzounov, F. R. Ahmad, D. Müller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, “Generation of megawatt optical solitons in hollow-Core photonic band-gap fibers,” Science **301**, 1702–1704 (2003) [CrossRef] [PubMed] .

13. F. Gérome, P. Dupriez, J. Clowes, J. C. Knight, and W. J Wadsworth, “High power tunable femtosecond soliton source using hollow-core photonic bandgap fiber, and its use for frequency doubling,” Opt. Express **16**, 2381–2386 (2008) [CrossRef] [PubMed] .

14. A. V Gorbach and D. V Skryabin, “Soliton self-frequency shift, non-solitonic radiation and self-induced transparency in air-core fibers,” Opt. Express **16**, 4858–4865 (2008) [CrossRef] [PubMed] .

## 2. Theory and numerical procedure

*d*, the pitch, Λ, the diameter of curvature at the corners,

*d*, the circle diameter,

_{c}*d*, the silica ring thickness,

_{p}*t*, and the core size,

*R*. The core design of the fiber has a direct impact on the modal properties of the fiber. In this way, the rounded hexagonal holes in the structure of the fiber were chosen mainly for two important reasons: firstly, they increase the width of the transmission band of HC-PBGFs [16

_{c}16. R. Amezcua-Correa, N. G. Broderick, M. N. Petrovich, F. Poletti, and D. J. Richardson, “Optimizing the usable bandwidth and loss through core design in realistic hollow-core photonic bandgap fibers,” Opt. Express **14**, 7974–7985 (2006) [CrossRef] [PubMed] .

*β*(

*ω*), around the central frequency

*ω*

_{0}as [17] where Ω =

*ω*−

*ω*

_{0}, and are the

*k*-order dispersion parameters. The dispersion slope is quantified by the figure of merit, RDS, given by the ratio [9

9. J. Lægsgaard, “Soliton formation in hollow-core photonic bandgap fibers,” Appl. Phys. B **95**, 2093–3000 (2009) [CrossRef] .

18. C. J. Hensley, D. G. Ouzounov, and A. L. Gaeta, “Silica-glass contribution to the effective non-linearity of hollow-core photonic band-gap fibers,” Opt. Express **15**, 3507–3512 (2007) [CrossRef] [PubMed] .

19. J. Lægsgaard, J. Riishede, A. Bjarklev, and N. A. Mortensen, “Material effects in air-guiding photonic band gap fibers,” J. Opt. Soc. Am. B **20**, 2046–2051 (2003) [CrossRef] .

*i*can be

*a*or

*s*referring to air or silica, respectively.

*i*-th material, correspondingly [20

20. N. González Baquedano, S. Vargas, N. Arzate, I. Torres-Gómez, A. Martínez-Ríos, D. E. Ceballos-Herrera, A. Ferrando, and C. Milián, “Modeling the tapering effects on the modal parameters of a hollow-core photonic bandgap fiber,” in *Eight Symposium Optics in Industry*,E. Rosas, N. Arzate, I. Torres, and J. Sumaya, eds., Proc. SPIE 8287, 828701 (2011).

*β*

_{2}) and third-order (

*β*

_{3}) dispersion, as well as non-linear response (

*γ*) and intra-pulse stimulated Raman scattering terms on the Schrödinger equation. The propagation equation is numerically solved by using the symmetric split-step Fourier method. For the non-linear response and Raman function, we take into account their corresponding contributions of the silica and of the air [14

14. A. V Gorbach and D. V Skryabin, “Soliton self-frequency shift, non-solitonic radiation and self-induced transparency in air-core fibers,” Opt. Express **16**, 4858–4865 (2008) [CrossRef] [PubMed] .

*A*=

*A*(

*t*,

*z*) is the slowly-varying pulse envelope in a co-moving frame and

*z*is the spatial coordinate along the fiber. The corresponding contributions to the Raman response function due to air,

*R*, and silica,

_{a}*R*, are described by [17]: where Θ(

_{s}*t*) is the Heaviside function,

*τ*

_{1}and

*τ*

_{2}are the Raman parameters, which values for silica are well known and have the following values [17]:

*f*= 0.18. Meanwhile, the estimated values for air are [14

_{s}14. A. V Gorbach and D. V Skryabin, “Soliton self-frequency shift, non-solitonic radiation and self-induced transparency in air-core fibers,” Opt. Express **16**, 4858–4865 (2008) [CrossRef] [PubMed] .

*f*= 0.5.

_{a}**16**, 4858–4865 (2008) [CrossRef] [PubMed] .

*t*

_{0}is the pulse width and

*P*

_{0}is the peak power. The fundamental optical soliton (with order

*N*= 1) is a light pulse whose temporal and spectral profiles does not change with propagation. If a higher-order,

*N*> 1, soliton propagates along the fiber, it undergoes stages of periodical compression and broadening of its temporal and spectral shape. However, in the presence of perturbation, the higher-order soliton breaks up into lower amplitudes sub-pulses. Such break up is known as soliton fission. In the femtosecond regime, higher-order dispersion and Raman scattering are the main effects that causes soliton fission. The distance at which fission starts usually corresponds to the point where the evolving input higher-order soliton reaches its maximum bandwidth [22

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

*z*, is predicted by the following equation [23]: where

_{opt}*L*is the dispersion length [17]. The pulse compression is quantified by the compression factor defined by [24]: where

_{D}*t*and

_{FWHM}*t*are the full-width at half maximum (FWHM) of the input and output compressed pulse, respectively.

_{comp}*E*

_{pedestal}is the pedestal energy that gives the percentage of the total input energy that is contained in the pedestal of the output (either compressed or shifted) pulse. It is defined as [25

25. K-T. Chai and W-H. Cao, “Enhanced compression of fundamentals solitons in dispersion decreasing fibers due to the combined effects of negative third-order dispersion and Raman self-scattering,” Opt. Commun. **184**, 463–474 (2000) [CrossRef] .

*E*

_{total}is the total energy contained in the output pulse and

*E*

_{sech}is the energy of a hyperbolic-secant pulse having the same peak power and FWHM as the output pulse.

## 3. Results and discussion

*d*= 2.46

*μ*m, Λ = 2.53

*μ*m,

*d*= 0.66

_{p}*μ*m,

*d*= 1.32

_{c}*μ*m and

*R*= 3.61

_{c}*μ*m. Meanwhile, the cross-section size of the B and C fiber structures have been reduced to 1 and 2 %, respectively, with respect to that of the A structure. In other words, we consider that the fiber preserves its original form and geometry and only experiences an uniform decrease of its transversal dimensions. Second- and third-order dispersion parameters as a function of wavelength for such structures are depicted in Fig. 2. The transmission bandwidth is ≈ 130 nm. Most of the allowed wavelengths are in the anomalous region. The zero-dispersion wavelengths (ZDWs) for the studied HC-PBGFs are located at 1015, 1005 and 995 nm, respectively. In addition, the second-order dispersion parameter values, for the A, B, and C fiber structures, at

*λ*

_{0}= 1060 nm, are the following: −120, −245 and −457 ps

^{2}/km, respectively. As expected, the effect of reducing the cross-section size of the HC-PBGF is the shift of the ZDW to shorter wavelengths and, consequently, the second-order dispersion takes more negative values Fig. 2(a). From Fig. 2(b), it can be seen that

*β*

_{3}presents the same qualitative behavior for the three structures. TOD curves shift to shorter wavelengths and the value of

*β*

_{3}at 1060 nm gets increased as the cross-section size of the fiber is reduced. Their corresponding

*β*

_{3}values are the following: 5, 10 and 16 ps

^{3}/km, respectively. The respective energy of input solitons with orders

*N*=2, 2.5 and 3 are: 223.1 nJ, 348.6 nJ and 501.98 nJ, for the A fiber structure; 426 nJ, 666.51 nJ and 960 nJ, for the B fiber structure; and 0.751

*μ*J, 1.173

*μ*J and 1.69

*μ*J for the C fiber structure, respectively.

*γ*, at the wavelength of 1060 nm, of 0.057 × 10

_{T}^{−5}and 0.131 × 10

^{−5}1/(W · km), respectively. We observe that the main contribution to the non-linear parameter comes from the air region. The principal feature of

*γ*, seen in all corresponding curves, is the almost flat region that is present in the middle of the transmission bandwidth. In addition, there is an increase in both the low and the upper sides of the respective curves. Besides,

_{T}*γ*takes higher values as the cross-section size is reduced.

_{T}*N*, as it propagates along the HC-PBGF taking into account the effects of second- and third-order dispersion, self-phase modulation and intra-pulse Raman scattering. During the propagation, the pulse experiences an initial stage of compression (or a broadening of the spectrum) and, after some distance it reaches maximum compression (or maximum bandwidth), which corresponds to the optimum length,

*z*, that indicates the onset of the soliton fission. The resultant sub-pulse undergoes stages of compression and broadening experiencing a continuous shift to longer wavelengths due to the Raman gain [22

_{opt}22. J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. **78**, 1135–1184 (2006) [CrossRef] .

*N*= 2, as it propagates along ten meters of the A HC-PBGF. In the following, we will study both the temporal and spectral evolution of a soliton pulse. Firstly, we will study the optimum compressed soliton pulse and, secondly, the maximum soliton self-frequency shift.

*z*[see Eq. 8]. Later, a second stage is observed, in which there is an oscillatory behavior of compression and broadening of the pulse width; and, finally, it follows a decreasing tendency indicating the formation of a fundamental soliton which is fissioned from the input pulse. We can also observe from Figs. 6(a)–6(c) that the maximum compression factor increases with a higher value of the soliton order. Furthermore, we point out that the maximum values of the compression factor of the pulse in all three studied HC-PBGFs are approximately equal but the propagation length at which those values are reached decreases as the soliton order increases, and the cross-section size of the fiber is reduced (or for those structures with larger negative values of

_{opt}*β*

_{2}).

*N*= 2, 2.5 and 3, the quality factors of the redshifted solitons is ≈ 0.9, 0.85 and 0.8, respectively. Since, for higher-order input solitons, their quality factors are negatively affected, we only present results for up to

*N*= 3. It can be seen, from both Fig. 7 and Fig. 6, that in order to achieve higher compression factors, it is necessary to increase the value of the soliton order. However, by doing so, it results in a decrease of the quality of the compressed pulse.

*N*= 2, the compression factor reaches a value of 3.3, in 23 cm, with a pulse quality factor of 0.88. Meanwhile, for an input soliton pulse of

*N*= 3, its

*F*increases until 5.6, in 12 cm; however, the pulse quality factor decreases to a value of 0.73. Similar behavior is observed for the compressed pulses for the A and B fiber structures. Table 1 summarizes the results obtained for the SPC in the three studied HC-PBGFs structures.

_{C}*N*= 3 reaches a central wavelength of

*λ*

_{0}= 1076.5 nm.

*N*= 3 reaches the largest SSFS after a propagation length of 6 m:

*λ*

_{0}= 1088.4 nm. Such an improvement can be understood if we recall that the C structure presents higher values for its non-linear parameter than those corresponding to the A and B fiber structures. We can also see from Figs. 9(d)–9(f), lower panels, that the higher value of the soliton order, the larger initial shift of the fundamental soliton is. After an initial stage of accelerated soliton redshift, it decelerates to a lower value. For example: for

*N*= 2, after a propagation length of 5 m, the fundamental soliton redshifts 11.6 nm; meanwhile, in the following 5 m of propagation, it only redshifts 3.2 nm. We underline that, according to our results, if the soliton order is increased, the SSFS also does. Table 2 lists the output parameters of soliton self-frequency shift for input soliton pulses of order

*N*= 2, 2.5, 3, respectively, for the three HC-PBGFs structures.

*N*results in a reduction in its quality. The impact of the nonlinear parameter on SSFS is clearly visible, since for the same order of soliton, the fiber structure wherein the SSFS is greater is that with the largest nonlinear parameter. On the other hand, it also seen that a larger SSFS is reached, at shorter propagation distance, when the order of the soliton takes greater values and the second-order dispersion is more highly anomalous. The input soliton order, influences on both the SSFS and the amount of energy that will be present in the output pulse, or energy conversion from the input to the output soliton pulse. It is important to note, a high value of the soliton order produces a reduction in the amount of energy contained in shifted soliton pulse. However, the results show that for a value of

*N*= 3, the output pulse will contain approximately 80% of the energy of the higher-order input soliton.

## 4. Conclusions

*λ*

_{0}= 1060 nm. We have focused on the analysis of the pulse quality evolution in soliton pulse compression and soliton self-frequency shift. Our results show that the seven-cell HC-PBGFs, with a cross-section size reduction of 2%, presents larger anomalous values of the second-order dispersion and greater values of the non-linear parameter. If an input soliton pulse with order of

*N*= 3 (which corresponds to an energy of 1.69

*μ*J) propagates a distance of 12 cm, it gets compressed with a compression factor of 5.5 and quality factor of 0.73. Meanwhile, after the input soliton pulse propagates 6 m, its central wavelength redshifts to a shift value of Δ

*= 28 nm and presents a quality factor of ≈ 0.8. This work shows that in both phenomena SPC and SSFS is not only important to have either a high compression factor or a large displacement of the output soliton pulse, respectively, but also a high quality of the output pulse. For the SPC it is desirable that the compressed pulse has the minimum pedestal energy, which implies a high quality factor. On the other hand, in the case of SSFS phenomenon, a high pulse quality results in that most of the energy of the input soliton pulse is transferred to the shifted output soliton pulse. Therefore, an analysis of the pulse quality during the propagation of soliton pulses along HC-PBGFs is necessary in order to find an appropriate fiber structure as well as the input soliton pulse that promotes both SPC and SSFS.*

_{λ}## Acknowledgments

## References and links

1. | J. C. Knight, “Photonic crystal fibres,” Nature |

2. | D. G. Ouzounov, C. J. Hensley, A. L. Gaeta, N. Venkataraman, M. T. Gallagher, and K. W. Koch, “Soliton pulse compression in photonic band-gap fibers,” Opt. Express |

3. | F. Gérôme, K. Cook, A. K. George, W. Wadsworth, and J. C. Knight, “Delivery of sub-100fs pulses through 8m of hollow-core fiber using soliton compression,” Opt. Express |

4. | D. G. Ouzounov, F. R. Ahmad, D. Müller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, “Generation of megawatt optical solitons in hollow-Core photonic band-gap fibers,” Science |

5. | F. Luan, J. C. Knight, P. S. J. Russell, S. Campbell, D. Xiao, D. T. Reid, B. J. Mangan, D. P. Williams, and P. J. Roberts, “Femtosecond soliton pulse delivery at 800 nm wavelength in hollow-core photonic bandgap fibers,” Opt. Express |

6. | D. V. Skryabin, “Coupled core-surface solitons in photonics crystal fibers,” Opt. Express |

7. | J. C. Knight, F. Gérôme, and W. J. Wadsworth, “Hollow-core photonic crystal fibres for delivery and compression of ultrashort optical pulses,” IEEE J. Quantum Electron. |

8. | J. Lægsgaard and P. J. Roberts, “Dispersive pulse compression in hollow-core photonic band gap fibers,” Opt. Express |

9. | J. Lægsgaard, “Soliton formation in hollow-core photonic bandgap fibers,” Appl. Phys. B |

10. | M. G. Welch, K. Cook, R. A. Correa, F. Gerome, W. J. Wadsworth, A. V. Gorbach, D. V. Skryabin, and J. C. Knight, “Solitons in hollow core photonic crystal fiber: engineering nonlinearity and compressing pulses,” J. Lightwave Technol. |

11. | A. A. Ivanov, A. A. Podshivalov, and A. M. Zheltikov, “Frequency-shifted megawatt soliton output of a hollow photonic-crystal fiber for time-resolved coherent anti-Stokes Raman scattering microspectroscopy,” Opt. Lett. |

12. | B-W. Liu, M-L. Hu, X-H. Fang, Y-F. Li, L. Chai, C-Y. Wang, W. Tong, J. Luo, A. A. Voronin, and A. M. Zheltikov, “Stabilized soliton self-frequency shift and 0.1-PHz sideband generation in a photonic-crystal fiber with an air-hole-modified core,” Opt. Express |

13. | F. Gérome, P. Dupriez, J. Clowes, J. C. Knight, and W. J Wadsworth, “High power tunable femtosecond soliton source using hollow-core photonic bandgap fiber, and its use for frequency doubling,” Opt. Express |

14. | A. V Gorbach and D. V Skryabin, “Soliton self-frequency shift, non-solitonic radiation and self-induced transparency in air-core fibers,” Opt. Express |

15. | N. González-Baquedano, N. Arzate, I. Torres-Gómez, A. Ferrando, D. E. Ceballos-Herrera, and C. Milián, “Femtosecond pulse compression in a hollow-core photonic bandgap fiber by tuning its cross section,” Photonics and Nanostructures – Fundamentals and Applications |

16. | R. Amezcua-Correa, N. G. Broderick, M. N. Petrovich, F. Poletti, and D. J. Richardson, “Optimizing the usable bandwidth and loss through core design in realistic hollow-core photonic bandgap fibers,” Opt. Express |

17. | G. P. Agrawal, |

18. | C. J. Hensley, D. G. Ouzounov, and A. L. Gaeta, “Silica-glass contribution to the effective non-linearity of hollow-core photonic band-gap fibers,” Opt. Express |

19. | J. Lægsgaard, J. Riishede, A. Bjarklev, and N. A. Mortensen, “Material effects in air-guiding photonic band gap fibers,” J. Opt. Soc. Am. B |

20. | N. González Baquedano, S. Vargas, N. Arzate, I. Torres-Gómez, A. Martínez-Ríos, D. E. Ceballos-Herrera, A. Ferrando, and C. Milián, “Modeling the tapering effects on the modal parameters of a hollow-core photonic bandgap fiber,” in |

21. | F. Poli, A. Cucinotta, and S. Selleri, |

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

23. | E. M. Dianov, Z. S. Nikonova, A. M. Prokhorov, and V. N. Serkin, “Optimal compression of multi-soliton pulses in optical fibers,” Sov. Tech. Phys. Lett. |

24. | G. P. Agrawal, |

25. | K-T. Chai and W-H. Cao, “Enhanced compression of fundamentals solitons in dispersion decreasing fibers due to the combined effects of negative third-order dispersion and Raman self-scattering,” Opt. Commun. |

**OCIS Codes**

(190.4370) Nonlinear optics : Nonlinear optics, fibers

(190.5530) Nonlinear optics : Pulse propagation and temporal solitons

(060.5295) Fiber optics and optical communications : Photonic crystal fibers

**ToC Category:**

Nonlinear Optics

**History**

Original Manuscript: January 11, 2013

Revised Manuscript: March 13, 2013

Manuscript Accepted: March 14, 2013

Published: April 5, 2013

**Citation**

N. González-Baquedano, I. Torres-Gómez, N. Arzate, A. Ferrando, and D. E. Ceballos-Herrera, "Pulse quality analysis on soliton pulse compression and soliton self-frequency shift in a hollow-core photonic bandgap fiber," Opt. Express **21**, 9132-9143 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-7-9132

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### References

- J. C. Knight, “Photonic crystal fibres,” Nature424, 847–851 (2003). [CrossRef] [PubMed]
- D. G. Ouzounov, C. J. Hensley, A. L. Gaeta, N. Venkataraman, M. T. Gallagher, and K. W. Koch, “Soliton pulse compression in photonic band-gap fibers,” Opt. Express13, 6153–6159 (2005). [CrossRef] [PubMed]
- F. Gérôme, K. Cook, A. K. George, W. Wadsworth, and J. C. Knight, “Delivery of sub-100fs pulses through 8m of hollow-core fiber using soliton compression,” Opt. Express15, 7126–7131 (2007). [CrossRef] [PubMed]
- D. G. Ouzounov, F. R. Ahmad, D. Müller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, “Generation of megawatt optical solitons in hollow-Core photonic band-gap fibers,” Science301, 1702–1704 (2003). [CrossRef] [PubMed]
- F. Luan, J. C. Knight, P. S. J. Russell, S. Campbell, D. Xiao, D. T. Reid, B. J. Mangan, D. P. Williams, and P. J. Roberts, “Femtosecond soliton pulse delivery at 800 nm wavelength in hollow-core photonic bandgap fibers,” Opt. Express12, 835–840 (2004). [CrossRef] [PubMed]
- D. V. Skryabin, “Coupled core-surface solitons in photonics crystal fibers,” Opt. Express12, 4841–4846 (2004). [CrossRef] [PubMed]
- J. C. Knight, F. Gérôme, and W. J. Wadsworth, “Hollow-core photonic crystal fibres for delivery and compression of ultrashort optical pulses,” IEEE J. Quantum Electron.39, 1047–1056 (2007). [CrossRef]
- J. Lægsgaard and P. J. Roberts, “Dispersive pulse compression in hollow-core photonic band gap fibers,” Opt. Express16, 9268–9644 (2008). [CrossRef]
- J. Lægsgaard, “Soliton formation in hollow-core photonic bandgap fibers,” Appl. Phys. B95, 2093–3000 (2009). [CrossRef]
- M. G. Welch, K. Cook, R. A. Correa, F. Gerome, W. J. Wadsworth, A. V. Gorbach, D. V. Skryabin, and J. C. Knight, “Solitons in hollow core photonic crystal fiber: engineering nonlinearity and compressing pulses,” J. Lightwave Technol.27, 1644–1652 (2009). [CrossRef]
- A. A. Ivanov, A. A. Podshivalov, and A. M. Zheltikov, “Frequency-shifted megawatt soliton output of a hollow photonic-crystal fiber for time-resolved coherent anti-Stokes Raman scattering microspectroscopy,” Opt. Lett.31, 3318–3320 (2006). [CrossRef] [PubMed]
- B-W. Liu, M-L. Hu, X-H. Fang, Y-F. Li, L. Chai, C-Y. Wang, W. Tong, J. Luo, A. A. Voronin, and A. M. Zheltikov, “Stabilized soliton self-frequency shift and 0.1-PHz sideband generation in a photonic-crystal fiber with an air-hole-modified core,” Opt. Express16, 14987–14996 (2008). [CrossRef] [PubMed]
- F. Gérome, P. Dupriez, J. Clowes, J. C. Knight, and W. J Wadsworth, “High power tunable femtosecond soliton source using hollow-core photonic bandgap fiber, and its use for frequency doubling,” Opt. Express16, 2381–2386 (2008). [CrossRef] [PubMed]
- A. V Gorbach and D. V Skryabin, “Soliton self-frequency shift, non-solitonic radiation and self-induced transparency in air-core fibers,” Opt. Express16, 4858–4865 (2008). [CrossRef] [PubMed]
- N. González-Baquedano, N. Arzate, I. Torres-Gómez, A. Ferrando, D. E. Ceballos-Herrera, and C. Milián, “Femtosecond pulse compression in a hollow-core photonic bandgap fiber by tuning its cross section,” Photonics and Nanostructures – Fundamentals and Applications10, 594–601 (2012). [CrossRef]
- R. Amezcua-Correa, N. G. Broderick, M. N. Petrovich, F. Poletti, and D. J. Richardson, “Optimizing the usable bandwidth and loss through core design in realistic hollow-core photonic bandgap fibers,” Opt. Express14, 7974–7985 (2006). [CrossRef] [PubMed]
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