## Real time noise and wavelength correlations in octave-spanning supercontinuum generation |

Optics Express, Vol. 21, Issue 15, pp. 18452-18460 (2013)

http://dx.doi.org/10.1364/OE.21.018452

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### Abstract

We use dispersive Fourier transformation to measure shot-to-shot spectral instabilities in femtosecond supercontinuum generation. We study both the onset phase of supercontinuum generation with distinct dispersive wave generation, as well as a highly-unstable supercontinuum regime spanning an octave in bandwidth. Wavelength correlation maps allow interactions between separated spectral components to be identified, even when such interactions are not apparent in shot-to-shot or average measurements. Experimental results are interpreted using numerical simulations. Our results show the clear advantages of dispersive Fourier transformation for studying spectral noise during supercontinuum generation.

© 2013 OSA

## 1. Introduction

3. B. Wetzel, K. J. Blow, S. K. Turitsyn, G. Millot, L. Larger, and J. M. Dudley, “Random walks and random numbers from supercontinuum generation,” Opt. Express **20**(10), 11143–11152 (2012). [CrossRef] [PubMed]

6. B. Kibler, J. Fatome, C. Finot, G. Millot, G. Genty, B. Wetzel, N. Akhmediev, F. Dias, and J. M. Dudley, “Observation of Kuznetsov-Ma soliton dynamics in optical fibre,” Sci. Rep. **2**, 463 (2012). [CrossRef] [PubMed]

7. D. R. Solli, G. Herink, B. Jalali, and C. Ropers, “Fluctuations and correlations in modulation instability,” Nat. Photonics **6**(7), 463–468 (2012). [CrossRef]

8. K. Goda and B. Jalali, “Dispersive Fourier transformation for fast continuous single-shot measurements,” Nat. Photonics **7**(2), 102–112 (2013). [CrossRef]

9. B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, “Real-time full bandwidth measurement of spectral noise in supercontinuum generation,” Sci. Rep. **2**, 882 (2012). [CrossRef] [PubMed]

9. B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, “Real-time full bandwidth measurement of spectral noise in supercontinuum generation,” Sci. Rep. **2**, 882 (2012). [CrossRef] [PubMed]

10. J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. **78**(4), 1135–1184 (2006). [CrossRef]

## 2. Experimental setup

7. D. R. Solli, G. Herink, B. Jalali, and C. Ropers, “Fluctuations and correlations in modulation instability,” Nat. Photonics **6**(7), 463–468 (2012). [CrossRef]

9. B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, “Real-time full bandwidth measurement of spectral noise in supercontinuum generation,” Sci. Rep. **2**, 882 (2012). [CrossRef] [PubMed]

*L*of “stretching” fiber of second–order dispersion

*β*

_{2S}yields (for large

*β*

_{2S}

*L*) a temporally-stretched output pulse with intensity

*v*(in Hz) where 2πν =

*t*/

*β*

_{2S}

*L.*This is the principle of the dispersive Fourier transformation.

*β*

_{2S}

*L*= + 4.030 ps

^{2}and third order dispersion of + 2.344 × 10

^{−3}ps

^{3}. Over our measurement bandwidth, the effect of third order dispersion is not negligible, but rather introduces a curvature into the time-frequency mapping. The red line in Fig. 1(b) shows the calculated nonlinear frequency-time transfer function. To confirm the calculation of this transfer function, we performed an initial series of experiments to generate SC with distinct spectral features that we could clearly identify in both the OSA spectra and the dispersive FT spectra. We were thus able to determine an experimental time delay for a range of different wavelengths. These results are shown as the circles in Fig. 1(b), confirming the dispersion parameters used in calculating the transfer function. Such a small degree of curvature in the transfer function can be readily incorporated in the time-to-frequency mapping to calibrate the frequency axis of the dispersive FT spectra [8

8. K. Goda and B. Jalali, “Dispersive Fourier transformation for fast continuous single-shot measurements,” Nat. Photonics **7**(2), 102–112 (2013). [CrossRef]

## 3. Wavelength correlation mapping

*at any given wavelength*[11

11. S. T. Sørensen, O. Bang, B. Wetzel, and J. M. Dudley, “Describing supercontinuum noise and rogue wave statistics using higher-order moments,” Opt. Commun. **285**(9), 2451–2455 (2012). [CrossRef]

*between pairs of wavelengths*in the SC to be quantified [12

12. E. Schmidt, L. Knöll, D. G. Welsch, M. Zielonka, F. König, and A. Sizmann, “Enhanced Quantum Correlations in Bound Higher-Order Solitons,” Phys. Rev. Lett. **85**(18), 3801–3804 (2000). [CrossRef] [PubMed]

16. D. Majus and A. Dubietis, “Statistical properties of ultrafast supercontinuum generated by femtosecond Gaussian and Bessel beams: a comparative study,” J. Opt. Soc. Am. B **30**(4), 994–999 (2013). [CrossRef]

**2**, 882 (2012). [CrossRef] [PubMed]

12. E. Schmidt, L. Knöll, D. G. Welsch, M. Zielonka, F. König, and A. Sizmann, “Enhanced Quantum Correlations in Bound Higher-Order Solitons,” Phys. Rev. Lett. **85**(18), 3801–3804 (2000). [CrossRef] [PubMed]

15. P. Béjot, J. Kasparian, E. Salmon, R. Ackermann, and J. P. Wolf, “Spectral correlation and noise reduction in laser filaments,” Appl. Phys. B **87**(1), 1–4 (2007). [CrossRef]

*I*(λ) is a time- series array of intensities at any particular wavelength

*λ*in the SC obtained from an ensemble of measurements, the spectral correlation between any two wavelengths

*λ*

_{1}and

*λ*

_{2}in the SC is given by

*:*where angle brackets represent the average over the ensemble. The correlation varies over the range −1<

*ρ*<1 with a positive correlation

*ρ*(

*λ*

_{1},

*λ*

_{2}) > 0 indicating that the intensities at the two wavelengths

*λ*

_{1},

*λ*

_{2}increase or decrease together, and a negative correlation (sometimes called anti-correlation)

*ρ*(

*λ*

_{1},

*λ*

_{2}) < 0 indicating that as the intensity at one wavelength e.g.

*λ*

_{1}increases, that at

*λ*

_{2}decreases and vice-versa.

*λ*

_{0}is a normally-distributed random variable with mean 820 nm and standard deviation of 20 nm. Figure 2(a) plots the correlation matrix from numerical simulations of an ensemble of 1000 spectra undergoing such wavelength jitter. The correlation plot can be understood more readily by referring its structure (the different regions of positive and negative correlation) to the spectral fluctuations shown on each axis. In these spectral plots, the grey curves show a sample of 200 realisations and the black curve is the calculated mean.

## 4. Results for pump spectral broadening and dispersive wave generation

_{fiss}~9 cm (using β

_{2}= −2.2 x 10

^{−2}ps

^{2}m

^{−1}, β

_{3}= 1.2 x 10

^{−4}ps

^{3}m

^{−1}, γ = 50 W

^{−1}m

^{−1}at 820 nm). In this regime with pumping in the anomalous dispersion regime, clear signatures of pump spectral broadening and dispersive wave generation are seen in the OSA spectrum measured at the PCF output, shown as the solid red line in Fig. 3(a). Dispersive FT measurements of the PCF output spectrum were also performed as described above, and used to record an ensemble of 1000 shot-to-shot spectra also shown in Fig. 3(a). With the high soliton number of the input pulse, the initial soliton dynamics are expected to be sensitive to input pulse noise [10

10. J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. **78**(4), 1135–1184 (2006). [CrossRef]

17. N. Akhmediev and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fibers,” Phys. Rev. A **51**(3), 2602–2607 (1995). [CrossRef] [PubMed]

18. M. Erkintalo, Y. Q. Xu, S. G. Murdoch, J. M. Dudley, and G. Genty, “Cascaded phase matching and nonlinear symmetry breaking in fiber frequency combs,” Phys. Rev. Lett. **109**(22), 223904 (2012). [CrossRef] [PubMed]

16. D. Majus and A. Dubietis, “Statistical properties of ultrafast supercontinuum generated by femtosecond Gaussian and Bessel beams: a comparative study,” J. Opt. Soc. Am. B **30**(4), 994–999 (2013). [CrossRef]

## 5. Unstable octave-spanning SC generation

5. D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature **450**(7172), 1054–1057 (2007). [CrossRef] [PubMed]

16. D. Majus and A. Dubietis, “Statistical properties of ultrafast supercontinuum generated by femtosecond Gaussian and Bessel beams: a comparative study,” J. Opt. Soc. Am. B **30**(4), 994–999 (2013). [CrossRef]

## 6. Conclusions

## Acknowledgments

## References and links

1. | J. M. Dudley and J. R. Taylor, |

2. | G. P. Agrawal, |

3. | B. Wetzel, K. J. Blow, S. K. Turitsyn, G. Millot, L. Larger, and J. M. Dudley, “Random walks and random numbers from supercontinuum generation,” Opt. Express |

4. | A. Kudlinski, B. Barviau, A. Leray, C. Spriet, L. Héliot, and A. Mussot, “Control of pulse-to-pulse fluctuations in visible supercontinuum,” Opt. Express |

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

6. | B. Kibler, J. Fatome, C. Finot, G. Millot, G. Genty, B. Wetzel, N. Akhmediev, F. Dias, and J. M. Dudley, “Observation of Kuznetsov-Ma soliton dynamics in optical fibre,” Sci. Rep. |

7. | D. R. Solli, G. Herink, B. Jalali, and C. Ropers, “Fluctuations and correlations in modulation instability,” Nat. Photonics |

8. | K. Goda and B. Jalali, “Dispersive Fourier transformation for fast continuous single-shot measurements,” Nat. Photonics |

9. | B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, “Real-time full bandwidth measurement of spectral noise in supercontinuum generation,” Sci. Rep. |

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

11. | S. T. Sørensen, O. Bang, B. Wetzel, and J. M. Dudley, “Describing supercontinuum noise and rogue wave statistics using higher-order moments,” Opt. Commun. |

12. | E. Schmidt, L. Knöll, D. G. Welsch, M. Zielonka, F. König, and A. Sizmann, “Enhanced Quantum Correlations in Bound Higher-Order Solitons,” Phys. Rev. Lett. |

13. | R. K. Lee, Y. C. Lai, and Y. Kivshar, “Quantum correlations in soliton collisions,” Phys. Rev. A |

14. | P. Béjot, J. Kasparian, E. Salmon, R. Ackermann, N. Gisin, and J. P. Wolf, “Laser noise reduction in air,” Appl. Phys. Lett. |

15. | P. Béjot, J. Kasparian, E. Salmon, R. Ackermann, and J. P. Wolf, “Spectral correlation and noise reduction in laser filaments,” Appl. Phys. B |

16. | D. Majus and A. Dubietis, “Statistical properties of ultrafast supercontinuum generated by femtosecond Gaussian and Bessel beams: a comparative study,” J. Opt. Soc. Am. B |

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

18. | M. Erkintalo, Y. Q. Xu, S. G. Murdoch, J. M. Dudley, and G. Genty, “Cascaded phase matching and nonlinear symmetry breaking in fiber frequency combs,” Phys. Rev. Lett. |

**OCIS Codes**

(070.4340) Fourier optics and signal processing : Nonlinear optical signal processing

(190.3100) Nonlinear optics : Instabilities and chaos

(190.4370) Nonlinear optics : Nonlinear optics, fibers

(320.7110) Ultrafast optics : Ultrafast nonlinear optics

(320.6629) Ultrafast optics : Supercontinuum generation

(070.7145) Fourier optics and signal processing : Ultrafast processing

**ToC Category:**

Ultrafast Optics

**History**

Original Manuscript: April 23, 2013

Revised Manuscript: July 12, 2013

Manuscript Accepted: July 21, 2013

Published: July 24, 2013

**Citation**

T. Godin, B. Wetzel, T. Sylvestre, L. Larger, A. Kudlinski, A. Mussot, A. Ben Salem, M. Zghal, G. Genty, F. Dias, and J. M. Dudley, "Real time noise and wavelength correlations in octave-spanning supercontinuum generation," Opt. Express **21**, 18452-18460 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-15-18452

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### References

- J. M. Dudley and J. R. Taylor, Supercontinuum Generation in Optical Fibers (Cambridge University, 2010).
- G. P. Agrawal, Nonlinear Fiber Optics, 5th ed. (Academic Press, 2012).
- B. Wetzel, K. J. Blow, S. K. Turitsyn, G. Millot, L. Larger, and J. M. Dudley, “Random walks and random numbers from supercontinuum generation,” Opt. Express20(10), 11143–11152 (2012). [CrossRef] [PubMed]
- A. Kudlinski, B. Barviau, A. Leray, C. Spriet, L. Héliot, and A. Mussot, “Control of pulse-to-pulse fluctuations in visible supercontinuum,” Opt. Express18(26), 27445–27454 (2010). [CrossRef] [PubMed]
- D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature450(7172), 1054–1057 (2007). [CrossRef] [PubMed]
- B. Kibler, J. Fatome, C. Finot, G. Millot, G. Genty, B. Wetzel, N. Akhmediev, F. Dias, and J. M. Dudley, “Observation of Kuznetsov-Ma soliton dynamics in optical fibre,” Sci. Rep.2, 463 (2012). [CrossRef] [PubMed]
- D. R. Solli, G. Herink, B. Jalali, and C. Ropers, “Fluctuations and correlations in modulation instability,” Nat. Photonics6(7), 463–468 (2012). [CrossRef]
- K. Goda and B. Jalali, “Dispersive Fourier transformation for fast continuous single-shot measurements,” Nat. Photonics7(2), 102–112 (2013). [CrossRef]
- B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, “Real-time full bandwidth measurement of spectral noise in supercontinuum generation,” Sci. Rep.2, 882 (2012). [CrossRef] [PubMed]
- J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys.78(4), 1135–1184 (2006). [CrossRef]
- S. T. Sørensen, O. Bang, B. Wetzel, and J. M. Dudley, “Describing supercontinuum noise and rogue wave statistics using higher-order moments,” Opt. Commun.285(9), 2451–2455 (2012). [CrossRef]
- E. Schmidt, L. Knöll, D. G. Welsch, M. Zielonka, F. König, and A. Sizmann, “Enhanced Quantum Correlations in Bound Higher-Order Solitons,” Phys. Rev. Lett.85(18), 3801–3804 (2000). [CrossRef] [PubMed]
- R. K. Lee, Y. C. Lai, and Y. Kivshar, “Quantum correlations in soliton collisions,” Phys. Rev. A71(3), 035801 (2005). [CrossRef]
- P. Béjot, J. Kasparian, E. Salmon, R. Ackermann, N. Gisin, and J. P. Wolf, “Laser noise reduction in air,” Appl. Phys. Lett.88(25), 251112 (2006). [CrossRef]
- P. Béjot, J. Kasparian, E. Salmon, R. Ackermann, and J. P. Wolf, “Spectral correlation and noise reduction in laser filaments,” Appl. Phys. B87(1), 1–4 (2007). [CrossRef]
- D. Majus and A. Dubietis, “Statistical properties of ultrafast supercontinuum generated by femtosecond Gaussian and Bessel beams: a comparative study,” J. Opt. Soc. Am. B30(4), 994–999 (2013). [CrossRef]
- N. Akhmediev and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fibers,” Phys. Rev. A51(3), 2602–2607 (1995). [CrossRef] [PubMed]
- M. Erkintalo, Y. Q. Xu, S. G. Murdoch, J. M. Dudley, and G. Genty, “Cascaded phase matching and nonlinear symmetry breaking in fiber frequency combs,” Phys. Rev. Lett.109(22), 223904 (2012). [CrossRef] [PubMed]

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