Abstract

Numerical simulations of the onset phase of continuous wave supercontinuum generation from modulation instability show that the structure of the field as it develops can be interpreted in terms of the properties of Akhmediev Breathers. Numerical and analytical results are compared with experimental measurements of spectral broadening in photonic crystal fiber using nanosecond pulses.

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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  37. B. Barviau, C. Finot, J. Fatome, and G. Millot, “Generation from continuous waves of frequency combs with large overall bandwidth and tunable central wavelength,” Electron. Lett. 43(16), 886–887 (2007).
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    [CrossRef] [PubMed]
  39. J. M. Dudley and J. R. Taylor, “Ten years of nonlinear optics in photonic crystal fibre,” Nat. Photonics 3(2), 85–90 (2009).
    [CrossRef]
  40. D. R. Solli, C. Ropers, and B. Jalali, “Active control of rogue waves for stimulated supercontinuum generation,” Phys. Rev. Lett. 101(23), 233902 (2008).
    [CrossRef] [PubMed]
  41. G. Genty, J. M. Dudley, and B. J. Eggleton, “Modulation control and spectral shaping of optical fiber supercontinuum generation in the picosecond regime,” Appl. Phys. B 94(2), 187–194 (2009).
    [CrossRef]

2009

J. M. Dudley and J. R. Taylor, “Ten years of nonlinear optics in photonic crystal fibre,” Nat. Photonics 3(2), 85–90 (2009).
[CrossRef]

G. Genty, J. M. Dudley, and B. J. Eggleton, “Modulation control and spectral shaping of optical fiber supercontinuum generation in the picosecond regime,” Appl. Phys. B 94(2), 187–194 (2009).
[CrossRef]

2008

F. C. Cruz, “Optical frequency combs generated by four-wave mixing in optical fibers for astrophysical spectrometer calibration and metrology,” Opt. Express 16(17), 13267–13275 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-17-13267U .
[CrossRef] [PubMed]

D. R. Solli, C. Ropers, and B. Jalali, “Active control of rogue waves for stimulated supercontinuum generation,” Phys. Rev. Lett. 101(23), 233902 (2008).
[CrossRef] [PubMed]

J. C. Travers, A. B. Rulkov, B. A. Cumberland, S. V. Popov, and J. R. Taylor, “Visible supercontinuum generation in photonic crystal fibers with a 400W continuous wave fiber laser,” Opt. Express 16(19), 14435–14447 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-19-14435 .
[CrossRef] [PubMed]

J. M. Dudley, G. Genty, and B. J. Eggleton, “Harnessing and control of optical rogue waves in supercontinuum generation,” Opt. Express 16(6), 3644–3651 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-6-3644U .
[CrossRef] [PubMed]

V. V. Voronovich, V. I. Shrira, and G. Thomas, “Can bottom friction suppress ‘freak wave’ formation?” J. Fluid Mech. 604, 263–296 (2008).
[CrossRef]

S. M. Kobtsev and S. V. Smirnov, “Influence of noise amplification on generation of regular short pulse trains in optical fibre pumped by intensity-modulated CW radiation,” Opt. Express 16(10), 7428–7434 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-10-7428 .
[CrossRef] [PubMed]

N. Korneev, E. A. Kuzin, B. Ibarra-Escamilla, M. Bello-Jiménez, and A. Flores-Rosas, “Initial development of supercontinuum in fibers with anomalous dispersion pumped by nanosecond-long pulses,” Opt. Express 16(4), 2636–2645 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-4-2636 .
[CrossRef] [PubMed]

2007

T. Inoue, J. Hiroishi, T. Yagi, and Y. Mimura, “Generation of in-phase pulse train from optical beat signal,” Opt. Lett. 32(11), 1596–1598 (2007).
[CrossRef] [PubMed]

B. Barviau, C. Finot, J. Fatome, and G. Millot, “Generation from continuous waves of frequency combs with large overall bandwidth and tunable central wavelength,” Electron. Lett. 43(16), 886–887 (2007).
[CrossRef]

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

J. Beeckman, X. Hutsebaut, M. Haelterman, and K. Neyts, “Induced modulation instability and recurrence in nematic liquid crystals,” Opt. Express 15(18), 11185–11195 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-18-11185 .
[CrossRef] [PubMed]

2006

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

S. Liu, “Four-wave mixing and modulation instability of continuous optical waves in single-mode optical fibers,” Appl. Phys. Lett. 89(17), 171118 (2006).
[CrossRef]

2005

2001

G. Van Simaeys, Ph. Emplit, and M. Haelterman, “Experimental demonstration of the Fermi-Pasta-Ulam recurrence in a modulationally unstable optical wave,” Phys. Rev. Lett. 87(3), 033902 (2001).
[CrossRef] [PubMed]

N. N. Akhmediev, “Nonlinear physics. Déjà vu in optics,” Nature 413(6853), 267–268 (2001).
[CrossRef] [PubMed]

J. M. Dudley, F. Gutty, S. Pitois, and G. Millot, “Complete characterization of THz pulse trains generated from nonlinear processes in optical fibers,” IEEE J. Quantum Electron. 37(4), 587–594 (2001).
[CrossRef]

2000

J. K. Ranka, R. S. Windeler, and A. J. Stentz, “Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm,” Opt. Lett. 25(1), 25–27 (2000).
[CrossRef] [PubMed]

A. R. Osborne, M. Onorato, and M. Serio, “The nonlinear dynamics of rogue waves and holes in deep-water gravity wave trains,” Phys. Lett. A 275(5-6), 386–393 (2000).
[CrossRef]

1999

K. B. Dysthe and K. Trulsen, “Note on Breather type Solutions of the NLS as models for freak-waves,” Phys. Scr. T82(1), 48–52 (1999).
[CrossRef]

1998

D. L. Hart, A. F. Judy, R. Roy, and J. W. Beletic, “Dynamical evolution of multiple four-wave-mixing processes in an optical fiber,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 57(4), 4757–4774 (1998).
[CrossRef]

1994

S. Trillo, S. Wabnitz, and T. A. B. Kennedy, “Nonlinear dynamics of dual-frequency-pumped multiwave mixing in optical fibers,” Phys. Rev. A 50(2), 1732–1747 (1994).
[CrossRef] [PubMed]

1991

1990

M. J. Ablowitz and B. M. Herbst, “On homoclinic structure and numerically induced chaos for the nonlinear Schrödinger equation,” SIAM J. Appl. Math. 50(2), 339–351 (1990).
[CrossRef]

V. I. Karpman, A. G. Shagalov, and J. J. Rasmussen, “Modulational instability due to nonlinear coupling between high- and low-frequency waves: a study of truncated systems,” Phys. Lett. A 147(2-3), 119–124 (1990).
[CrossRef]

1989

E. J. Greer, D. M. Patrick, P. G. J. Wigley, and J. R. Taylor, “Generation of 2 THz repetition rate pulse trains through induced modulational instability,” Electron. Lett. 25(18), 1246–1248 (1989).
[CrossRef]

1988

N. Akhmediev, V. I. Korneev, and N. V. Mitskevich, “N-modulation signals in a single-mode optical waveguide under nonlinear conditions,” Sov. Phys. JETP 67, 89–95 (1988).

1987

N. Akhmediev, V. M. Eleonskii, and N. E. Kulagin, “Exact first-order solutions of the nonlinear Schrodinger equation,” Theor. Math. Phys. 72(2), 809–818 (1987).
[CrossRef]

G. P. Agrawal, “Modulation instability induced by cross-phase modulation,” Phys. Rev. Lett. 59(8), 880–883 (1987).
[CrossRef] [PubMed]

1986

K. Tai, A. Hasegawa, and A. Tomita, “Observation of modulational instability in optical fibers,” Phys. Rev. Lett. 56(2), 135–138 (1986).
[CrossRef] [PubMed]

N. Akhmediev and V. I. Korneev, “Modulation instability and periodic solutions of the nonlinear Schrodinger equation,” Theor. Math. Phys. 69(2), 1089–1093 (1986).
[CrossRef]

1985

N. Akhmediev, V. M. Eleonskii, and N. E. Kulagin, “Generation of periodic trains of picosecond pulses in an optical fiber: exact solutions,” Sov. Phys. JETP 62, 894–899 (1985).

1967

T. B. Benjamin and J. E. Feir, “The disintegration of wavetrains on deep water. Part 1: Theory,” J. Fluid Mech. 27(03), 417–430 (1967).
[CrossRef]

1966

V. I. Bespalov and V. I. Talanov, “Filamentary structure of light beams in nonlinear liquids,” JETP Lett. 3, 307–310 (1966).

Ablowitz, M. J.

M. J. Ablowitz and B. M. Herbst, “On homoclinic structure and numerically induced chaos for the nonlinear Schrödinger equation,” SIAM J. Appl. Math. 50(2), 339–351 (1990).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, “Modulation instability induced by cross-phase modulation,” Phys. Rev. Lett. 59(8), 880–883 (1987).
[CrossRef] [PubMed]

Akhmediev, N.

N. Akhmediev, V. I. Korneev, and N. V. Mitskevich, “N-modulation signals in a single-mode optical waveguide under nonlinear conditions,” Sov. Phys. JETP 67, 89–95 (1988).

N. Akhmediev, V. M. Eleonskii, and N. E. Kulagin, “Exact first-order solutions of the nonlinear Schrodinger equation,” Theor. Math. Phys. 72(2), 809–818 (1987).
[CrossRef]

N. Akhmediev and V. I. Korneev, “Modulation instability and periodic solutions of the nonlinear Schrodinger equation,” Theor. Math. Phys. 69(2), 1089–1093 (1986).
[CrossRef]

N. Akhmediev, V. M. Eleonskii, and N. E. Kulagin, “Generation of periodic trains of picosecond pulses in an optical fiber: exact solutions,” Sov. Phys. JETP 62, 894–899 (1985).

Akhmediev, N. N.

N. N. Akhmediev, “Nonlinear physics. Déjà vu in optics,” Nature 413(6853), 267–268 (2001).
[CrossRef] [PubMed]

Bandelow, U.

A. Demircan and U. Bandelow, “Supercontinuum generation by the modulation instability,” Opt. Commun. 244(1-6), 181–185 (2005).
[CrossRef]

Barviau, B.

B. Barviau, C. Finot, J. Fatome, and G. Millot, “Generation from continuous waves of frequency combs with large overall bandwidth and tunable central wavelength,” Electron. Lett. 43(16), 886–887 (2007).
[CrossRef]

Beeckman, J.

Beletic, J. W.

D. L. Hart, A. F. Judy, R. Roy, and J. W. Beletic, “Dynamical evolution of multiple four-wave-mixing processes in an optical fiber,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 57(4), 4757–4774 (1998).
[CrossRef]

Bello-Jiménez, M.

Benjamin, T. B.

T. B. Benjamin and J. E. Feir, “The disintegration of wavetrains on deep water. Part 1: Theory,” J. Fluid Mech. 27(03), 417–430 (1967).
[CrossRef]

Bespalov, V. I.

V. I. Bespalov and V. I. Talanov, “Filamentary structure of light beams in nonlinear liquids,” JETP Lett. 3, 307–310 (1966).

Coen, S.

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

Cruz, F. C.

Cumberland, B. A.

Demircan, A.

A. Demircan and U. Bandelow, “Supercontinuum generation by the modulation instability,” Opt. Commun. 244(1-6), 181–185 (2005).
[CrossRef]

Dudley, J. M.

J. M. Dudley and J. R. Taylor, “Ten years of nonlinear optics in photonic crystal fibre,” Nat. Photonics 3(2), 85–90 (2009).
[CrossRef]

G. Genty, J. M. Dudley, and B. J. Eggleton, “Modulation control and spectral shaping of optical fiber supercontinuum generation in the picosecond regime,” Appl. Phys. B 94(2), 187–194 (2009).
[CrossRef]

J. M. Dudley, G. Genty, and B. J. Eggleton, “Harnessing and control of optical rogue waves in supercontinuum generation,” Opt. Express 16(6), 3644–3651 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-6-3644U .
[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]

J. M. Dudley, F. Gutty, S. Pitois, and G. Millot, “Complete characterization of THz pulse trains generated from nonlinear processes in optical fibers,” IEEE J. Quantum Electron. 37(4), 587–594 (2001).
[CrossRef]

Dysthe, K. B.

K. B. Dysthe and K. Trulsen, “Note on Breather type Solutions of the NLS as models for freak-waves,” Phys. Scr. T82(1), 48–52 (1999).
[CrossRef]

Eggleton, B. J.

Eleonskii, V. M.

N. Akhmediev, V. M. Eleonskii, and N. E. Kulagin, “Exact first-order solutions of the nonlinear Schrodinger equation,” Theor. Math. Phys. 72(2), 809–818 (1987).
[CrossRef]

N. Akhmediev, V. M. Eleonskii, and N. E. Kulagin, “Generation of periodic trains of picosecond pulses in an optical fiber: exact solutions,” Sov. Phys. JETP 62, 894–899 (1985).

Emplit, Ph.

G. Van Simaeys, Ph. Emplit, and M. Haelterman, “Experimental demonstration of the Fermi-Pasta-Ulam recurrence in a modulationally unstable optical wave,” Phys. Rev. Lett. 87(3), 033902 (2001).
[CrossRef] [PubMed]

Fatome, J.

B. Barviau, C. Finot, J. Fatome, and G. Millot, “Generation from continuous waves of frequency combs with large overall bandwidth and tunable central wavelength,” Electron. Lett. 43(16), 886–887 (2007).
[CrossRef]

Feir, J. E.

T. B. Benjamin and J. E. Feir, “The disintegration of wavetrains on deep water. Part 1: Theory,” J. Fluid Mech. 27(03), 417–430 (1967).
[CrossRef]

Finot, C.

B. Barviau, C. Finot, J. Fatome, and G. Millot, “Generation from continuous waves of frequency combs with large overall bandwidth and tunable central wavelength,” Electron. Lett. 43(16), 886–887 (2007).
[CrossRef]

Flores-Rosas, A.

Genty, G.

G. Genty, J. M. Dudley, and B. J. Eggleton, “Modulation control and spectral shaping of optical fiber supercontinuum generation in the picosecond regime,” Appl. Phys. B 94(2), 187–194 (2009).
[CrossRef]

J. M. Dudley, G. Genty, and B. J. Eggleton, “Harnessing and control of optical rogue waves in supercontinuum generation,” Opt. Express 16(6), 3644–3651 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-6-3644U .
[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]

Greer, E. J.

E. J. Greer, D. M. Patrick, P. G. J. Wigley, and J. R. Taylor, “Generation of 2 THz repetition rate pulse trains through induced modulational instability,” Electron. Lett. 25(18), 1246–1248 (1989).
[CrossRef]

Gutty, F.

J. M. Dudley, F. Gutty, S. Pitois, and G. Millot, “Complete characterization of THz pulse trains generated from nonlinear processes in optical fibers,” IEEE J. Quantum Electron. 37(4), 587–594 (2001).
[CrossRef]

Haelterman, M.

J. Beeckman, X. Hutsebaut, M. Haelterman, and K. Neyts, “Induced modulation instability and recurrence in nematic liquid crystals,” Opt. Express 15(18), 11185–11195 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-18-11185 .
[CrossRef] [PubMed]

G. Van Simaeys, Ph. Emplit, and M. Haelterman, “Experimental demonstration of the Fermi-Pasta-Ulam recurrence in a modulationally unstable optical wave,” Phys. Rev. Lett. 87(3), 033902 (2001).
[CrossRef] [PubMed]

Hart, D. L.

D. L. Hart, A. F. Judy, R. Roy, and J. W. Beletic, “Dynamical evolution of multiple four-wave-mixing processes in an optical fiber,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 57(4), 4757–4774 (1998).
[CrossRef]

Hasegawa, A.

K. Tai, A. Hasegawa, and A. Tomita, “Observation of modulational instability in optical fibers,” Phys. Rev. Lett. 56(2), 135–138 (1986).
[CrossRef] [PubMed]

Herbst, B. M.

M. J. Ablowitz and B. M. Herbst, “On homoclinic structure and numerically induced chaos for the nonlinear Schrödinger equation,” SIAM J. Appl. Math. 50(2), 339–351 (1990).
[CrossRef]

Hiroishi, J.

Hutsebaut, X.

Ibarra-Escamilla, B.

Inoue, T.

Jalali, B.

D. R. Solli, C. Ropers, and B. Jalali, “Active control of rogue waves for stimulated supercontinuum generation,” Phys. Rev. Lett. 101(23), 233902 (2008).
[CrossRef] [PubMed]

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

Judy, A. F.

D. L. Hart, A. F. Judy, R. Roy, and J. W. Beletic, “Dynamical evolution of multiple four-wave-mixing processes in an optical fiber,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 57(4), 4757–4774 (1998).
[CrossRef]

Karpman, V. I.

V. I. Karpman, A. G. Shagalov, and J. J. Rasmussen, “Modulational instability due to nonlinear coupling between high- and low-frequency waves: a study of truncated systems,” Phys. Lett. A 147(2-3), 119–124 (1990).
[CrossRef]

Kennedy, T. A. B.

S. Trillo, S. Wabnitz, and T. A. B. Kennedy, “Nonlinear dynamics of dual-frequency-pumped multiwave mixing in optical fibers,” Phys. Rev. A 50(2), 1732–1747 (1994).
[CrossRef] [PubMed]

Kobtsev, S. M.

Koonath, P.

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

Korneev, N.

Korneev, V. I.

N. Akhmediev, V. I. Korneev, and N. V. Mitskevich, “N-modulation signals in a single-mode optical waveguide under nonlinear conditions,” Sov. Phys. JETP 67, 89–95 (1988).

N. Akhmediev and V. I. Korneev, “Modulation instability and periodic solutions of the nonlinear Schrodinger equation,” Theor. Math. Phys. 69(2), 1089–1093 (1986).
[CrossRef]

Kulagin, N. E.

N. Akhmediev, V. M. Eleonskii, and N. E. Kulagin, “Exact first-order solutions of the nonlinear Schrodinger equation,” Theor. Math. Phys. 72(2), 809–818 (1987).
[CrossRef]

N. Akhmediev, V. M. Eleonskii, and N. E. Kulagin, “Generation of periodic trains of picosecond pulses in an optical fiber: exact solutions,” Sov. Phys. JETP 62, 894–899 (1985).

Kutz, J. N.

Kuzin, E. A.

Liu, S.

S. Liu, “Four-wave mixing and modulation instability of continuous optical waves in single-mode optical fibers,” Appl. Phys. Lett. 89(17), 171118 (2006).
[CrossRef]

Lyngå, C.

Millot, G.

B. Barviau, C. Finot, J. Fatome, and G. Millot, “Generation from continuous waves of frequency combs with large overall bandwidth and tunable central wavelength,” Electron. Lett. 43(16), 886–887 (2007).
[CrossRef]

J. M. Dudley, F. Gutty, S. Pitois, and G. Millot, “Complete characterization of THz pulse trains generated from nonlinear processes in optical fibers,” IEEE J. Quantum Electron. 37(4), 587–594 (2001).
[CrossRef]

Mimura, Y.

Mitskevich, N. V.

N. Akhmediev, V. I. Korneev, and N. V. Mitskevich, “N-modulation signals in a single-mode optical waveguide under nonlinear conditions,” Sov. Phys. JETP 67, 89–95 (1988).

Neyts, K.

Onorato, M.

A. R. Osborne, M. Onorato, and M. Serio, “The nonlinear dynamics of rogue waves and holes in deep-water gravity wave trains,” Phys. Lett. A 275(5-6), 386–393 (2000).
[CrossRef]

Osborne, A. R.

A. R. Osborne, M. Onorato, and M. Serio, “The nonlinear dynamics of rogue waves and holes in deep-water gravity wave trains,” Phys. Lett. A 275(5-6), 386–393 (2000).
[CrossRef]

Patrick, D. M.

E. J. Greer, D. M. Patrick, P. G. J. Wigley, and J. R. Taylor, “Generation of 2 THz repetition rate pulse trains through induced modulational instability,” Electron. Lett. 25(18), 1246–1248 (1989).
[CrossRef]

Pitois, S.

J. M. Dudley, F. Gutty, S. Pitois, and G. Millot, “Complete characterization of THz pulse trains generated from nonlinear processes in optical fibers,” IEEE J. Quantum Electron. 37(4), 587–594 (2001).
[CrossRef]

Popov, S. V.

Ranka, J. K.

Rasmussen, J. J.

V. I. Karpman, A. G. Shagalov, and J. J. Rasmussen, “Modulational instability due to nonlinear coupling between high- and low-frequency waves: a study of truncated systems,” Phys. Lett. A 147(2-3), 119–124 (1990).
[CrossRef]

Ropers, C.

D. R. Solli, C. Ropers, and B. Jalali, “Active control of rogue waves for stimulated supercontinuum generation,” Phys. Rev. Lett. 101(23), 233902 (2008).
[CrossRef] [PubMed]

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

Roy, R.

D. L. Hart, A. F. Judy, R. Roy, and J. W. Beletic, “Dynamical evolution of multiple four-wave-mixing processes in an optical fiber,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 57(4), 4757–4774 (1998).
[CrossRef]

Rulkov, A. B.

Serio, M.

A. R. Osborne, M. Onorato, and M. Serio, “The nonlinear dynamics of rogue waves and holes in deep-water gravity wave trains,” Phys. Lett. A 275(5-6), 386–393 (2000).
[CrossRef]

Shagalov, A. G.

V. I. Karpman, A. G. Shagalov, and J. J. Rasmussen, “Modulational instability due to nonlinear coupling between high- and low-frequency waves: a study of truncated systems,” Phys. Lett. A 147(2-3), 119–124 (1990).
[CrossRef]

Shrira, V. I.

V. V. Voronovich, V. I. Shrira, and G. Thomas, “Can bottom friction suppress ‘freak wave’ formation?” J. Fluid Mech. 604, 263–296 (2008).
[CrossRef]

Smirnov, S. V.

Solli, D. R.

D. R. Solli, C. Ropers, and B. Jalali, “Active control of rogue waves for stimulated supercontinuum generation,” Phys. Rev. Lett. 101(23), 233902 (2008).
[CrossRef] [PubMed]

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

Stentz, A. J.

Tai, K.

K. Tai, A. Hasegawa, and A. Tomita, “Observation of modulational instability in optical fibers,” Phys. Rev. Lett. 56(2), 135–138 (1986).
[CrossRef] [PubMed]

Talanov, V. I.

V. I. Bespalov and V. I. Talanov, “Filamentary structure of light beams in nonlinear liquids,” JETP Lett. 3, 307–310 (1966).

Taylor, J. R.

J. M. Dudley and J. R. Taylor, “Ten years of nonlinear optics in photonic crystal fibre,” Nat. Photonics 3(2), 85–90 (2009).
[CrossRef]

J. C. Travers, A. B. Rulkov, B. A. Cumberland, S. V. Popov, and J. R. Taylor, “Visible supercontinuum generation in photonic crystal fibers with a 400W continuous wave fiber laser,” Opt. Express 16(19), 14435–14447 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-19-14435 .
[CrossRef] [PubMed]

E. J. Greer, D. M. Patrick, P. G. J. Wigley, and J. R. Taylor, “Generation of 2 THz repetition rate pulse trains through induced modulational instability,” Electron. Lett. 25(18), 1246–1248 (1989).
[CrossRef]

Thomas, G.

V. V. Voronovich, V. I. Shrira, and G. Thomas, “Can bottom friction suppress ‘freak wave’ formation?” J. Fluid Mech. 604, 263–296 (2008).
[CrossRef]

Tomita, A.

K. Tai, A. Hasegawa, and A. Tomita, “Observation of modulational instability in optical fibers,” Phys. Rev. Lett. 56(2), 135–138 (1986).
[CrossRef] [PubMed]

Travers, J. C.

Trillo, S.

S. Trillo, S. Wabnitz, and T. A. B. Kennedy, “Nonlinear dynamics of dual-frequency-pumped multiwave mixing in optical fibers,” Phys. Rev. A 50(2), 1732–1747 (1994).
[CrossRef] [PubMed]

S. Trillo and S. Wabnitz, “Dynamics of the nonlinear modulational instability in optical fibers,” Opt. Lett. 16(13), 986–988 (1991).
[CrossRef] [PubMed]

Trulsen, K.

K. B. Dysthe and K. Trulsen, “Note on Breather type Solutions of the NLS as models for freak-waves,” Phys. Scr. T82(1), 48–52 (1999).
[CrossRef]

Van Simaeys, G.

G. Van Simaeys, Ph. Emplit, and M. Haelterman, “Experimental demonstration of the Fermi-Pasta-Ulam recurrence in a modulationally unstable optical wave,” Phys. Rev. Lett. 87(3), 033902 (2001).
[CrossRef] [PubMed]

Voronovich, V. V.

V. V. Voronovich, V. I. Shrira, and G. Thomas, “Can bottom friction suppress ‘freak wave’ formation?” J. Fluid Mech. 604, 263–296 (2008).
[CrossRef]

Wabnitz, S.

S. Trillo, S. Wabnitz, and T. A. B. Kennedy, “Nonlinear dynamics of dual-frequency-pumped multiwave mixing in optical fibers,” Phys. Rev. A 50(2), 1732–1747 (1994).
[CrossRef] [PubMed]

S. Trillo and S. Wabnitz, “Dynamics of the nonlinear modulational instability in optical fibers,” Opt. Lett. 16(13), 986–988 (1991).
[CrossRef] [PubMed]

Wigley, P. G. J.

E. J. Greer, D. M. Patrick, P. G. J. Wigley, and J. R. Taylor, “Generation of 2 THz repetition rate pulse trains through induced modulational instability,” Electron. Lett. 25(18), 1246–1248 (1989).
[CrossRef]

Windeler, R. S.

Yagi, T.

Appl. Phys. B

G. Genty, J. M. Dudley, and B. J. Eggleton, “Modulation control and spectral shaping of optical fiber supercontinuum generation in the picosecond regime,” Appl. Phys. B 94(2), 187–194 (2009).
[CrossRef]

Appl. Phys. Lett.

S. Liu, “Four-wave mixing and modulation instability of continuous optical waves in single-mode optical fibers,” Appl. Phys. Lett. 89(17), 171118 (2006).
[CrossRef]

Electron. Lett.

B. Barviau, C. Finot, J. Fatome, and G. Millot, “Generation from continuous waves of frequency combs with large overall bandwidth and tunable central wavelength,” Electron. Lett. 43(16), 886–887 (2007).
[CrossRef]

E. J. Greer, D. M. Patrick, P. G. J. Wigley, and J. R. Taylor, “Generation of 2 THz repetition rate pulse trains through induced modulational instability,” Electron. Lett. 25(18), 1246–1248 (1989).
[CrossRef]

IEEE J. Quantum Electron.

J. M. Dudley, F. Gutty, S. Pitois, and G. Millot, “Complete characterization of THz pulse trains generated from nonlinear processes in optical fibers,” IEEE J. Quantum Electron. 37(4), 587–594 (2001).
[CrossRef]

J. Fluid Mech.

V. V. Voronovich, V. I. Shrira, and G. Thomas, “Can bottom friction suppress ‘freak wave’ formation?” J. Fluid Mech. 604, 263–296 (2008).
[CrossRef]

T. B. Benjamin and J. E. Feir, “The disintegration of wavetrains on deep water. Part 1: Theory,” J. Fluid Mech. 27(03), 417–430 (1967).
[CrossRef]

JETP Lett.

V. I. Bespalov and V. I. Talanov, “Filamentary structure of light beams in nonlinear liquids,” JETP Lett. 3, 307–310 (1966).

Nat. Photonics

J. M. Dudley and J. R. Taylor, “Ten years of nonlinear optics in photonic crystal fibre,” Nat. Photonics 3(2), 85–90 (2009).
[CrossRef]

Nature

N. N. Akhmediev, “Nonlinear physics. Déjà vu in optics,” Nature 413(6853), 267–268 (2001).
[CrossRef] [PubMed]

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

Opt. Commun.

A. Demircan and U. Bandelow, “Supercontinuum generation by the modulation instability,” Opt. Commun. 244(1-6), 181–185 (2005).
[CrossRef]

Opt. Express

J. Beeckman, X. Hutsebaut, M. Haelterman, and K. Neyts, “Induced modulation instability and recurrence in nematic liquid crystals,” Opt. Express 15(18), 11185–11195 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-18-11185 .
[CrossRef] [PubMed]

J. M. Dudley, G. Genty, and B. J. Eggleton, “Harnessing and control of optical rogue waves in supercontinuum generation,” Opt. Express 16(6), 3644–3651 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-6-3644U .
[CrossRef] [PubMed]

J. C. Travers, A. B. Rulkov, B. A. Cumberland, S. V. Popov, and J. R. Taylor, “Visible supercontinuum generation in photonic crystal fibers with a 400W continuous wave fiber laser,” Opt. Express 16(19), 14435–14447 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-19-14435 .
[CrossRef] [PubMed]

F. C. Cruz, “Optical frequency combs generated by four-wave mixing in optical fibers for astrophysical spectrometer calibration and metrology,” Opt. Express 16(17), 13267–13275 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-17-13267U .
[CrossRef] [PubMed]

J. N. Kutz, C. Lyngå, and B. J. Eggleton, “Enhanced supercontinuum generation through dispersion-management,” Opt. Express 13(11), 3989–3998 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-11-3989 .
[CrossRef] [PubMed]

N. Korneev, E. A. Kuzin, B. Ibarra-Escamilla, M. Bello-Jiménez, and A. Flores-Rosas, “Initial development of supercontinuum in fibers with anomalous dispersion pumped by nanosecond-long pulses,” Opt. Express 16(4), 2636–2645 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-4-2636 .
[CrossRef] [PubMed]

S. M. Kobtsev and S. V. Smirnov, “Influence of noise amplification on generation of regular short pulse trains in optical fibre pumped by intensity-modulated CW radiation,” Opt. Express 16(10), 7428–7434 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-10-7428 .
[CrossRef] [PubMed]

Opt. Lett.

Phys. Lett. A

A. R. Osborne, M. Onorato, and M. Serio, “The nonlinear dynamics of rogue waves and holes in deep-water gravity wave trains,” Phys. Lett. A 275(5-6), 386–393 (2000).
[CrossRef]

V. I. Karpman, A. G. Shagalov, and J. J. Rasmussen, “Modulational instability due to nonlinear coupling between high- and low-frequency waves: a study of truncated systems,” Phys. Lett. A 147(2-3), 119–124 (1990).
[CrossRef]

Phys. Rev. A

S. Trillo, S. Wabnitz, and T. A. B. Kennedy, “Nonlinear dynamics of dual-frequency-pumped multiwave mixing in optical fibers,” Phys. Rev. A 50(2), 1732–1747 (1994).
[CrossRef] [PubMed]

Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics

D. L. Hart, A. F. Judy, R. Roy, and J. W. Beletic, “Dynamical evolution of multiple four-wave-mixing processes in an optical fiber,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 57(4), 4757–4774 (1998).
[CrossRef]

Phys. Rev. Lett.

D. R. Solli, C. Ropers, and B. Jalali, “Active control of rogue waves for stimulated supercontinuum generation,” Phys. Rev. Lett. 101(23), 233902 (2008).
[CrossRef] [PubMed]

K. Tai, A. Hasegawa, and A. Tomita, “Observation of modulational instability in optical fibers,” Phys. Rev. Lett. 56(2), 135–138 (1986).
[CrossRef] [PubMed]

G. Van Simaeys, Ph. Emplit, and M. Haelterman, “Experimental demonstration of the Fermi-Pasta-Ulam recurrence in a modulationally unstable optical wave,” Phys. Rev. Lett. 87(3), 033902 (2001).
[CrossRef] [PubMed]

G. P. Agrawal, “Modulation instability induced by cross-phase modulation,” Phys. Rev. Lett. 59(8), 880–883 (1987).
[CrossRef] [PubMed]

Phys. Scr.

K. B. Dysthe and K. Trulsen, “Note on Breather type Solutions of the NLS as models for freak-waves,” Phys. Scr. T82(1), 48–52 (1999).
[CrossRef]

Rev. Mod. Phys.

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

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M. J. Ablowitz and B. M. Herbst, “On homoclinic structure and numerically induced chaos for the nonlinear Schrödinger equation,” SIAM J. Appl. Math. 50(2), 339–351 (1990).
[CrossRef]

Sov. Phys. JETP

N. Akhmediev, V. M. Eleonskii, and N. E. Kulagin, “Generation of periodic trains of picosecond pulses in an optical fiber: exact solutions,” Sov. Phys. JETP 62, 894–899 (1985).

N. Akhmediev, V. I. Korneev, and N. V. Mitskevich, “N-modulation signals in a single-mode optical waveguide under nonlinear conditions,” Sov. Phys. JETP 67, 89–95 (1988).

Theor. Math. Phys.

N. Akhmediev and V. I. Korneev, “Modulation instability and periodic solutions of the nonlinear Schrodinger equation,” Theor. Math. Phys. 69(2), 1089–1093 (1986).
[CrossRef]

N. Akhmediev, V. M. Eleonskii, and N. E. Kulagin, “Exact first-order solutions of the nonlinear Schrodinger equation,” Theor. Math. Phys. 72(2), 809–818 (1987).
[CrossRef]

Other

N. Akhmediev, and A. Ankiewicz, Solitons, Nonlinear Pulses and Beams, (Chapman and Hall, London, 1997)

G. P. Agrawal, Nonlinear Fiber Optics. 4th Edition. Academic Press, Boston (2007)

D. Clamond, M. Francius, J. Grue, C. Kharif, “Long time interaction of envelope solitons and freak wave formations,” European J. Mech. B – Fluids/B 25, 536–553 (2006)

I. Ten, and H. Tomita, “Simulation of the ocean waves and appearance of freak waves,” Reports of RIAM Symposium No.17SP1–2, Chikushi Campus, Kyushu University, Kasuga, Fukuoka, Japan, March 10 – 11 (2006).

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Figures (6)

Fig. 1
Fig. 1

Grayscale plots show simulated spectral and temporal evolution for a = 0.25; fmod = 289.12 GHz and with modulation amplitudes αmod as shown. Arrows and labels indicate the point of maximum temporal compression during the first growth-return cycle. Graphs A, B, C below compare simulation results (circles) with analytic results describing the maximally-compressed AB sub-pulses (lines) from Eq. (3).

Fig. 2
Fig. 2

Grayscale plots show simulated spectral and temporal evolution for fixed α mod = 0.01 but varying modulation parameters (a and thus f mod) as shown. Arrows and labels indicate the point of maximum temporal compression during the first growth-return cycle. Graphs A, B, C below compare simulation results (circles) with analytic results describing the maximally-compressed AB sub-pulses (lines) from Eq. (3).

Fig. 3
Fig. 3

Experimental (left) and simulation (right) results for 1 ns pulses at 1064 nm injected into highly nonlinear PCF at peak powers as shown. Simulation results are averaged and convolved with a spectral resolution function matching the bandwidth of the spectrum analyzer used in the experiments (0.1 nm for 26 W results; 0.4 nm for 43 W results; 1.6 nm for 98 W results).

Fig. 4
Fig. 4

Single shot NLSE simulations for a CW field undergoing spontaneous MI showing: (a) temporal and (b) spectral evolution over 3.9 m. The figure also shows temporal and spectral profiles at 3.5 m. The shaded region in the temporal trace is shown in detail in the rightmost figure comparing simulations (solid line) with the AB solution calculated for a modulation frequency corresponding to peak MI gain (dashed line). The axes in the grayscale plots are normalized relative to the frequency of peak MI gain: f mod = 1.32 THz.

Fig. 5
Fig. 5

Time and frequency domain characteristics of the ideal maximally-compressed AB. The modulation frequency fmod = 1.32 THz determines the spectral mode separation.

Fig. 6
Fig. 6

Comparison between experiments (solid black line), numerical simulations using the full GNLSE (blue dashed line), numerical simulations using the NLSE only (red dashed line), and the calculated spectrum of the maximally-compressed AB (green lines from zero).

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

i A z + β 2 2 2 A T 2 + γ | A | 2 A = 0 ​     ​ ,
A ( z , T ) = P 0       ( 1 4 a ) cosh ( b z ) + i b sinh ( b z ) + 2 a cos ( ω mod T ) 2 a cos ( ω mod T ) cosh ( b z ) ,
A ( z = 0 , T ) = P 0       ( 1 4 a ) + 2 a cos ( ω mod T ) 2 a cos ( ω mod T ) 1 .

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