Abstract

We experimentally demonstrate the existence of multiple, simultaneous, independent four-wave mixing processes in optical fibers. In particular we observe competition between phase-matched and non-phase-matched processes involving the same mixed coherent-incoherent pump. Further investigation reveals that narrow-band degenerate four-wave mixing with an incoherent pump can lead to efficient wavelength conversion.

© 2010 OSA

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References

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  1. R. H. Stolen, J. E. Bjorkholm, and A. Ashkin, “Phase-matched three-wave mixing in silica fiber optical waveguides,” Appl. Phys. Lett. 24, 308–310 (1974).
    [CrossRef]
  2. A. C. Sodre, J. M. C. Boggio, A. A. Rieznik, H. E. Hernandez-Figueroa, H. L. Fragnito, and J. C. Knight, “Highly efficient generation of broadband cascaded four-wave mixing products,” Opt. Express 16, 2816–2828 (2008).
    [CrossRef]
  3. 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 57, 4757–4774 (1998).
    [CrossRef]
  4. G. Millot, “Multiple four-wave mixing-induced modulational instability in highly birefringent fibers,” Opt. Lett. 26, 1391–1393 (2001).
    [CrossRef]
  5. G. Cappellini and S. Trillo, “Third-order three-wave mixing in single-mode fibers: exact solutions and spatial instability effects,” J. Opt. Soc. Am. B 8, 824–838 (1991).
    [CrossRef]
  6. A. S. Y. Hsieh, G. K. L. Wong, S. G. Murdoch, S. Coen, F. Vanholsbeeck, R. Leonhardt, and J. D. Harvey, “Combined effect of Raman and parametric gain on single-pump parametric amplifiers,” Opt. Express 15, 8104–8114 (2007).
    [CrossRef] [PubMed]
  7. S. Coen, D. A. Wardle, and J. D. Harvey, “Observation of non-phase-matched parametric amplification in resonant nonlinear optics,” Phys. Rev. Lett. 89, 273901 (2002).
    [CrossRef]
  8. Y. Chen and A. W. Snyder, “Four-photon parametric mixing in optical fibers: effect of pump depletion,” Opt. Lett. 14, 87–89 (1989).
    [CrossRef] [PubMed]
  9. R. Stolen and J. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” IEEE J. Quantum Electron. 18, 1062–1072 (1982).
    [CrossRef]
  10. J. Hansryd, P. Andrekson, M. Westlund, J. Li, and P.-O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. 8, 506–520 (2002).
    [CrossRef]
  11. M. Islam and O. Boyraz, “Fiber parametric amplifiers for wavelength band conversion,” IEEE J. Sel. Top. Quantum Electron. 8, 527–537 (2002).
    [CrossRef]
  12. M. E. Marhic, Y. Park, F. S. Yang, and L. G. Kazovsky, “Broadband fiber-optical parametric amplifiers and wavelength converters with low-ripple Chebyshev gain spectra,” Opt. Lett. 21, 1354 (1996).
    [CrossRef] [PubMed]
  13. S. Coen and M. Haelterman, “Continuous-wave ultrahigh-repetition-rate pulse-train generation through modulational instability in a passive fiber cavity,” Opt. Lett. 26, 39–41 (2001).
    [CrossRef]
  14. J. Fatome, S. Pitois, and G. Millot, “20-GHz-to-1-THz repetition rate pulse sources based on multiple four-wave mixing in optical fibers,” IEEE J. Quantum Electron. 42, 1038–1046 (2006).
    [CrossRef]
  15. J. Schröder, S. Coen, F. Vanholsbeeck, and T. Sylvestre, “Passively mode-locked Raman fiber laser with 100 GHz repetition rate,” Opt. Lett. 31, 3489–3491 (2006).
    [CrossRef] [PubMed]
  16. R. K. Jain and K. Stenersen, “Phase-matched four-photon mixing processes in birefringent fibers,” Appl. Phys. B 35, 49–57 (1984).
    [CrossRef]
  17. J. R. Thompson and R. Roy, “Multiple four-wave mixing process in an optical fiber,” Opt. Lett. 16, 557–559 (1991).
    [CrossRef] [PubMed]
  18. J. R. Thompson and R. Roy, “Nonlinear dynamics of multiple four-wave mixing processes in a single-mode fiber,” Phys. Rev. A 43, 4987–4996 (1991).
    [CrossRef] [PubMed]
  19. S. Trillo, S. Wabnitz, and T. A. B. Kennedy, “Nonlinear dynamics of dual-frequency-pumped multiwave mixing in optical fibers,” Phys. Rev. A 50, 1732–1747 (1994).
    [CrossRef] [PubMed]
  20. X. Liu, X. Zhou, and C. Lu, “Multiple four-wave mixing self-stability in optical fibers,” Phys. Rev. A 72, 013811 (2005).
    [CrossRef]
  21. C. J. McKinstrie and M. G. Raymer, “Four-wave-mixing cascades near the zero-dispersion frequency,” Opt. Express 14, 9600–9610 (2006).
    [CrossRef] [PubMed]
  22. E. Lantz, D. Gindre, H. Maillotte, and J. Monneret, “Phase matching for parametric amplification in a single-mode birefringent fiber: influence of the non-phase-matched waves,” J. Opt. Soc. Am. B 14, 116–125 (1997).
    [CrossRef]
  23. T. Sylvestre, H. Maillotte, E. Lantz, and P. T. Dinda, “Raman-assisted parametric frequency conversion in a normally dispersive single-mode fiber,” Opt. Lett. 24, 1561–1563 (1999).
    [CrossRef]
  24. Y. S. Jang and Y. C. Chung, “Four-wave mixing of incoherent light in a dispersion-shifted fiber using a spectrum-sliced fiber amplifier light source,” IEEE Photon. Technol. Lett. 10, 218–220 (1998).
    [CrossRef]
  25. A. Sauter, S. Pitois, G. Millot, and A. Picozzi, “Incoherent modulation instability in instantaneous nonlinear Kerr media,” Opt. Lett. 30, 2143–2145 (2005).
    [CrossRef] [PubMed]
  26. S. Gao, C. Yang, X. Xiao, Y. Tian, Z. You, and G. Jin, “Wavelength conversion of spectrum-sliced broadband amplified spontaneous emission light by hybrid four-wave mixing in highly nonlinear, dispersion-shifted fibers,” Opt. Express 14, 2873–2879 (2006).
    [CrossRef] [PubMed]
  27. J. M. Chávez Boggio and H. L. Fragnito, “Simple four-wave-mixing-based method for measuring the ratio between the third- and fourth-order dispersion in optical fibers,” J. Opt. Soc. Am. B 24, 2046–2054 (2007).
    [CrossRef]
  28. Y. Q. Xu and S. G. Murdoch, “Gain spectrum of an optical parametric amplifier with a temporally incoherent pump,” Opt. Lett,  35, 169–171 (2010).
    [CrossRef] [PubMed]
  29. Y. Q. Xu and S. G. Murdoch, “Gain statistics of a fiber optical parametric amplifier with a temporally incoherent pump,” Opt. Lett.,  35, 826–829 (2010).
    [CrossRef] [PubMed]
  30. J. D. Harvey, R. Leonhardt, S. Coen, G. K. L. Wong, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “Scalar modulation instability in the normal dispersion regime by use of a photonic crystal fiber,” Opt. Lett. 28, 2225–2227 (2003).
    [CrossRef] [PubMed]
  31. M. Marhic, K.-Y. Wong, and L. Kazovsky, “Wide-band tuning of the gain spectra of one-pump fiber optical parametric amplifiers,” IEEE J. Sel. Top. Quantum Electron. 10, 1133–1141 (2004).
    [CrossRef]

2010 (2)

Y. Q. Xu and S. G. Murdoch, “Gain spectrum of an optical parametric amplifier with a temporally incoherent pump,” Opt. Lett,  35, 169–171 (2010).
[CrossRef] [PubMed]

Y. Q. Xu and S. G. Murdoch, “Gain statistics of a fiber optical parametric amplifier with a temporally incoherent pump,” Opt. Lett.,  35, 826–829 (2010).
[CrossRef] [PubMed]

2008 (1)

2007 (2)

2006 (4)

2005 (2)

2004 (1)

M. Marhic, K.-Y. Wong, and L. Kazovsky, “Wide-band tuning of the gain spectra of one-pump fiber optical parametric amplifiers,” IEEE J. Sel. Top. Quantum Electron. 10, 1133–1141 (2004).
[CrossRef]

2003 (1)

2002 (3)

J. Hansryd, P. Andrekson, M. Westlund, J. Li, and P.-O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. 8, 506–520 (2002).
[CrossRef]

M. Islam and O. Boyraz, “Fiber parametric amplifiers for wavelength band conversion,” IEEE J. Sel. Top. Quantum Electron. 8, 527–537 (2002).
[CrossRef]

S. Coen, D. A. Wardle, and J. D. Harvey, “Observation of non-phase-matched parametric amplification in resonant nonlinear optics,” Phys. Rev. Lett. 89, 273901 (2002).
[CrossRef]

2001 (2)

1999 (1)

1998 (2)

Y. S. Jang and Y. C. Chung, “Four-wave mixing of incoherent light in a dispersion-shifted fiber using a spectrum-sliced fiber amplifier light source,” IEEE Photon. Technol. Lett. 10, 218–220 (1998).
[CrossRef]

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 57, 4757–4774 (1998).
[CrossRef]

1997 (1)

1996 (1)

1994 (1)

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

1991 (3)

1989 (1)

1984 (1)

R. K. Jain and K. Stenersen, “Phase-matched four-photon mixing processes in birefringent fibers,” Appl. Phys. B 35, 49–57 (1984).
[CrossRef]

1982 (1)

R. Stolen and J. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” IEEE J. Quantum Electron. 18, 1062–1072 (1982).
[CrossRef]

1974 (1)

R. H. Stolen, J. E. Bjorkholm, and A. Ashkin, “Phase-matched three-wave mixing in silica fiber optical waveguides,” Appl. Phys. Lett. 24, 308–310 (1974).
[CrossRef]

Andrekson, P.

J. Hansryd, P. Andrekson, M. Westlund, J. Li, and P.-O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. 8, 506–520 (2002).
[CrossRef]

Ashkin, A.

R. H. Stolen, J. E. Bjorkholm, and A. Ashkin, “Phase-matched three-wave mixing in silica fiber optical waveguides,” Appl. Phys. Lett. 24, 308–310 (1974).
[CrossRef]

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 57, 4757–4774 (1998).
[CrossRef]

Bjorkholm, J.

R. Stolen and J. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” IEEE J. Quantum Electron. 18, 1062–1072 (1982).
[CrossRef]

Bjorkholm, J. E.

R. H. Stolen, J. E. Bjorkholm, and A. Ashkin, “Phase-matched three-wave mixing in silica fiber optical waveguides,” Appl. Phys. Lett. 24, 308–310 (1974).
[CrossRef]

Boggio, J. M. C.

Boyraz, O.

M. Islam and O. Boyraz, “Fiber parametric amplifiers for wavelength band conversion,” IEEE J. Sel. Top. Quantum Electron. 8, 527–537 (2002).
[CrossRef]

Cappellini, G.

Chávez Boggio, J. M.

Chen, Y.

Chung, Y. C.

Y. S. Jang and Y. C. Chung, “Four-wave mixing of incoherent light in a dispersion-shifted fiber using a spectrum-sliced fiber amplifier light source,” IEEE Photon. Technol. Lett. 10, 218–220 (1998).
[CrossRef]

Coen, S.

Dinda, P. T.

Fatome, J.

J. Fatome, S. Pitois, and G. Millot, “20-GHz-to-1-THz repetition rate pulse sources based on multiple four-wave mixing in optical fibers,” IEEE J. Quantum Electron. 42, 1038–1046 (2006).
[CrossRef]

Fragnito, H. L.

Gao, S.

Gindre, D.

Haelterman, M.

Hansryd, J.

J. Hansryd, P. Andrekson, M. Westlund, J. Li, and P.-O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. 8, 506–520 (2002).
[CrossRef]

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 57, 4757–4774 (1998).
[CrossRef]

Harvey, J. D.

Hedekvist, P.-O.

J. Hansryd, P. Andrekson, M. Westlund, J. Li, and P.-O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. 8, 506–520 (2002).
[CrossRef]

Hernandez-Figueroa, H. E.

Hsieh, A. S. Y.

Islam, M.

M. Islam and O. Boyraz, “Fiber parametric amplifiers for wavelength band conversion,” IEEE J. Sel. Top. Quantum Electron. 8, 527–537 (2002).
[CrossRef]

Jain, R. K.

R. K. Jain and K. Stenersen, “Phase-matched four-photon mixing processes in birefringent fibers,” Appl. Phys. B 35, 49–57 (1984).
[CrossRef]

Jang, Y. S.

Y. S. Jang and Y. C. Chung, “Four-wave mixing of incoherent light in a dispersion-shifted fiber using a spectrum-sliced fiber amplifier light source,” IEEE Photon. Technol. Lett. 10, 218–220 (1998).
[CrossRef]

Jin, G.

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 57, 4757–4774 (1998).
[CrossRef]

Kazovsky, L.

M. Marhic, K.-Y. Wong, and L. Kazovsky, “Wide-band tuning of the gain spectra of one-pump fiber optical parametric amplifiers,” IEEE J. Sel. Top. Quantum Electron. 10, 1133–1141 (2004).
[CrossRef]

Kazovsky, L. G.

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, 1732–1747 (1994).
[CrossRef] [PubMed]

Knight, J. C.

Lantz, E.

Leonhardt, R.

Li, J.

J. Hansryd, P. Andrekson, M. Westlund, J. Li, and P.-O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. 8, 506–520 (2002).
[CrossRef]

Liu, X.

X. Liu, X. Zhou, and C. Lu, “Multiple four-wave mixing self-stability in optical fibers,” Phys. Rev. A 72, 013811 (2005).
[CrossRef]

Lu, C.

X. Liu, X. Zhou, and C. Lu, “Multiple four-wave mixing self-stability in optical fibers,” Phys. Rev. A 72, 013811 (2005).
[CrossRef]

Maillotte, H.

Marhic, M.

M. Marhic, K.-Y. Wong, and L. Kazovsky, “Wide-band tuning of the gain spectra of one-pump fiber optical parametric amplifiers,” IEEE J. Sel. Top. Quantum Electron. 10, 1133–1141 (2004).
[CrossRef]

Marhic, M. E.

McKinstrie, C. J.

Millot, G.

Monneret, J.

Murdoch, S. G.

Park, Y.

Picozzi, A.

Pitois, S.

J. Fatome, S. Pitois, and G. Millot, “20-GHz-to-1-THz repetition rate pulse sources based on multiple four-wave mixing in optical fibers,” IEEE J. Quantum Electron. 42, 1038–1046 (2006).
[CrossRef]

A. Sauter, S. Pitois, G. Millot, and A. Picozzi, “Incoherent modulation instability in instantaneous nonlinear Kerr media,” Opt. Lett. 30, 2143–2145 (2005).
[CrossRef] [PubMed]

Raymer, M. G.

Rieznik, A. A.

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 57, 4757–4774 (1998).
[CrossRef]

J. R. Thompson and R. Roy, “Nonlinear dynamics of multiple four-wave mixing processes in a single-mode fiber,” Phys. Rev. A 43, 4987–4996 (1991).
[CrossRef] [PubMed]

J. R. Thompson and R. Roy, “Multiple four-wave mixing process in an optical fiber,” Opt. Lett. 16, 557–559 (1991).
[CrossRef] [PubMed]

Russell, P. St. J.

Sauter, A.

Schröder, J.

Snyder, A. W.

Sodre, A. C.

Stenersen, K.

R. K. Jain and K. Stenersen, “Phase-matched four-photon mixing processes in birefringent fibers,” Appl. Phys. B 35, 49–57 (1984).
[CrossRef]

Stolen, R.

R. Stolen and J. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” IEEE J. Quantum Electron. 18, 1062–1072 (1982).
[CrossRef]

Stolen, R. H.

R. H. Stolen, J. E. Bjorkholm, and A. Ashkin, “Phase-matched three-wave mixing in silica fiber optical waveguides,” Appl. Phys. Lett. 24, 308–310 (1974).
[CrossRef]

Sylvestre, T.

Thompson, J. R.

J. R. Thompson and R. Roy, “Multiple four-wave mixing process in an optical fiber,” Opt. Lett. 16, 557–559 (1991).
[CrossRef] [PubMed]

J. R. Thompson and R. Roy, “Nonlinear dynamics of multiple four-wave mixing processes in a single-mode fiber,” Phys. Rev. A 43, 4987–4996 (1991).
[CrossRef] [PubMed]

Tian, Y.

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, 1732–1747 (1994).
[CrossRef] [PubMed]

G. Cappellini and S. Trillo, “Third-order three-wave mixing in single-mode fibers: exact solutions and spatial instability effects,” J. Opt. Soc. Am. B 8, 824–838 (1991).
[CrossRef]

Vanholsbeeck, F.

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, 1732–1747 (1994).
[CrossRef] [PubMed]

Wadsworth, W. J.

Wardle, D. A.

S. Coen, D. A. Wardle, and J. D. Harvey, “Observation of non-phase-matched parametric amplification in resonant nonlinear optics,” Phys. Rev. Lett. 89, 273901 (2002).
[CrossRef]

Westlund, M.

J. Hansryd, P. Andrekson, M. Westlund, J. Li, and P.-O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. 8, 506–520 (2002).
[CrossRef]

Wong, G. K. L.

Wong, K.-Y.

M. Marhic, K.-Y. Wong, and L. Kazovsky, “Wide-band tuning of the gain spectra of one-pump fiber optical parametric amplifiers,” IEEE J. Sel. Top. Quantum Electron. 10, 1133–1141 (2004).
[CrossRef]

Xiao, X.

Xu, Y. Q.

Y. Q. Xu and S. G. Murdoch, “Gain spectrum of an optical parametric amplifier with a temporally incoherent pump,” Opt. Lett,  35, 169–171 (2010).
[CrossRef] [PubMed]

Y. Q. Xu and S. G. Murdoch, “Gain statistics of a fiber optical parametric amplifier with a temporally incoherent pump,” Opt. Lett.,  35, 826–829 (2010).
[CrossRef] [PubMed]

Yang, C.

Yang, F. S.

You, Z.

Zhou, X.

X. Liu, X. Zhou, and C. Lu, “Multiple four-wave mixing self-stability in optical fibers,” Phys. Rev. A 72, 013811 (2005).
[CrossRef]

Appl. Phys. B (1)

R. K. Jain and K. Stenersen, “Phase-matched four-photon mixing processes in birefringent fibers,” Appl. Phys. B 35, 49–57 (1984).
[CrossRef]

Appl. Phys. Lett. (1)

R. H. Stolen, J. E. Bjorkholm, and A. Ashkin, “Phase-matched three-wave mixing in silica fiber optical waveguides,” Appl. Phys. Lett. 24, 308–310 (1974).
[CrossRef]

IEEE J. Quantum Electron. (2)

R. Stolen and J. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” IEEE J. Quantum Electron. 18, 1062–1072 (1982).
[CrossRef]

J. Fatome, S. Pitois, and G. Millot, “20-GHz-to-1-THz repetition rate pulse sources based on multiple four-wave mixing in optical fibers,” IEEE J. Quantum Electron. 42, 1038–1046 (2006).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (3)

J. Hansryd, P. Andrekson, M. Westlund, J. Li, and P.-O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. 8, 506–520 (2002).
[CrossRef]

M. Islam and O. Boyraz, “Fiber parametric amplifiers for wavelength band conversion,” IEEE J. Sel. Top. Quantum Electron. 8, 527–537 (2002).
[CrossRef]

M. Marhic, K.-Y. Wong, and L. Kazovsky, “Wide-band tuning of the gain spectra of one-pump fiber optical parametric amplifiers,” IEEE J. Sel. Top. Quantum Electron. 10, 1133–1141 (2004).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

Y. S. Jang and Y. C. Chung, “Four-wave mixing of incoherent light in a dispersion-shifted fiber using a spectrum-sliced fiber amplifier light source,” IEEE Photon. Technol. Lett. 10, 218–220 (1998).
[CrossRef]

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

Opt. Express (4)

Opt. Lett (1)

Y. Q. Xu and S. G. Murdoch, “Gain spectrum of an optical parametric amplifier with a temporally incoherent pump,” Opt. Lett,  35, 169–171 (2010).
[CrossRef] [PubMed]

Opt. Lett. (10)

Y. Q. Xu and S. G. Murdoch, “Gain statistics of a fiber optical parametric amplifier with a temporally incoherent pump,” Opt. Lett.,  35, 826–829 (2010).
[CrossRef] [PubMed]

J. D. Harvey, R. Leonhardt, S. Coen, G. K. L. Wong, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “Scalar modulation instability in the normal dispersion regime by use of a photonic crystal fiber,” Opt. Lett. 28, 2225–2227 (2003).
[CrossRef] [PubMed]

T. Sylvestre, H. Maillotte, E. Lantz, and P. T. Dinda, “Raman-assisted parametric frequency conversion in a normally dispersive single-mode fiber,” Opt. Lett. 24, 1561–1563 (1999).
[CrossRef]

A. Sauter, S. Pitois, G. Millot, and A. Picozzi, “Incoherent modulation instability in instantaneous nonlinear Kerr media,” Opt. Lett. 30, 2143–2145 (2005).
[CrossRef] [PubMed]

M. E. Marhic, Y. Park, F. S. Yang, and L. G. Kazovsky, “Broadband fiber-optical parametric amplifiers and wavelength converters with low-ripple Chebyshev gain spectra,” Opt. Lett. 21, 1354 (1996).
[CrossRef] [PubMed]

S. Coen and M. Haelterman, “Continuous-wave ultrahigh-repetition-rate pulse-train generation through modulational instability in a passive fiber cavity,” Opt. Lett. 26, 39–41 (2001).
[CrossRef]

J. Schröder, S. Coen, F. Vanholsbeeck, and T. Sylvestre, “Passively mode-locked Raman fiber laser with 100 GHz repetition rate,” Opt. Lett. 31, 3489–3491 (2006).
[CrossRef] [PubMed]

G. Millot, “Multiple four-wave mixing-induced modulational instability in highly birefringent fibers,” Opt. Lett. 26, 1391–1393 (2001).
[CrossRef]

Y. Chen and A. W. Snyder, “Four-photon parametric mixing in optical fibers: effect of pump depletion,” Opt. Lett. 14, 87–89 (1989).
[CrossRef] [PubMed]

J. R. Thompson and R. Roy, “Multiple four-wave mixing process in an optical fiber,” Opt. Lett. 16, 557–559 (1991).
[CrossRef] [PubMed]

Phys. Rev. A (3)

J. R. Thompson and R. Roy, “Nonlinear dynamics of multiple four-wave mixing processes in a single-mode fiber,” Phys. Rev. A 43, 4987–4996 (1991).
[CrossRef] [PubMed]

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

X. Liu, X. Zhou, and C. Lu, “Multiple four-wave mixing self-stability in optical fibers,” Phys. Rev. A 72, 013811 (2005).
[CrossRef]

Phys. Rev. E (1)

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 57, 4757–4774 (1998).
[CrossRef]

Phys. Rev. Lett. (1)

S. Coen, D. A. Wardle, and J. D. Harvey, “Observation of non-phase-matched parametric amplification in resonant nonlinear optics,” Phys. Rev. Lett. 89, 273901 (2002).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Experimental setup. RFL: Raman fiber laser, EDFL and EDFA: Erbium-doped fiber laser and amplifier, WDM: wavelength division multiplexer, DSF: dispersion shifted fiber, OSA: optical spectrum analyzer.

Fig. 2
Fig. 2

Output spectra for EDFL wavelengths 1536 to 1554 nm: (a) line plot, (b) color plot.

Fig. 3
Fig. 3

(a), (b) Enlargement of Figs. 2(a) and (b) around the MI region respectively. In (b), the solid and dashed lines correspond to the boundaries of the MI gain band, i.e. solutions of Eqs. (1) and (2) respectively. The dotted vertical and horizontal lines indicate the ZDW.

Fig. 4
Fig. 4

Enlargement of Fig. 2 around the two Stokes waves, S1 (fixed) and S2 (variable). (a) Line plot, (b) color plot. In (b), the theoretical wavelength of S2 calculated from energy conservation considerations (2ωEDFL = ωRFL + ωS2) is superimposed as a black line.

Fig. 5
Fig. 5

(a) Output spectra demonstrating FWM between the RFL and the ASE pump for a constant RFL power of 1 W and ASE powers of 28 dBm (solid) and 33 dBm (dotted). (b) Output spectra for constant ASE pump power of 30 dBm and RFL power of 100 mW (solid) and 900 mW (dotted).

Equations (2)

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β 2 + β 4 Ω 2 / 12 < 0
| β 2 + β 4 Ω 2 / 12 | Ω 2 < 4 γ P

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