Abstract

We study experimentally the statistical fluctuations observed in a supercontinuum generated in the normal dispersion regime through cascaded stimulated Raman scattering. Specifically, we show that the statistical distribution of shot-to-shot spectral variations evolves from a quasi-Gaussian in the saturated regime for Stokes orders near the pump to a long-tailed extreme-value distribution for Stokes orders at a large separation from the pump in the unsaturated regime.

© 2010 Optical Society of America

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References

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  1. J. M. Dudley, G. Genty, and S. Coen, "Supercontinuum generation in photonic crystal fiber," Rev. Mod. Phys. 78, 1135-1184 (2006).
    [CrossRef]
  2. D. Solli, C. Ropers, P. Koonath, and B. Jalali, "Optical rogue waves," Nature 450, 1054-1057 (2007).
    [CrossRef] [PubMed]
  3. K. Hammani, C. Finot, J. M. Dudley, and G. Millot, "Optical rogue-wave-like extreme value fluctuations in fiber Raman amplifiers," Opt. Express 16, 16467-16474 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-21-16467.
    [CrossRef] [PubMed]
  4. D. Borlaug and B. Jalali, "Extreme value statistics in silicon photonics," in proceedings of the 21st Annual Meeting of the IEEE Lasers & Electro-Optics Society, Newport Beach, USA, 2008.
  5. A. Maluckov, L. Hadžievski, N. Lazarides, and G. P. Tsironis, "Extreme events in discrete nonlinear lattices," Phys. Rev. E 79, 025601 (2009).
    [CrossRef]
  6. J. Kasparian, P. Béjot, J. P. Wolf, and J. Dudley, "Optical rogue wave statistics in laser filamentation," Opt. Express 17, 12070-12075 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-14-12070.
    [CrossRef] [PubMed]
  7. M. Erkintalo, G. Genty, and J. M. Dudley, "Rogue wave like characteristics in femtosecond supercontinuum generation," Opt. Lett. 34, 2468-2470 (2009).
    [CrossRef] [PubMed]
  8. A. S. Grabtchikov, S. Ya. Kilin, V. P. Kozich, and N. M. Iodo, "Statistics of the energy fluctuations of Stokes pulses in stimulated Raman scattering in various situations," JETP Lett. 43, 151-156 (1986).
  9. A. S. Grabtchikov, A. I. Vodtchits, and V. A. Orlovich, "Pulse-energy statistics in the linear regime of stimulated Raman scattering with a broad-band pump," Phys. Rev. A 56, 1666-1669 (1997).
    [CrossRef]
  10. E. Landahl, D. Baiocchi, and J. R. Thompson, "A simple analytic model for noise shaping by an optical fiber Raman generator," Opt. Commun. 150, 339-347 (1998).
    [CrossRef]
  11. L. Garcia, J. Jenkins, Y. Lee, N. Poole, K. Salit, P. Sidereas, C. G. Goedde, and J. R. Thompson, "Influence of classical pump noise on long-pulse multiorder stimulated Raman scattering in optical fiber," J. Opt. Soc. Am. B 19, 2727-2736 (2002).
    [CrossRef]
  12. A. Betlej, P. Schmitt, P. Sidereas, R. Tracy, C. G. Goedde, and J. R. Thompson, "Increased Stokes pulse energy variation from amplified classical noise in a fiber Raman generator," Opt. Express 13, 2948-2960 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-8-2948.
    [CrossRef] [PubMed]
  13. R. H. Stolen, C. Lee, and R. K. Jain, "Development of the stimulated Raman spectrum in single-mode silica fibers," J. Opt. Soc. Am. B 1, 652-657 (1984).
    [CrossRef]
  14. K. X. Liu and E. Garmire, "Understanding the Formation of the SRS Stokes Spectrum in Fused Silica Fibers," IEEE J. Quantum Electron. 27, 1022-1030 (1991).
    [CrossRef]
  15. B. R. Rankin, R. R. Kellner, and S. W. Hell, "Stimulated-emission-depletion microscopy with a multicolor stimulated-Raman-scattering light source," Opt. Lett. 33, 2491-2493 (2008).
    [PubMed]

2009 (3)

2008 (2)

2007 (1)

D. Solli, C. Ropers, P. Koonath, and B. Jalali, "Optical rogue waves," Nature 450, 1054-1057 (2007).
[CrossRef] [PubMed]

2006 (1)

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

2005 (1)

2002 (1)

1998 (1)

E. Landahl, D. Baiocchi, and J. R. Thompson, "A simple analytic model for noise shaping by an optical fiber Raman generator," Opt. Commun. 150, 339-347 (1998).
[CrossRef]

1997 (1)

A. S. Grabtchikov, A. I. Vodtchits, and V. A. Orlovich, "Pulse-energy statistics in the linear regime of stimulated Raman scattering with a broad-band pump," Phys. Rev. A 56, 1666-1669 (1997).
[CrossRef]

1991 (1)

K. X. Liu and E. Garmire, "Understanding the Formation of the SRS Stokes Spectrum in Fused Silica Fibers," IEEE J. Quantum Electron. 27, 1022-1030 (1991).
[CrossRef]

1986 (1)

A. S. Grabtchikov, S. Ya. Kilin, V. P. Kozich, and N. M. Iodo, "Statistics of the energy fluctuations of Stokes pulses in stimulated Raman scattering in various situations," JETP Lett. 43, 151-156 (1986).

1984 (1)

Baiocchi, D.

E. Landahl, D. Baiocchi, and J. R. Thompson, "A simple analytic model for noise shaping by an optical fiber Raman generator," Opt. Commun. 150, 339-347 (1998).
[CrossRef]

Béjot, P.

Betlej, A.

Coen, S.

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

Dudley, J.

Dudley, J. M.

Erkintalo, M.

Finot, C.

Garcia, L.

Garmire, E.

K. X. Liu and E. Garmire, "Understanding the Formation of the SRS Stokes Spectrum in Fused Silica Fibers," IEEE J. Quantum Electron. 27, 1022-1030 (1991).
[CrossRef]

Genty, G.

M. Erkintalo, G. Genty, and J. M. Dudley, "Rogue wave like characteristics in femtosecond supercontinuum generation," Opt. Lett. 34, 2468-2470 (2009).
[CrossRef] [PubMed]

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

Goedde, C. G.

Grabtchikov, A. S.

A. S. Grabtchikov, A. I. Vodtchits, and V. A. Orlovich, "Pulse-energy statistics in the linear regime of stimulated Raman scattering with a broad-band pump," Phys. Rev. A 56, 1666-1669 (1997).
[CrossRef]

A. S. Grabtchikov, S. Ya. Kilin, V. P. Kozich, and N. M. Iodo, "Statistics of the energy fluctuations of Stokes pulses in stimulated Raman scattering in various situations," JETP Lett. 43, 151-156 (1986).

Hadžievski, L.

A. Maluckov, L. Hadžievski, N. Lazarides, and G. P. Tsironis, "Extreme events in discrete nonlinear lattices," Phys. Rev. E 79, 025601 (2009).
[CrossRef]

Hammani, K.

Hell, S. W.

Iodo, N. M.

A. S. Grabtchikov, S. Ya. Kilin, V. P. Kozich, and N. M. Iodo, "Statistics of the energy fluctuations of Stokes pulses in stimulated Raman scattering in various situations," JETP Lett. 43, 151-156 (1986).

Jain, R. K.

Jalali, B.

D. Solli, C. Ropers, P. Koonath, and B. Jalali, "Optical rogue waves," Nature 450, 1054-1057 (2007).
[CrossRef] [PubMed]

Jenkins, J.

Kasparian, J.

Kellner, R. R.

Kilin, S. Ya.

A. S. Grabtchikov, S. Ya. Kilin, V. P. Kozich, and N. M. Iodo, "Statistics of the energy fluctuations of Stokes pulses in stimulated Raman scattering in various situations," JETP Lett. 43, 151-156 (1986).

Koonath, P.

D. Solli, C. Ropers, P. Koonath, and B. Jalali, "Optical rogue waves," Nature 450, 1054-1057 (2007).
[CrossRef] [PubMed]

Kozich, V. P.

A. S. Grabtchikov, S. Ya. Kilin, V. P. Kozich, and N. M. Iodo, "Statistics of the energy fluctuations of Stokes pulses in stimulated Raman scattering in various situations," JETP Lett. 43, 151-156 (1986).

Landahl, E.

E. Landahl, D. Baiocchi, and J. R. Thompson, "A simple analytic model for noise shaping by an optical fiber Raman generator," Opt. Commun. 150, 339-347 (1998).
[CrossRef]

Lazarides, N.

A. Maluckov, L. Hadžievski, N. Lazarides, and G. P. Tsironis, "Extreme events in discrete nonlinear lattices," Phys. Rev. E 79, 025601 (2009).
[CrossRef]

Lee, C.

Lee, Y.

Liu, K. X.

K. X. Liu and E. Garmire, "Understanding the Formation of the SRS Stokes Spectrum in Fused Silica Fibers," IEEE J. Quantum Electron. 27, 1022-1030 (1991).
[CrossRef]

Maluckov, A.

A. Maluckov, L. Hadžievski, N. Lazarides, and G. P. Tsironis, "Extreme events in discrete nonlinear lattices," Phys. Rev. E 79, 025601 (2009).
[CrossRef]

Millot, G.

Orlovich, V. A.

A. S. Grabtchikov, A. I. Vodtchits, and V. A. Orlovich, "Pulse-energy statistics in the linear regime of stimulated Raman scattering with a broad-band pump," Phys. Rev. A 56, 1666-1669 (1997).
[CrossRef]

Poole, N.

Rankin, B. R.

Ropers, C.

D. Solli, C. Ropers, P. Koonath, and B. Jalali, "Optical rogue waves," Nature 450, 1054-1057 (2007).
[CrossRef] [PubMed]

Salit, K.

Schmitt, P.

Sidereas, P.

Solli, D.

D. Solli, C. Ropers, P. Koonath, and B. Jalali, "Optical rogue waves," Nature 450, 1054-1057 (2007).
[CrossRef] [PubMed]

Stolen, R. H.

Thompson, J. R.

Tracy, R.

Tsironis, G. P.

A. Maluckov, L. Hadžievski, N. Lazarides, and G. P. Tsironis, "Extreme events in discrete nonlinear lattices," Phys. Rev. E 79, 025601 (2009).
[CrossRef]

Vodtchits, A. I.

A. S. Grabtchikov, A. I. Vodtchits, and V. A. Orlovich, "Pulse-energy statistics in the linear regime of stimulated Raman scattering with a broad-band pump," Phys. Rev. A 56, 1666-1669 (1997).
[CrossRef]

Wolf, J. P.

IEEE J. Quantum Electron. (1)

K. X. Liu and E. Garmire, "Understanding the Formation of the SRS Stokes Spectrum in Fused Silica Fibers," IEEE J. Quantum Electron. 27, 1022-1030 (1991).
[CrossRef]

J. Opt. Soc. Am. B (2)

JETP Lett. (1)

A. S. Grabtchikov, S. Ya. Kilin, V. P. Kozich, and N. M. Iodo, "Statistics of the energy fluctuations of Stokes pulses in stimulated Raman scattering in various situations," JETP Lett. 43, 151-156 (1986).

Nature (1)

D. Solli, C. Ropers, P. Koonath, and B. Jalali, "Optical rogue waves," Nature 450, 1054-1057 (2007).
[CrossRef] [PubMed]

Opt. Commun. (1)

E. Landahl, D. Baiocchi, and J. R. Thompson, "A simple analytic model for noise shaping by an optical fiber Raman generator," Opt. Commun. 150, 339-347 (1998).
[CrossRef]

Opt. Express (3)

Opt. Lett. (2)

Phys. Rev. A (1)

A. S. Grabtchikov, A. I. Vodtchits, and V. A. Orlovich, "Pulse-energy statistics in the linear regime of stimulated Raman scattering with a broad-band pump," Phys. Rev. A 56, 1666-1669 (1997).
[CrossRef]

Phys. Rev. E (1)

A. Maluckov, L. Hadžievski, N. Lazarides, and G. P. Tsironis, "Extreme events in discrete nonlinear lattices," Phys. Rev. E 79, 025601 (2009).
[CrossRef]

Rev. Mod. Phys. (1)

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

Other (1)

D. Borlaug and B. Jalali, "Extreme value statistics in silicon photonics," in proceedings of the 21st Annual Meeting of the IEEE Lasers & Electro-Optics Society, Newport Beach, USA, 2008.

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Figures (5)

Fig. 1.
Fig. 1.

(a) Experimental setup. (b) Example of a generated SC spectrum.

Fig. 2.
Fig. 2.

(a-d) Examples of pump pulse envelopes captured prior to coupling together with the measured peak power distribution (e). Inset shows the histogram on a log-log scale.

Fig. 3.
Fig. 3.

(a) Superimposed experimental single-shot spectra (for clarity, only 500 spectra are shown) and the mean calculated over the 9000 spectra (black line). Arrows indicate the wavelengths at which the intensity histograms are calculated. (b), (c), (d) Examples of individual SC spectra highlighting the significant shot-to-shot variations.

Fig. 4.
Fig. 4.

Histograms of recorded spectral intensity at selected wavelengths of (a) 386 nm, (b) 408 nm, (c) 415 nm, and (d) 427 nm. Insets show the histograms on a log-log scale.

Fig. 5.
Fig. 5.

Mean spectrum (left axis) together with Pareto metric M(λ) (right axis) for (a) low input energy measurement, (b) high energy measurement. (c) Simulated results (see text above for more details).

Equations (1)

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M ( λ 0 ) = i = 1 0.2 N I i ( λ 0 ) / i = 1 N I i ( λ 0 ) ,

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