## Supercontinuum generation by multiple scatterings at a group velocity horizon |

Optics Express, Vol. 22, Issue 4, pp. 3866-3879 (2014)

http://dx.doi.org/10.1364/OE.22.003866

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### Abstract

A new scheme for supercontinuum generation covering more than one octave and exhibiting extraordinary high coherence properties has recently been proposed [Phys. Rev. Lett. **110**, 233901 (2013)]. The scheme is based on two-pulse collision at a group velocity horizon between a dispersive wave and a soliton. Here we demonstrate that the same scheme can be exploited for the generation of supercontinua encompassing the entire transparency region of fused silica, ranging from 300 to 2300nm. At this bandwidth extension, the Raman effect becomes detrimental, yet may be compensated by using a cascaded collision process. Consequently, the high degree of coherence does not degrade even in this extreme scenario.

© 2014 Optical Society of America

## 1. Introduction

17. T. G. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. König, and U. Leonhardt, “Fiber-optical analog of the event horizon,” Science **319**, 1367–1370 (2008). [CrossRef] [PubMed]

23. N. G. R. Broderick, D. Taverner, D. J. Richardson, M. Ibsen, and R. I. Laming, “Optical pulse compression in fiber Bragg gratings,” Phys. Rev. Lett. **79**, 4566–4569 (1997). [CrossRef]

27. M. Wimmer, A. Regensburger, C. Bersch, M.-A. Miri, S. Batz, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Optical diametric drive acceleration through action-reaction symmetry breaking,” Nat. Phys. **9**, 780–784 (2013). [CrossRef]

28. L. Tartara, “Frequency shifting of femtosecond pulses by reflection at solitons,” IEEE J. Quantum Electron. **12**, 1439–1442 (2012). [CrossRef]

29. 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]

30. A. Demircan, S. Amiranashvili, and G. Steinmeyer, “Controlling light by light with an optical event horizon,” Phys. Rev. Lett. **106**, 163901 (2011). [CrossRef] [PubMed]

31. E. Rubino, A. Lotti, F. Belgiorno, S. L. Cacciatori, A. Couairon, U. Leonhardt, and D. Faccio, “Soliton-induced relativistic-scattering and amplification,” Sci. Rep. **2**, 932 (2012). [CrossRef] [PubMed]

32. P. V. Mamyshev, P. G. J. Wigley, J. Wilson, G. I. Stegeman, V. A. Semeonov, E. M. Dianov, and S. I. Miroshnichenko, “Adiabatic compression of Schrödinger solitons due to the combined perturbations of higher-order dispersion and delayed nonlinear response” Phys. Rev. Lett. **71**, 73–76 (2003). [CrossRef]

33. M. F. Saleh, W. Chang, P. Hölzer, A. Nazarkin, J. C. Travers, N. Y. Joly, P. St. J. Russell, and F. Biancalana, “Theory of photoionization-induced blueshift of ultrashort solitons in gas-filled hollow-core photonic crystal fibers,” Phys. Rev. Lett. **107**, 203902 (2011). [CrossRef] [PubMed]

## 2. Propagation model in terms of the analytical signal

34. S. Amiranashvili and A. Demircan, “Hamiltonian structure of propagation equations for ultrashort optical pulses,” Phys. Rev. A **82**, 013812 (2010). [CrossRef]

35. S. Amiranashvili and A. Demircan, “Ultrashort optical pulse propagation in terms of analytic signal,” Adv. Opt. Technol. **2011**, 989515 (2011). [CrossRef]

36. V. E. Zakharov, V. S. Lvov, and G. E. Falkovich, *Kolmogorov Spectra of Turbulence I – Wave Turbulence* (Springer, 1992). [CrossRef]

*E*(

*z*,

*t*) Here

*c*is the speed of light,

*χ*

^{(3)}is the third-order nonlinear susceptibility. Both bulk and geometric contributions to the fiber dispersion are encoded in the linear operator

*ε̃*, which is defined via convolution with some effective dispersion function

*ε*

_{eff}(

*ω*). For the time being the fiber is dissipation-free, the Raman effect will be accounted for later on. For the Fourier components

*E*(

_{ω}*z*) we obtain where

*β*

^{2}(

*ω*)

*c*

^{2}=

*ω*

^{2}

*ε*

_{eff}(

*ω*), and (

*E*

^{3})

*denotes Fourier transform of the nonlinear terms. The key idea is to consider Eq. (2) as a system of weakly coupled nonlinear oscillators with the “frequency” |*

_{ω}*β*(

*ω*)| and to transform the left-hand-side of Eq. (2) to the normal form,

*i*∂

*+ |*

_{z}𝒜_{ω}*β*(

*ω*)|

*𝒜*, for a suitable normal variable

_{ω}*𝒜*(

_{ω}*z*). Equation (2) is then treated as a Hamiltonian where

*H*

_{nonlin}generates the nonlinear terms in Eq. (2). Equation (3) provides a

*z*-propagation version of the standard time-evolution Hamiltonian equation of the form which is usually used to quantize fields. Remarkably, representation (4) is of importance not only for the second quantization formalism but also for the classical nonlinear waves [36

36. V. E. Zakharov, V. S. Lvov, and G. E. Falkovich, *Kolmogorov Spectra of Turbulence I – Wave Turbulence* (Springer, 1992). [CrossRef]

*𝒜*(

*z*,

*t*) is introduced by the relations It is important to stress that we perform a change of variables which works in both directions as opposed by the usual envelope definition

*E*(

*z*,

*t*) = Re[Ψ(

*z*,

*t*)

*e*

^{−iω0t}], where it is impossible to express Ψ(

*z*,

*t*) in terms of

*E*(

*z*,

*t*) without further assumptions such as the slowly-varying envelope approximation (SVEA). Equation (1) is transformed to the form where we use short notations

*β*=

*β*(

*ω*) does not support the third-harmonics generation process. Neglecting then all non-resonant terms, one obtains a much more simple expression and Eq. (6) is reduced to the form where

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

## 3. Optical event horizon inducing collisions between dispersive waves and solitons

*β*

_{2}profile and the relative group delay

*β*

_{1}= 1/

*v*profile are shown in Fig. 1, together with a selection of three exemplary frequency combinations. The fiber group index is taken from [37

_{g}37. J. M. Stone and J. C. Knight, “Visibly ‘white’ light generation in uniform photonic crystal fiber using a microchip laser,” Opt. Express **16**, 2670–2675 (2008). [CrossRef] [PubMed]

*ℰ*,

_{s,p}*t*,

_{s,p}*ω*correspond to the initial field, the temporal width, and the center frequency, respectively. The pulses are injected at an initial time delay of Δ

_{s,p}*T*= 450 fs into the fiber on either side of the zero dispersion wavelength. For demonstration of the main mechanism, we first neglect the Raman effect. In principle, such pure Raman-free behavior can be realized in hollow-core fibers filled with noble gases [33

33. M. F. Saleh, W. Chang, P. Hölzer, A. Nazarkin, J. C. Travers, N. Y. Joly, P. St. J. Russell, and F. Biancalana, “Theory of photoionization-induced blueshift of ultrashort solitons in gas-filled hollow-core photonic crystal fibers,” Phys. Rev. Lett. **107**, 203902 (2011). [CrossRef] [PubMed]

30. A. Demircan, S. Amiranashvili, and G. Steinmeyer, “Controlling light by light with an optical event horizon,” Phys. Rev. Lett. **106**, 163901 (2011). [CrossRef] [PubMed]

38. S. Batz and U. Peschel, “Diametrically driven self-accelerating pulses in a photonic crystal fiber,” Phys. Rev. Lett. **110**, 193901 (2013). [CrossRef] [PubMed]

*β*

_{3}coefficient. The elementary collision process is completely elastic, causing a mutual shift of optical frequencies, yet without transferring photons from the normal dispersion regime into the soliton regime or vice versa. With the photon number of the soliton being conserved, the soliton blueshift is automatically accompanied by a mild energy increase. However, the blue-shifted soliton is located closer to the zero-dispersion wavelength and therefore also experiences a reduced second-order dispersion after the collision. Depending on the initial frequency of the soliton, an induced frequency shift of only a few nm may result in a considerable change of the dispersion parameter, depending on the strength of the

*β*

_{3}coefficient. Considering that the energy

*E*of a fundamental soliton relates to

*P*

_{0}and

*β*

_{2}via the reduction of

*β*

_{2}cannot be compensated by a decrease of

*E*because

*E*is nearly constant and may even slightly grow due to the increase of photon energy. As

*γ*also does not vary appreciably with wavelength, Eq. (23) therefore affects a massive growth of

*P*

_{0}as a result of the blue shift. Moreover, as the pulse energy is nearly conserved, this peak power growth is automatically accompanied by a decrease in pulse width. In summary, one can understand the reshaping process of the soliton as an adiabatic compression mechanism that is induced by the DW via mutual four-wave mixing processes. A reverse scenario where the DW is reflected at the trailing edge of the soliton also results in the opposite effect. In the latter case both pulses are decelerated due to their interaction. Consequently, the soliton is not compressed, which renders this situation unsuitable for SC generation.

## 4. SC generation by soliton collision with dispersive waves

9. D. V. Skryabin and A. V. Gorbach, “Colloquim: Looking at a soliton through the prism of optical supercontinuum,” Rev. Mod. Phys. **82**, 1287–1299 (2010). [CrossRef]

15. R. Driben, F. Mitschke, and N. Zhavoronkov, “Cascaded interactions between Raman induced solitons and dispersive waves in photonic crystal fibers at the advanced stage of supercontinuum generation,” Opt. Express **18**, 25993–25998 (2010). [CrossRef] [PubMed]

39. G. Genty, M. Lehtonen, and H. Ludvigsen, “Route to broadband blue-light generation in microstructured fibers,” Opt. Lett. **30**, 756–758 (2005). [CrossRef] [PubMed]

*t*,

*z*)-plane, which is typical for the interaction behavior at an optical event horizon. However, we have a natural limitation of the acceleration process as the group-velocity must not exceed its maximum value given by the minimum of

*β*

_{1}at the ZDW. At this point the soliton can no longer be accelerated, which terminates soliton compression. Subsequently, we finally observe a transfer of energy from the soliton into the normal dispersion regime. This final process also contributes to the SC generation.

40. K. R. Tamura and M. Nakazawa, “Femtosecond soliton generation over a 32-nm wavelength range using a dispersion-flattened dispersion-decreasing fiber,” IEEE Photonics Technol. Lett. **11**, 319–321 (1999). [CrossRef]

41. A. A. Voronin and A. M. Zheltikov, “Soliton-number analysis of soliton-effect pulse compression to single-cycle pulse widths,” Phys. Rev. A **78**, 063834 (2008). [CrossRef]

14. A. Demircan, S. Amiranashvili, C. Brée, and G. Steinmeyer, “Compressible octave spanning supercontinuum generation by two-pulse collisions,” Phys. Rev. Lett. **110**, 233901 (2013). [CrossRef]

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

14. A. Demircan, S. Amiranashvili, C. Brée, and G. Steinmeyer, “Compressible octave spanning supercontinuum generation by two-pulse collisions,” Phys. Rev. Lett. **110**, 233901 (2013). [CrossRef]

11. A. Demircan and U. Bandelow, “Analysis of the interplay between soliton fission and modulation instability in supercontinuum generation,” Appl. Phys. B **86**, 31–39 (2007). [CrossRef]

## 5. Supercontinuum generation under consideration of the Raman effect

7. A. V. Gorbach and D. V. Skryabin, “Bouncing of a dispersive pulse on an accelerating soliton and stepwise frequency conversion in optical fibers,” Opt. Express **15**, 14560–14565 (2008). [CrossRef]

17. T. G. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. König, and U. Leonhardt, “Fiber-optical analog of the event horizon,” Science **319**, 1367–1370 (2008). [CrossRef] [PubMed]

42. S. Robertson and U. Leonhardt, “Frequency shifting at fiber-optical event horizons: The effect of Raman deceleration,” Phys. Rev. A **81**, 063835 (2010). [CrossRef]

45. A. Demircan, S. Amiranashvili, C. Brée, C. Mahnke, F. Mitschke, and G. Steinmeyer, “Rogue wave formation by accelerated solitons at an optical event horizon,” Appl. Phys. B, doi: [CrossRef] (2013).

14. A. Demircan, S. Amiranashvili, C. Brée, and G. Steinmeyer, “Compressible octave spanning supercontinuum generation by two-pulse collisions,” Phys. Rev. Lett. **110**, 233901 (2013). [CrossRef]

46. F. M. Mitschke and L. F. Mollenauer, “Discovery of the soliton self-frequency shift,” Opt. Lett. **11**, 659–661 (1986). [CrossRef] [PubMed]

47. G. Genty, M. Surakka, J. Turunen, and A. T. Friberg, “Complete characterization of supercontinuum coherence,” J. Opt. Soc. Am. B **28**, 2301–2309 (2011). [CrossRef]

*E*

_{1}(

*λ*,

*t*),

*E*

_{2}(

*λ*,

*t*)] obtained from 512 simulations.

*z*of the fiber, using the same parameters as in Fig. 5(b). The corresponding degree of coherence [Fig. 6(b)] reflects the expected insensitivity to noise. We observe similar coherence properties for a SC that covers the whole transparency region as was previously reported for an only 1.5 octave spanning SC in Ref. [14

**110**, 233901 (2013). [CrossRef]

## 6. Conclusion

## Acknowledgments

## References and links

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

2. | R. Holzwarth, M. Zimmermann, T. Udem, T. W. Hänsch, P. Russbüldt, K. Gäbel, R. Poprawe, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “White-light frequency comb generation with a diode-pumped Cr:LiSAF laser,” Opt. Lett. |

3. | R. Holzwarth, T. Udem, T. W. Hänsch, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “Optical frequency synthesizer for precision spectroscopy,” Phys. Rev. Lett. |

4. | K. Saitoh and M. Koshiba, “Highly nonlinear dispersion-flattened photonic crystal fibers for supercontinuum generation in a telecommunication window,” Opt. Express |

5. | 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. |

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

7. | A. V. Gorbach and D. V. Skryabin, “Bouncing of a dispersive pulse on an accelerating soliton and stepwise frequency conversion in optical fibers,” Opt. Express |

8. | D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature |

9. | D. V. Skryabin and A. V. Gorbach, “Colloquim: Looking at a soliton through the prism of optical supercontinuum,” Rev. Mod. Phys. |

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

11. | A. Demircan and U. Bandelow, “Analysis of the interplay between soliton fission and modulation instability in supercontinuum generation,” Appl. Phys. B |

12. | U. Møller, S. T. Sorensen, C. Jacobsen, J. Johansen, P. M. Moselund, C. L. Thomsen, and O. Bang, “Power dependence of supercontinuum noise in uniform and tapered PCFs,” Opt. Express |

13. | U. Møller and O. Bang, “Intensity noise in normal-pumped picoseconds supercontinuum generation, where higher-order Raman lines cross into the anomalous dispersion regime,” Electron. Lett. |

14. | A. Demircan, S. Amiranashvili, C. Brée, and G. Steinmeyer, “Compressible octave spanning supercontinuum generation by two-pulse collisions,” Phys. Rev. Lett. |

15. | R. Driben, F. Mitschke, and N. Zhavoronkov, “Cascaded interactions between Raman induced solitons and dispersive waves in photonic crystal fibers at the advanced stage of supercontinuum generation,” Opt. Express |

16. | A. Demircan, S. Amiranashvili, C. Brée, C. Mahnke, F. Mitschke, and G. Steinmeyer, “Rogue events in the group velocity horizon,” Sci. Rep. |

17. | T. G. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. König, and U. Leonhardt, “Fiber-optical analog of the event horizon,” Science |

18. | F. Belgiorno, S. L. Cacciatori, M. Clerici, V. Gorini, G. Ortenzi, L. Rizzi, E. Rubino, V. G. Sala, and D. Faccio, “Hawking radiation from ultrashort laser pulse filaments,” Phys. Rev. Lett. |

19. | D. Faccio, “Laser pulse analogues of gravity and analogue Hawking radiation,” Cont. Phys. |

20. | R. Smith, “Reflection of short gravity waves on a non-uniform current,” Math. Proc. Cambridge Philos. Soc. |

21. | J.-C. Nardin, G. Rousseax, and P. Coullet, “Wave-current interaction as a spatial dynamical system: analogies with rainbow and black hole physics,” Phys. Rev. Lett. |

22. | C. M. De Sterke, “Optical push broom,” Opt. Lett. |

23. | N. G. R. Broderick, D. Taverner, D. J. Richardson, M. Ibsen, and R. I. Laming, “Optical pulse compression in fiber Bragg gratings,” Phys. Rev. Lett. |

24. | N. Rosanov, “Transformation of electromagnetic radiation at moving inhomogeneities of a medium,” JETP Lett. |

25. | N. Rozanov, “Subluminal and superluminal parametric doppler effects in the case of light reflection from a moving smooth medium inhomogeneity,” JETP |

26. | V. E. Lobanov and A. P. Sukhorukov, “Total reflection, frequency, and velocity tuning in optical pulse collision in nonlinear dispersive media,” Phys. Rev. A |

27. | M. Wimmer, A. Regensburger, C. Bersch, M.-A. Miri, S. Batz, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Optical diametric drive acceleration through action-reaction symmetry breaking,” Nat. Phys. |

28. | L. Tartara, “Frequency shifting of femtosecond pulses by reflection at solitons,” IEEE J. Quantum Electron. |

29. | 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. |

30. | A. Demircan, S. Amiranashvili, and G. Steinmeyer, “Controlling light by light with an optical event horizon,” Phys. Rev. Lett. |

31. | E. Rubino, A. Lotti, F. Belgiorno, S. L. Cacciatori, A. Couairon, U. Leonhardt, and D. Faccio, “Soliton-induced relativistic-scattering and amplification,” Sci. Rep. |

32. | P. V. Mamyshev, P. G. J. Wigley, J. Wilson, G. I. Stegeman, V. A. Semeonov, E. M. Dianov, and S. I. Miroshnichenko, “Adiabatic compression of Schrödinger solitons due to the combined perturbations of higher-order dispersion and delayed nonlinear response” Phys. Rev. Lett. |

33. | M. F. Saleh, W. Chang, P. Hölzer, A. Nazarkin, J. C. Travers, N. Y. Joly, P. St. J. Russell, and F. Biancalana, “Theory of photoionization-induced blueshift of ultrashort solitons in gas-filled hollow-core photonic crystal fibers,” Phys. Rev. Lett. |

34. | S. Amiranashvili and A. Demircan, “Hamiltonian structure of propagation equations for ultrashort optical pulses,” Phys. Rev. A |

35. | S. Amiranashvili and A. Demircan, “Ultrashort optical pulse propagation in terms of analytic signal,” Adv. Opt. Technol. |

36. | V. E. Zakharov, V. S. Lvov, and G. E. Falkovich, |

37. | J. M. Stone and J. C. Knight, “Visibly ‘white’ light generation in uniform photonic crystal fiber using a microchip laser,” Opt. Express |

38. | S. Batz and U. Peschel, “Diametrically driven self-accelerating pulses in a photonic crystal fiber,” Phys. Rev. Lett. |

39. | G. Genty, M. Lehtonen, and H. Ludvigsen, “Route to broadband blue-light generation in microstructured fibers,” Opt. Lett. |

40. | K. R. Tamura and M. Nakazawa, “Femtosecond soliton generation over a 32-nm wavelength range using a dispersion-flattened dispersion-decreasing fiber,” IEEE Photonics Technol. Lett. |

41. | A. A. Voronin and A. M. Zheltikov, “Soliton-number analysis of soliton-effect pulse compression to single-cycle pulse widths,” Phys. Rev. A |

42. | S. Robertson and U. Leonhardt, “Frequency shifting at fiber-optical event horizons: The effect of Raman deceleration,” Phys. Rev. A |

43. | A. V. Yulin, R. Driben, B. A. Malomed, and D. V. Skryabin, “Soliton interaction mediated by cascaded four wave mixing with dispersive waves,” Opt. Express |

44. | R. Driben, A. V. Yulin, A. Efimov, and B. A. Malomed, “Trapping of light in solitonic cavities and its role in the supercontinuum generation,” Opt. Express |

45. | A. Demircan, S. Amiranashvili, C. Brée, C. Mahnke, F. Mitschke, and G. Steinmeyer, “Rogue wave formation by accelerated solitons at an optical event horizon,” Appl. Phys. B, doi: [CrossRef] (2013). |

46. | F. M. Mitschke and L. F. Mollenauer, “Discovery of the soliton self-frequency shift,” Opt. Lett. |

47. | G. Genty, M. Surakka, J. Turunen, and A. T. Friberg, “Complete characterization of supercontinuum coherence,” J. Opt. Soc. Am. B |

**OCIS Codes**

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

(320.5520) Ultrafast optics : Pulse compression

(320.6629) Ultrafast optics : Supercontinuum generation

**ToC Category:**

Nonlinear sources

**History**

Original Manuscript: January 6, 2014

Revised Manuscript: January 31, 2014

Manuscript Accepted: February 3, 2014

Published: February 12, 2014

**Virtual Issues**

2013 Advanced Solid State Lasers (2013) *Optics Express*

**Citation**

Ayhan Demircan, Shalva Amiranashvili, Carsten Brée, Uwe Morgner, and Günter Steinmeyer, "Supercontinuum generation by multiple scatterings at a group velocity horizon," Opt. Express **22**, 3866-3879 (2014)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-4-3866

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### References

- J. M. Dudley, G. Genty, S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006). [CrossRef]
- R. Holzwarth, M. Zimmermann, T. Udem, T. W. Hänsch, P. Russbüldt, K. Gäbel, R. Poprawe, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, “White-light frequency comb generation with a diode-pumped Cr:LiSAF laser,” Opt. Lett. 26, 1376–1378 (2001). [CrossRef]
- R. Holzwarth, T. Udem, T. W. Hänsch, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, “Optical frequency synthesizer for precision spectroscopy,” Phys. Rev. Lett. 85, 2264–2267 (2000). [CrossRef] [PubMed]
- K. Saitoh, M. Koshiba, “Highly nonlinear dispersion-flattened photonic crystal fibers for supercontinuum generation in a telecommunication window,” Opt. Express 12, 2027–2032 (2004). [CrossRef] [PubMed]
- I. Hartl, X. D. Li, C. Chudoba, R. K. Ghanta, T. H. Ko, J. G. Fujimoto, J. K. Ranka, 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. V. Husakou, J. Herrmann, “Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers,” Phys. Rev. Lett. 87, 203901 (2001). [CrossRef] [PubMed]
- A. V. Gorbach, D. V. Skryabin, “Bouncing of a dispersive pulse on an accelerating soliton and stepwise frequency conversion in optical fibers,” Opt. Express 15, 14560–14565 (2008). [CrossRef]
- D. R. Solli, C. Ropers, P. Koonath, B. Jalali, “Optical rogue waves,” Nature 450, 1054 (2007). [CrossRef] [PubMed]
- D. V. Skryabin, A. V. Gorbach, “Colloquim: Looking at a soliton through the prism of optical supercontinuum,” Rev. Mod. Phys. 82, 1287–1299 (2010). [CrossRef]
- A. Demircan, U. Bandelow, “Supercontinuum generation by the modulation instability,” Opt. Commun. 244, 181–185 (2005). [CrossRef]
- A. Demircan, U. Bandelow, “Analysis of the interplay between soliton fission and modulation instability in supercontinuum generation,” Appl. Phys. B 86, 31–39 (2007). [CrossRef]
- U. Møller, S. T. Sorensen, C. Jacobsen, J. Johansen, P. M. Moselund, C. L. Thomsen, O. Bang, “Power dependence of supercontinuum noise in uniform and tapered PCFs,” Opt. Express 20, 2851–2857 (2012). [CrossRef] [PubMed]
- U. Møller, O. Bang, “Intensity noise in normal-pumped picoseconds supercontinuum generation, where higher-order Raman lines cross into the anomalous dispersion regime,” Electron. Lett. 49, 63–64 (2013). [CrossRef]
- A. Demircan, S. Amiranashvili, C. Brée, G. Steinmeyer, “Compressible octave spanning supercontinuum generation by two-pulse collisions,” Phys. Rev. Lett. 110, 233901 (2013). [CrossRef]
- R. Driben, F. Mitschke, N. Zhavoronkov, “Cascaded interactions between Raman induced solitons and dispersive waves in photonic crystal fibers at the advanced stage of supercontinuum generation,” Opt. Express 18, 25993–25998 (2010). [CrossRef] [PubMed]
- A. Demircan, S. Amiranashvili, C. Brée, C. Mahnke, F. Mitschke, G. Steinmeyer, “Rogue events in the group velocity horizon,” Sci. Rep. 2, 850 (2012). [CrossRef] [PubMed]
- T. G. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. König, U. Leonhardt, “Fiber-optical analog of the event horizon,” Science 319, 1367–1370 (2008). [CrossRef] [PubMed]
- F. Belgiorno, S. L. Cacciatori, M. Clerici, V. Gorini, G. Ortenzi, L. Rizzi, E. Rubino, V. G. Sala, D. Faccio, “Hawking radiation from ultrashort laser pulse filaments,” Phys. Rev. Lett. 105, 203901 (2010). [CrossRef]
- D. Faccio, “Laser pulse analogues of gravity and analogue Hawking radiation,” Cont. Phys. 1, 97–112 (2012). [CrossRef]
- R. Smith, “Reflection of short gravity waves on a non-uniform current,” Math. Proc. Cambridge Philos. Soc. 78, 517–525 (1975). [CrossRef]
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