Abstract

The noise properties of a supercontiuum can be significantly improved both in terms of coherence and intensity stability by modulating the input pulse with a seed. In this paper, we numerically investigate the influence of the seed wavelength, the pump power, and the modulation instability gain spectrum on the seeding process. The results can be clearly divided into a number of distinct dynamical regimes depending on the initial four-wave mixing process. We further demonstrate that seeding can be used to generate coherent and incoherent rogue waves, depending on the modulation instability gain spectrum. Finally, we show that the coherent pulse breakup afforded by seeding is washed out by turbulent solitonic dynamics when the pump power is increased to the kilowatt level. Thus our results show that seeding cannot improve the noise performance of a high power supercontinuum source.

© 2012 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. P. Beaud, W. Hodel, B. Zysset, and H. Weber, “Ultrashort pulse propagation, pulse breakup, and fundamental soliton formation in a single-mode optical fiber,” IEEE J. Quantum Electron. 23, 1938–1946 (1987).
    [CrossRef]
  3. J. M. Stone and J. C. Knight, “Visibly ‘white’ light generation in uniformphotonic crystal fiber using a microchip laser,” Opt. Express 16, 2670–2675 (2008).
    [CrossRef]
  4. J. C. Travers and J. R. Taylor, “Soliton trapping of dispersive waves in tapered optical fibers,” Opt. Lett. 34, 115–117(2009).
    [CrossRef]
  5. J. C. Travers, “Blue extension of optical fibre supercontinuum generation,” J. Opt. 12, 113001 (2010).
    [CrossRef]
  6. S. T. Sørensen, A. Judge, C. L. Thomsen, and O. Bang, “Optimum fiber tapers for increasing the power in the blue edge of a supercontinuum—group-acceleration matching,” Opt. Lett. 36, 816–818 (2011).
    [CrossRef]
  7. M. H. Frosz, P. M. Moselund, P. D. Rasmussen, C. L. Thomsen, and O. Bang, “Increasing the blue-shift of a supercontinuum by modifying the fiber glass composition,” Opt. Express 16, 21076–21086 (2008).
    [CrossRef]
  8. V. Tombelaine, C. Lesvigne, P. Leproux, L. Grossard, V. Couderc, J.-L. Auguste, J.-M. Blondy, G. Huss, and P.-H. Pioger, “Ultra wide band supercontinuum generation in air-silica holey fibers by SHG-induced modulation instabilities,” Opt. Express 13, 7399–7404 (2005).
    [CrossRef]
  9. J. C. Travers, S. V. Popov, and J. R. Taylor, “Extended blue supercontinuum generation in cascaded holey fibers,” Opt. Lett. 30, 3132–3134 (2005).
    [CrossRef]
  10. P. M. Moselund, M. H. Frosz, C. L. Thomsen, and O. Bang, “Back-seeding of higher order gain processes in picosecond supercontinuum generation,” Opt. Express 16, 11954–11968(2008).
    [CrossRef]
  11. P. M. Moselund, “Long-pulsed supercontinuum sources,” Ph.D. dissertation, DTU Fotonik, Dept. of Photonics Engineering, Technical Univ. of Denmark (2009).
  12. N. Brauckmann, M. Kues, T. Walbaum, P. Groß, and C. Fallnich, “Experimental investigations on nonlinear dynamics in supercontinuum generation with feedback,” Opt. Express 18, 7190–7202 (2010).
    [CrossRef]
  13. M. N. Islam, G. Sucha, I. Bar-Joseph, M. Wegener, J. P. Gordon, and D. S. Chemla, “Femtosecond distributed soliton spectrum in fibers,” J. Opt. Soc. Am. B 6, 1149–1158 (1989).
    [CrossRef]
  14. O. Bang and M. Peyrard, “Generation of high-energy localized vibrational modes in nonlinear Klein-Gordon lattices,” Phys. Rev. E 53, 4143–4152 (1996).
    [CrossRef]
  15. O. Bang and P. D. Miller, “Exploiting discreteness for switching in waveguide arrays,” Opt. Lett. 21, 1105–1107(1996).
    [CrossRef]
  16. F. Luan, D. V. Skryabin, A. V. Yulin, and J. C. Knight, “Energy exchange between colliding solitons in photonic crystal fibers,” Opt. Express 14, 9844–9853 (2006).
    [CrossRef]
  17. G. Genty, C. M. de Sterke, O. Bang, F. Dias, N. Akhmediev, and J. M. Dudley, “Collisions and turbulence in optical rogue wave formation,” Phys. Lett. A 374, 989–996 (2010).
    [CrossRef]
  18. D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450, 1054–1057 (2007).
    [CrossRef]
  19. D. R. Solli, C. Ropers, and B. Jalali, “Active control of rogue waves for stimulated supercontinuum generation,” Phys. Rev. Lett. 101, 233902 (2008).
    [CrossRef]
  20. G. Genty, J. Dudley, and B. Eggleton, “Modulation control and spectral shaping of optical fiber supercontinuum generation in the picosecond regime,” Appl. Phys. B 94, 187–194(2009).
    [CrossRef]
  21. G. Genty and J. Dudley, “Route to coherent supercontinuum generation in the long pulse regime,” IEEE J. Quantum Electron. 45, 1331–1335 (2009).
    [CrossRef]
  22. D. R. Solli, B. Jalali, and C. Ropers, “Seeded supercontinuum generation with optical parametric down-conversion,” Phys. Rev. Lett. 105, 233902 (2010).
    [CrossRef]
  23. K. K. Y. Cheung, C. Zhang, Y. Zhou, K. K. Y. Wong, and K. K. Tsia, “Manipulating supercontinuum generation by minute continuous wave,” Opt. Lett. 36, 160–162 (2011).
    [CrossRef]
  24. Q. Li, F. Li, K. K. Y. Wong, A. P. T. Lau, K. K. Tsia, and P. K. A. Wai, “Investigating the influence of a weak continuous-wave-trigger on picosecond supercontinuum generation,” Opt. Express 19, 13757–13769 (2011).
    [CrossRef]
  25. M. H. Frosz, T. Sørensen, and O. Bang, “Nanoengineering of photonic crystal fibers for supercontinuum spectral shaping,” J. Opt. Soc. Am. B 23, 1692–1699 (2006).
    [CrossRef]
  26. G. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic, 2007).
  27. C. Agger, C. Petersen, S. Dupont, H. Steffensen, J. K. Lyngsø, C. L. Thomsen, J. Thøgersen, S. R. Keiding, and O. Bang, “Supercontinuum generation in ZBLAN fibers–-detailed comparison between measurement and simulation,” J. Opt. Soc. Am. B 29, 635–645 (2012).
    [CrossRef]
  28. J. Laegsgaard, “Mode profile dispersion in the generalised nonlinear Schrödinger equation,” Opt. Express 15, 16110–16123 (2007).
    [CrossRef]
  29. J. Hult, “A fourth-order Runge–Kutta in the interaction picture method for simulating supercontinuum generation in optical fibers,” J. Lightwave Technol. 25, 3770–3775 (2007).
    [CrossRef]
  30. J. M. Dudley and S. Coen, “Coherence properties of supercontinuum spectra generated in photonic crystal and tapered optical fibers,” Opt. Lett. 27, 1180–1182 (2002).
    [CrossRef]
  31. 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, 2451–2455 (2012).
    [CrossRef]
  32. J. M. Dudley, G. Genty, and B. J. Eggleton, “Harnessing and control of optical rogue waves in supercontinuum generation,” Opt. Express 16, 3644–3651 (2008).
    [CrossRef]

2012 (2)

2011 (3)

2010 (4)

J. C. Travers, “Blue extension of optical fibre supercontinuum generation,” J. Opt. 12, 113001 (2010).
[CrossRef]

N. Brauckmann, M. Kues, T. Walbaum, P. Groß, and C. Fallnich, “Experimental investigations on nonlinear dynamics in supercontinuum generation with feedback,” Opt. Express 18, 7190–7202 (2010).
[CrossRef]

G. Genty, C. M. de Sterke, O. Bang, F. Dias, N. Akhmediev, and J. M. Dudley, “Collisions and turbulence in optical rogue wave formation,” Phys. Lett. A 374, 989–996 (2010).
[CrossRef]

D. R. Solli, B. Jalali, and C. Ropers, “Seeded supercontinuum generation with optical parametric down-conversion,” Phys. Rev. Lett. 105, 233902 (2010).
[CrossRef]

2009 (3)

G. Genty, J. Dudley, and B. Eggleton, “Modulation control and spectral shaping of optical fiber supercontinuum generation in the picosecond regime,” Appl. Phys. B 94, 187–194(2009).
[CrossRef]

G. Genty and J. Dudley, “Route to coherent supercontinuum generation in the long pulse regime,” IEEE J. Quantum Electron. 45, 1331–1335 (2009).
[CrossRef]

J. C. Travers and J. R. Taylor, “Soliton trapping of dispersive waves in tapered optical fibers,” Opt. Lett. 34, 115–117(2009).
[CrossRef]

2008 (5)

2007 (3)

2006 (3)

2005 (2)

2002 (1)

1996 (2)

O. Bang and M. Peyrard, “Generation of high-energy localized vibrational modes in nonlinear Klein-Gordon lattices,” Phys. Rev. E 53, 4143–4152 (1996).
[CrossRef]

O. Bang and P. D. Miller, “Exploiting discreteness for switching in waveguide arrays,” Opt. Lett. 21, 1105–1107(1996).
[CrossRef]

1989 (1)

1987 (1)

P. Beaud, W. Hodel, B. Zysset, and H. Weber, “Ultrashort pulse propagation, pulse breakup, and fundamental soliton formation in a single-mode optical fiber,” IEEE J. Quantum Electron. 23, 1938–1946 (1987).
[CrossRef]

Agger, C.

Agrawal, G.

G. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic, 2007).

Akhmediev, N.

G. Genty, C. M. de Sterke, O. Bang, F. Dias, N. Akhmediev, and J. M. Dudley, “Collisions and turbulence in optical rogue wave formation,” Phys. Lett. A 374, 989–996 (2010).
[CrossRef]

Auguste, J.-L.

Bang, O.

C. Agger, C. Petersen, S. Dupont, H. Steffensen, J. K. Lyngsø, C. L. Thomsen, J. Thøgersen, S. R. Keiding, and O. Bang, “Supercontinuum generation in ZBLAN fibers–-detailed comparison between measurement and simulation,” J. Opt. Soc. Am. B 29, 635–645 (2012).
[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, 2451–2455 (2012).
[CrossRef]

S. T. Sørensen, A. Judge, C. L. Thomsen, and O. Bang, “Optimum fiber tapers for increasing the power in the blue edge of a supercontinuum—group-acceleration matching,” Opt. Lett. 36, 816–818 (2011).
[CrossRef]

G. Genty, C. M. de Sterke, O. Bang, F. Dias, N. Akhmediev, and J. M. Dudley, “Collisions and turbulence in optical rogue wave formation,” Phys. Lett. A 374, 989–996 (2010).
[CrossRef]

P. M. Moselund, M. H. Frosz, C. L. Thomsen, and O. Bang, “Back-seeding of higher order gain processes in picosecond supercontinuum generation,” Opt. Express 16, 11954–11968(2008).
[CrossRef]

M. H. Frosz, P. M. Moselund, P. D. Rasmussen, C. L. Thomsen, and O. Bang, “Increasing the blue-shift of a supercontinuum by modifying the fiber glass composition,” Opt. Express 16, 21076–21086 (2008).
[CrossRef]

M. H. Frosz, T. Sørensen, and O. Bang, “Nanoengineering of photonic crystal fibers for supercontinuum spectral shaping,” J. Opt. Soc. Am. B 23, 1692–1699 (2006).
[CrossRef]

O. Bang and M. Peyrard, “Generation of high-energy localized vibrational modes in nonlinear Klein-Gordon lattices,” Phys. Rev. E 53, 4143–4152 (1996).
[CrossRef]

O. Bang and P. D. Miller, “Exploiting discreteness for switching in waveguide arrays,” Opt. Lett. 21, 1105–1107(1996).
[CrossRef]

Bar-Joseph, I.

Beaud, P.

P. Beaud, W. Hodel, B. Zysset, and H. Weber, “Ultrashort pulse propagation, pulse breakup, and fundamental soliton formation in a single-mode optical fiber,” IEEE J. Quantum Electron. 23, 1938–1946 (1987).
[CrossRef]

Blondy, J.-M.

Brauckmann, N.

Chemla, D. S.

Cheung, K. K. Y.

Coen, S.

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

J. M. Dudley and S. Coen, “Coherence properties of supercontinuum spectra generated in photonic crystal and tapered optical fibers,” Opt. Lett. 27, 1180–1182 (2002).
[CrossRef]

Couderc, V.

de Sterke, C. M.

G. Genty, C. M. de Sterke, O. Bang, F. Dias, N. Akhmediev, and J. M. Dudley, “Collisions and turbulence in optical rogue wave formation,” Phys. Lett. A 374, 989–996 (2010).
[CrossRef]

Dias, F.

G. Genty, C. M. de Sterke, O. Bang, F. Dias, N. Akhmediev, and J. M. Dudley, “Collisions and turbulence in optical rogue wave formation,” Phys. Lett. A 374, 989–996 (2010).
[CrossRef]

Dudley, J.

G. Genty, J. Dudley, and B. Eggleton, “Modulation control and spectral shaping of optical fiber supercontinuum generation in the picosecond regime,” Appl. Phys. B 94, 187–194(2009).
[CrossRef]

G. Genty and J. Dudley, “Route to coherent supercontinuum generation in the long pulse regime,” IEEE J. Quantum Electron. 45, 1331–1335 (2009).
[CrossRef]

Dudley, J. M.

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, 2451–2455 (2012).
[CrossRef]

G. Genty, C. M. de Sterke, O. Bang, F. Dias, N. Akhmediev, and J. M. Dudley, “Collisions and turbulence in optical rogue wave formation,” Phys. Lett. A 374, 989–996 (2010).
[CrossRef]

J. M. Dudley, G. Genty, and B. J. Eggleton, “Harnessing and control of optical rogue waves in supercontinuum generation,” Opt. Express 16, 3644–3651 (2008).
[CrossRef]

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

J. M. Dudley and S. Coen, “Coherence properties of supercontinuum spectra generated in photonic crystal and tapered optical fibers,” Opt. Lett. 27, 1180–1182 (2002).
[CrossRef]

Dupont, S.

Eggleton, B.

G. Genty, J. Dudley, and B. Eggleton, “Modulation control and spectral shaping of optical fiber supercontinuum generation in the picosecond regime,” Appl. Phys. B 94, 187–194(2009).
[CrossRef]

Eggleton, B. J.

Fallnich, C.

Frosz, M. H.

Genty, G.

G. Genty, C. M. de Sterke, O. Bang, F. Dias, N. Akhmediev, and J. M. Dudley, “Collisions and turbulence in optical rogue wave formation,” Phys. Lett. A 374, 989–996 (2010).
[CrossRef]

G. Genty, J. Dudley, and B. Eggleton, “Modulation control and spectral shaping of optical fiber supercontinuum generation in the picosecond regime,” Appl. Phys. B 94, 187–194(2009).
[CrossRef]

G. Genty and J. Dudley, “Route to coherent supercontinuum generation in the long pulse regime,” IEEE J. Quantum Electron. 45, 1331–1335 (2009).
[CrossRef]

J. M. Dudley, G. Genty, and B. J. Eggleton, “Harnessing and control of optical rogue waves in supercontinuum generation,” Opt. Express 16, 3644–3651 (2008).
[CrossRef]

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

Gordon, J. P.

Groß, P.

Grossard, L.

Hodel, W.

P. Beaud, W. Hodel, B. Zysset, and H. Weber, “Ultrashort pulse propagation, pulse breakup, and fundamental soliton formation in a single-mode optical fiber,” IEEE J. Quantum Electron. 23, 1938–1946 (1987).
[CrossRef]

Hult, J.

Huss, G.

Islam, M. N.

Jalali, B.

D. R. Solli, B. Jalali, and C. Ropers, “Seeded supercontinuum generation with optical parametric down-conversion,” Phys. Rev. Lett. 105, 233902 (2010).
[CrossRef]

D. R. Solli, C. Ropers, and B. Jalali, “Active control of rogue waves for stimulated supercontinuum generation,” Phys. Rev. Lett. 101, 233902 (2008).
[CrossRef]

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

Judge, A.

Keiding, S. R.

Knight, J. C.

Koonath, P.

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

Kues, M.

Laegsgaard, J.

Lau, A. P. T.

Leproux, P.

Lesvigne, C.

Li, F.

Li, Q.

Luan, F.

Lyngsø, J. K.

Miller, P. D.

Moselund, P. M.

Petersen, C.

Peyrard, M.

O. Bang and M. Peyrard, “Generation of high-energy localized vibrational modes in nonlinear Klein-Gordon lattices,” Phys. Rev. E 53, 4143–4152 (1996).
[CrossRef]

Pioger, P.-H.

Popov, S. V.

Rasmussen, P. D.

Ropers, C.

D. R. Solli, B. Jalali, and C. Ropers, “Seeded supercontinuum generation with optical parametric down-conversion,” Phys. Rev. Lett. 105, 233902 (2010).
[CrossRef]

D. R. Solli, C. Ropers, and B. Jalali, “Active control of rogue waves for stimulated supercontinuum generation,” Phys. Rev. Lett. 101, 233902 (2008).
[CrossRef]

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

Skryabin, D. V.

Solli, D. R.

D. R. Solli, B. Jalali, and C. Ropers, “Seeded supercontinuum generation with optical parametric down-conversion,” Phys. Rev. Lett. 105, 233902 (2010).
[CrossRef]

D. R. Solli, C. Ropers, and B. Jalali, “Active control of rogue waves for stimulated supercontinuum generation,” Phys. Rev. Lett. 101, 233902 (2008).
[CrossRef]

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

Sørensen, S. T.

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, 2451–2455 (2012).
[CrossRef]

S. T. Sørensen, A. Judge, C. L. Thomsen, and O. Bang, “Optimum fiber tapers for increasing the power in the blue edge of a supercontinuum—group-acceleration matching,” Opt. Lett. 36, 816–818 (2011).
[CrossRef]

Sørensen, T.

Steffensen, H.

Stone, J. M.

Sucha, G.

Taylor, J. R.

Thøgersen, J.

Thomsen, C. L.

Tombelaine, V.

Travers, J. C.

Tsia, K. K.

Wai, P. K. A.

Walbaum, T.

Weber, H.

P. Beaud, W. Hodel, B. Zysset, and H. Weber, “Ultrashort pulse propagation, pulse breakup, and fundamental soliton formation in a single-mode optical fiber,” IEEE J. Quantum Electron. 23, 1938–1946 (1987).
[CrossRef]

Wegener, M.

Wetzel, B.

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, 2451–2455 (2012).
[CrossRef]

Wong, K. K. Y.

Yulin, A. V.

Zhang, C.

Zhou, Y.

Zysset, B.

P. Beaud, W. Hodel, B. Zysset, and H. Weber, “Ultrashort pulse propagation, pulse breakup, and fundamental soliton formation in a single-mode optical fiber,” IEEE J. Quantum Electron. 23, 1938–1946 (1987).
[CrossRef]

Appl. Phys. B (1)

G. Genty, J. Dudley, and B. Eggleton, “Modulation control and spectral shaping of optical fiber supercontinuum generation in the picosecond regime,” Appl. Phys. B 94, 187–194(2009).
[CrossRef]

IEEE J. Quantum Electron. (2)

G. Genty and J. Dudley, “Route to coherent supercontinuum generation in the long pulse regime,” IEEE J. Quantum Electron. 45, 1331–1335 (2009).
[CrossRef]

P. Beaud, W. Hodel, B. Zysset, and H. Weber, “Ultrashort pulse propagation, pulse breakup, and fundamental soliton formation in a single-mode optical fiber,” IEEE J. Quantum Electron. 23, 1938–1946 (1987).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. (1)

J. C. Travers, “Blue extension of optical fibre supercontinuum generation,” J. Opt. 12, 113001 (2010).
[CrossRef]

J. Opt. Soc. Am. B (3)

Nature (1)

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

Opt. Commun. (1)

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, 2451–2455 (2012).
[CrossRef]

Opt. Express (9)

J. M. Dudley, G. Genty, and B. J. Eggleton, “Harnessing and control of optical rogue waves in supercontinuum generation,” Opt. Express 16, 3644–3651 (2008).
[CrossRef]

Q. Li, F. Li, K. K. Y. Wong, A. P. T. Lau, K. K. Tsia, and P. K. A. Wai, “Investigating the influence of a weak continuous-wave-trigger on picosecond supercontinuum generation,” Opt. Express 19, 13757–13769 (2011).
[CrossRef]

J. Laegsgaard, “Mode profile dispersion in the generalised nonlinear Schrödinger equation,” Opt. Express 15, 16110–16123 (2007).
[CrossRef]

F. Luan, D. V. Skryabin, A. V. Yulin, and J. C. Knight, “Energy exchange between colliding solitons in photonic crystal fibers,” Opt. Express 14, 9844–9853 (2006).
[CrossRef]

N. Brauckmann, M. Kues, T. Walbaum, P. Groß, and C. Fallnich, “Experimental investigations on nonlinear dynamics in supercontinuum generation with feedback,” Opt. Express 18, 7190–7202 (2010).
[CrossRef]

J. M. Stone and J. C. Knight, “Visibly ‘white’ light generation in uniformphotonic crystal fiber using a microchip laser,” Opt. Express 16, 2670–2675 (2008).
[CrossRef]

M. H. Frosz, P. M. Moselund, P. D. Rasmussen, C. L. Thomsen, and O. Bang, “Increasing the blue-shift of a supercontinuum by modifying the fiber glass composition,” Opt. Express 16, 21076–21086 (2008).
[CrossRef]

V. Tombelaine, C. Lesvigne, P. Leproux, L. Grossard, V. Couderc, J.-L. Auguste, J.-M. Blondy, G. Huss, and P.-H. Pioger, “Ultra wide band supercontinuum generation in air-silica holey fibers by SHG-induced modulation instabilities,” Opt. Express 13, 7399–7404 (2005).
[CrossRef]

P. M. Moselund, M. H. Frosz, C. L. Thomsen, and O. Bang, “Back-seeding of higher order gain processes in picosecond supercontinuum generation,” Opt. Express 16, 11954–11968(2008).
[CrossRef]

Opt. Lett. (6)

Phys. Lett. A (1)

G. Genty, C. M. de Sterke, O. Bang, F. Dias, N. Akhmediev, and J. M. Dudley, “Collisions and turbulence in optical rogue wave formation,” Phys. Lett. A 374, 989–996 (2010).
[CrossRef]

Phys. Rev. E (1)

O. Bang and M. Peyrard, “Generation of high-energy localized vibrational modes in nonlinear Klein-Gordon lattices,” Phys. Rev. E 53, 4143–4152 (1996).
[CrossRef]

Phys. Rev. Lett. (2)

D. R. Solli, C. Ropers, and B. Jalali, “Active control of rogue waves for stimulated supercontinuum generation,” Phys. Rev. Lett. 101, 233902 (2008).
[CrossRef]

D. R. Solli, B. Jalali, and C. Ropers, “Seeded supercontinuum generation with optical parametric down-conversion,” Phys. Rev. Lett. 105, 233902 (2010).
[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 (2)

P. M. Moselund, “Long-pulsed supercontinuum sources,” Ph.D. dissertation, DTU Fotonik, Dept. of Photonics Engineering, Technical Univ. of Denmark (2009).

G. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic, 2007).

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Figures (9)

Fig. 1.
Fig. 1.

(a) Dispersion and effective area for the used PCF with Λ = 3.6 μm and d / Λ = 0.52 . (b)–(c) MI gain spectra as a function of seed frequency offset relative to the pump for varying pump wavelength (b) and peak power (c). The peak power in (b) is 250 W and the pump wavelength in (c) is 1064 nm. The Raman gain is shown for comparison. (d) Walk-off length (solid lines) and MI gain length (dotted lines) as a function of frequency offset, calculated for T 0 = 3 ps / 1.665 and a peak power of 250 W.

Fig. 2.
Fig. 2.

Single-shot simulations of pumping at 1055 nm with a 250 W pump and a 5% seed at frequency offsets of (a)–(e) 0, 3, 13, 20, and 30 THz, respectively. The white lines indicate the MI gain bandwidth. The top rows in (a)–(e) show the ensemble calculated signal-to-noise ratio (SNR) and spectral coherence ( | g 12 ( 12 ) | ). (f) MI and Raman gain curves, the vertical lines correspond to the frequency offsets used in (a)–(e). The frequency offset of 13 THz (c) is the Raman gain peak and 20 THz (d) is the MI gain peak.

Fig. 3.
Fig. 3.

Single-shot simulation (a) with and (b) without the Raman effect. Parameters like in Fig. 2(c): 1055 nm pump with 250 W peak power and a 5% seed at 13 THz. The white lines indicate the MI gain bandwidth. The top rows show the ensemble calculated signal-to-noise ratio (SNR), spectral coherence ( | g 12 ( 12 ) | ), and averaged output spectrum.

Fig. 4.
Fig. 4.

Results of pumping at 1055 nm with a 5% seed. Density plots of the (a) output spectral density, (b) coherence, and (c) SNR as a function of wavelength and pump-seed frequency offset. The figures to the right of the density plots show the (a) MI gain, (b) overall coherence, and (c) overall SNR as a function of pump-seed frequency offset.

Fig. 5.
Fig. 5.

Overall SNR and coherence as a function of pump-seed frequency offset for seed peak powers ranging from 0.01% to 20% of the pump peak power, P P = 250 W [see legend in (f)]. The pump wavelength is (a)–(f) 1054.5, 1055, 1056, 1057.5, 1064, and 1075 nm, respectively, which gradually narrows the MI gain spectrum (full black line). The black circled line shows the Raman spectrum.

Fig. 6.
Fig. 6.

Single-shot simulations of a 5% seed with a 4 THz offset for the pump wavelengths in Fig. 5. The white lines indicate the MI gain bandwidth and the black dashed line the ZDW. The top rows show the ensemble calculated SNR and spectral coherence ( | g 12 ( 12 ) | ).

Fig. 7.
Fig. 7.

Temporal evolution and spectrogram at the fiber end (10 m) for a 5% seed with a 4 THz offset for pump wavelengths of (a) 1055 nm and (b) 1075 nm, corresponding to Figs. 6(b) and 6(f). The black dashed lines in the spectrograms mark the ZDW.

Fig. 8.
Fig. 8.

Single-shot simulations of pumping at 1064 nm with a 5% seed at a frequency offset of 3 THz for pump peak powers of (a)–(c) 500, 750, and 1500 W, respectively. The top rows show the signal-to-noise ratio (SNR) and spectral coherence ( | g 12 ( 12 ) | ). (d) MI and Raman gain spectra. The vertical line marks 3 THz offset.

Fig. 9.
Fig. 9.

Overall SNR and coherence as a function of pump-seed frequency offset, shown for seed peak powers of 1% and 5% of the pump peak power [see legend in (a)]. The pump wavelength was 1064 nm and the peak power (a)–(c) 500, 700, and 1500 W. The MI and Raman spectra are shown with the full and circled black lines, respectively.

Equations (8)

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g ( Ω ) = Im { Δ k o ± ( Δ k e + 2 γ P 0 R ˜ ( Ω ) ) Δ k e } ,
Δ k o = m = 1 β ¯ 2 m + 1 ( 2 m + 1 ) ! Ω 2 m + 1 , Δ k e = m = 1 β ¯ 2 m 2 m ! Ω 2 m ,
R ˜ ( Ω ) = ( 1 f R ) + f R τ 1 2 + τ 2 2 τ 2 2 τ 1 2 ( i + τ 2 Ω ) 2 ,
A ( t ) = ( P p + P s e i 2 π ν mod t ) exp ( t 2 2 T 0 2 ) ,
| g 12 ( 1 ) ( ω ) | = | A ˜ i * ( ω ) A ˜ j ( ω ) i j | A ˜ i ( ω ) | 2 | A ˜ j ( ω ) | 2 | ,
SNR ( ω ) = μ ( ω ) σ ( ω ) .
| g 12 ( 1 ) | = 0 | g 12 ( 1 ) ( ω ) | | A ˜ ( ω ) | 2 d ω 0 | A ˜ ( ω ) | 2 d ω .
SNR = 0 SNR ( ω ) | A ˜ ( ω ) | 2 d ω 0 | A ˜ ( ω ) | 2 d ω .

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