Abstract

The inverse modulation interaction is a degenerate four-wave mixing process in which two strong pumps drive a weak signal, whose frequency is the average of the pump frequencies. Theoretical analyses and numerical simulations of this process are made for wave frequencies that are near the zero-dispersion frequency of a fiber, in which case dispersion is unimportant, and wave frequencies that are far from the zero-dispersion frequency, in which case dispersion is important. The results show that the inverse modulation interaction in a strongly-birefringent fiber amplifies a linearly-polarized signal by an amount that depends on its phase angle, but not its polarization angle. Phase conjugation and Bragg scattering are nondegenerate four-wave mixing processes in which two strong pumps drive a weak signal and a weak idler. Studies show that phase conjugation and Bragg scattering in strongly-birefringent fibers produce polarization-independent phase-insensitive amplification and frequency conversion, respectively.

© 2008 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. Hansryd, P. A. Andrekson, M. Westlund, J. Li and P. O. Hedekvist, "Fiber-based optical parametric amplifiers and their applications," J. Sel. Top. Quantum Electron. 8, 506-520 (2002).
    [CrossRef]
  2. S. Radic and C. J. McKinstrie, "Two-pump fiber parametric amplifiers," Opt. Fiber Technol. 9, 7-23 (2003).
    [CrossRef]
  3. C. J. McKinstrie, S. Radic and A. H. Gnauck, "All-optical signal processing by fiber-based parametric devices," Opt. Photonics News 18, 34-40 (2007).
    [CrossRef]
  4. C. J. McKinstrie, S. Radic and C. Xie, "Parametric instabilities driven by orthogonal pump waves in birefringent fibers," Opt. Express 11, 2619-2633 (2003).
    [CrossRef] [PubMed]
  5. C. J. McKinstrie, H. Kogelnik, R. M. Jopson, S. Radic and A. V. Kanaev, "Four-wave mixing in fibers with random birefringence," Opt. Express 12, 2033-2055 (2004).
    [CrossRef] [PubMed]
  6. C. J. McKinstrie, H. Kogelnik and L. Schenato, "Four-wave mixing in a rapidly-spun fiber," Opt. Express 14, 8516-8534 (2006).
    [CrossRef] [PubMed]
  7. T. Hasegawa, K. Inoue and K. Oda, "Polarization independent frequency conversion by fiber four-wave mixing with a polarization diversity technique," IEEE Photon. Technol. Lett. 5, 947-949 (1993).
    [CrossRef]
  8. K. K. Chow, C. Shu, C. Lin and A. Bjarklev, "Polarization-insensitive widely tunable wavelength converter based on four-wave mixing in a dispersion-flattened nonlinear photonic crystal fiber," IEEE Photon. Technol. Lett. 17, 624-626 (2005).
    [CrossRef]
  9. Z. Wang, N. Deng, C. Lin and C. K. Chan, "Polarization-insensitive widely tunable wavelength conversion based on four-wave mixing using dispersion-flatened high-nonlinearity photonic crystal fiber with residual birefringence," ECOC 2006, paper We3.P.18.
  10. A. S. Lenihan and G. M. Carter, "Polarization-insensitive wavelength conversion at 40 Gb/s using birefringent nonlinear fiber," CLEO 2007, paper CThAA2.
  11. R. H. Stolen, M. A. Bosch and C. Lin, "Phase matching in birefringent fibers," Opt. Lett. 6, 213-215 (1981).
    [CrossRef] [PubMed]
  12. C. J. McKinstrie and S. Radic, "Phase-sensitive amplification in a fiber," Opt. Express 12, 4973-4979 (2004).
    [CrossRef] [PubMed]
  13. C. J. McKinstrie, R. O. Moore, S. Radic and R. Jiang, "Phase-sensitive amplification of chirped optical pulses in fibers," Opt. Express 15, 3737-3758 (2007).
    [CrossRef] [PubMed]
  14. C. J. McKinstrie and M. G. Raymer, "Four-wave-mixing cascades near the zero-dispersion frequency," Opt. Express 14, 9600-9610 (2006).
    [CrossRef] [PubMed]
  15. C. J. McKinstrie, S. Radic, M. G. Raymer and L. Schenato, "Unimpaired phase-sensitive amplification by vector four-wave mixing near the zero-dispersion frequency," Opt. Express 15, 2178-2189 (2007).
    [CrossRef] [PubMed]
  16. K. Croussore and G. Li, "Phase regeneration of NRZ-DPSK signals based on symmetric-pump phase-sensitive amplification," IEEE Photon. Technol. Lett. 19, 864-866 (2007).
    [CrossRef]
  17. C. J. McKinstrie, S. Radic and A. R. Chraplyvy, "Parametric amplifiers driven by two pump waves," IEEE J. Sel. Top. Quantum Electron.  8, 538-547 and 956 (2002).
    [CrossRef]
  18. C. R. Menyuk, "Nonlinear pulse propagation in birefringent optical fibers," IEEE J. Quantum Electron. 23, 174-176 (1987).
    [CrossRef]
  19. C. J. McKinstrie, H. Kogelnik, G. G. Luther and L. Schenato, "Stokes-space derivations of generalized Schr¨odinger equations for wave propagation in various fibers," Opt. Express 15, 10964-10983 (2007).
    [CrossRef] [PubMed]
  20. G. B. Whitham, Linear and Nonlinear Waves (Wiley, 1974).
  21. M. Karlsson, "Four-wave mixing in fibers with randomly varying zero-dispersion wavelength," J. Opt. Soc. Am. B 15, 2269-2275 (1998).
    [CrossRef]
  22. J. Rothenberg, "Modulational instability for normal dispersion," Phys. Rev. A 42, 682-685 (1990).
    [CrossRef] [PubMed]
  23. P. D. Drummond, T. A. B. Kennedy, J. M. Dudley, R. Leonhardt and J. D. Harvey, "Cross-phase modulational instability in high-birefringence fibers," Opt. Commun. 78, 137-142 (1990).
    [CrossRef]
  24. C. J. McKinstrie and S. Radic, "Parametric amplifiers driven by two pumps with dissimilar frequencies," Opt. Lett. 27, 1138-1140 (2002).
    [CrossRef]
  25. C. J. McKinstrie, J. D. Harvey, S. Radic and M. G. Raymer, "Translation of quantum states by four-wave mixing in fibers," Opt. Express 13, 9131-9142 (2005).
    [CrossRef] [PubMed]
  26. C. J. McKinstrie, S. Radic and C. Xie, "Phase conjugation driven by orthogonal pump waves in birefringent fibers," J. Opt. Soc. Am. B 20, 1437-1446 (2003).
    [CrossRef]
  27. R. Tang, P. Devgan, P. L. Voss, V. S. Grigoryan and P. Kumar, "In-line frequency-nondegenerate phase-sensitive fibre parametric amplifer for fibre-optic communication," IEEE Photon. Technol. Lett. 17, 1845-1847 (2005).
    [CrossRef]
  28. R. Tang, J. Lasri, P. S. Devgan, V. Grigoryan, P. Kumar and M. Vasilyev, "Gain characteristics of a frequency nondegenerate phase-sensitive fiber-optic parametric amplifier with phase self-stabilized input," Opt. Express 13, 10483-10493 (2005).
    [CrossRef] [PubMed]

2007

2006

2005

K. K. Chow, C. Shu, C. Lin and A. Bjarklev, "Polarization-insensitive widely tunable wavelength converter based on four-wave mixing in a dispersion-flattened nonlinear photonic crystal fiber," IEEE Photon. Technol. Lett. 17, 624-626 (2005).
[CrossRef]

C. J. McKinstrie, J. D. Harvey, S. Radic and M. G. Raymer, "Translation of quantum states by four-wave mixing in fibers," Opt. Express 13, 9131-9142 (2005).
[CrossRef] [PubMed]

R. Tang, P. Devgan, P. L. Voss, V. S. Grigoryan and P. Kumar, "In-line frequency-nondegenerate phase-sensitive fibre parametric amplifer for fibre-optic communication," IEEE Photon. Technol. Lett. 17, 1845-1847 (2005).
[CrossRef]

R. Tang, J. Lasri, P. S. Devgan, V. Grigoryan, P. Kumar and M. Vasilyev, "Gain characteristics of a frequency nondegenerate phase-sensitive fiber-optic parametric amplifier with phase self-stabilized input," Opt. Express 13, 10483-10493 (2005).
[CrossRef] [PubMed]

2004

2003

2002

C. J. McKinstrie and S. Radic, "Parametric amplifiers driven by two pumps with dissimilar frequencies," Opt. Lett. 27, 1138-1140 (2002).
[CrossRef]

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

1998

1993

T. Hasegawa, K. Inoue and K. Oda, "Polarization independent frequency conversion by fiber four-wave mixing with a polarization diversity technique," IEEE Photon. Technol. Lett. 5, 947-949 (1993).
[CrossRef]

1990

J. Rothenberg, "Modulational instability for normal dispersion," Phys. Rev. A 42, 682-685 (1990).
[CrossRef] [PubMed]

P. D. Drummond, T. A. B. Kennedy, J. M. Dudley, R. Leonhardt and J. D. Harvey, "Cross-phase modulational instability in high-birefringence fibers," Opt. Commun. 78, 137-142 (1990).
[CrossRef]

1987

C. R. Menyuk, "Nonlinear pulse propagation in birefringent optical fibers," IEEE J. Quantum Electron. 23, 174-176 (1987).
[CrossRef]

1981

Andrekson, P. A.

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

Bjarklev, A.

K. K. Chow, C. Shu, C. Lin and A. Bjarklev, "Polarization-insensitive widely tunable wavelength converter based on four-wave mixing in a dispersion-flattened nonlinear photonic crystal fiber," IEEE Photon. Technol. Lett. 17, 624-626 (2005).
[CrossRef]

Bosch, M. A.

Chow, K. K.

K. K. Chow, C. Shu, C. Lin and A. Bjarklev, "Polarization-insensitive widely tunable wavelength converter based on four-wave mixing in a dispersion-flattened nonlinear photonic crystal fiber," IEEE Photon. Technol. Lett. 17, 624-626 (2005).
[CrossRef]

Croussore, K.

K. Croussore and G. Li, "Phase regeneration of NRZ-DPSK signals based on symmetric-pump phase-sensitive amplification," IEEE Photon. Technol. Lett. 19, 864-866 (2007).
[CrossRef]

Devgan, P.

R. Tang, P. Devgan, P. L. Voss, V. S. Grigoryan and P. Kumar, "In-line frequency-nondegenerate phase-sensitive fibre parametric amplifer for fibre-optic communication," IEEE Photon. Technol. Lett. 17, 1845-1847 (2005).
[CrossRef]

Devgan, P. S.

Drummond, P. D.

P. D. Drummond, T. A. B. Kennedy, J. M. Dudley, R. Leonhardt and J. D. Harvey, "Cross-phase modulational instability in high-birefringence fibers," Opt. Commun. 78, 137-142 (1990).
[CrossRef]

Dudley, J. M.

P. D. Drummond, T. A. B. Kennedy, J. M. Dudley, R. Leonhardt and J. D. Harvey, "Cross-phase modulational instability in high-birefringence fibers," Opt. Commun. 78, 137-142 (1990).
[CrossRef]

Gnauck, A. H.

C. J. McKinstrie, S. Radic and A. H. Gnauck, "All-optical signal processing by fiber-based parametric devices," Opt. Photonics News 18, 34-40 (2007).
[CrossRef]

Grigoryan, V.

Grigoryan, V. S.

R. Tang, P. Devgan, P. L. Voss, V. S. Grigoryan and P. Kumar, "In-line frequency-nondegenerate phase-sensitive fibre parametric amplifer for fibre-optic communication," IEEE Photon. Technol. Lett. 17, 1845-1847 (2005).
[CrossRef]

Hansryd, J.

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

Harvey, J. D.

C. J. McKinstrie, J. D. Harvey, S. Radic and M. G. Raymer, "Translation of quantum states by four-wave mixing in fibers," Opt. Express 13, 9131-9142 (2005).
[CrossRef] [PubMed]

P. D. Drummond, T. A. B. Kennedy, J. M. Dudley, R. Leonhardt and J. D. Harvey, "Cross-phase modulational instability in high-birefringence fibers," Opt. Commun. 78, 137-142 (1990).
[CrossRef]

Hasegawa, T.

T. Hasegawa, K. Inoue and K. Oda, "Polarization independent frequency conversion by fiber four-wave mixing with a polarization diversity technique," IEEE Photon. Technol. Lett. 5, 947-949 (1993).
[CrossRef]

Hedekvist, P. O.

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

Inoue, K.

T. Hasegawa, K. Inoue and K. Oda, "Polarization independent frequency conversion by fiber four-wave mixing with a polarization diversity technique," IEEE Photon. Technol. Lett. 5, 947-949 (1993).
[CrossRef]

Jiang, R.

Jopson, R. M.

Kanaev, A. V.

Karlsson, M.

Kennedy, T. A. B.

P. D. Drummond, T. A. B. Kennedy, J. M. Dudley, R. Leonhardt and J. D. Harvey, "Cross-phase modulational instability in high-birefringence fibers," Opt. Commun. 78, 137-142 (1990).
[CrossRef]

Kogelnik, H.

Kumar, P.

R. Tang, P. Devgan, P. L. Voss, V. S. Grigoryan and P. Kumar, "In-line frequency-nondegenerate phase-sensitive fibre parametric amplifer for fibre-optic communication," IEEE Photon. Technol. Lett. 17, 1845-1847 (2005).
[CrossRef]

R. Tang, J. Lasri, P. S. Devgan, V. Grigoryan, P. Kumar and M. Vasilyev, "Gain characteristics of a frequency nondegenerate phase-sensitive fiber-optic parametric amplifier with phase self-stabilized input," Opt. Express 13, 10483-10493 (2005).
[CrossRef] [PubMed]

Lasri, J.

Leonhardt, R.

P. D. Drummond, T. A. B. Kennedy, J. M. Dudley, R. Leonhardt and J. D. Harvey, "Cross-phase modulational instability in high-birefringence fibers," Opt. Commun. 78, 137-142 (1990).
[CrossRef]

Li, G.

K. Croussore and G. Li, "Phase regeneration of NRZ-DPSK signals based on symmetric-pump phase-sensitive amplification," IEEE Photon. Technol. Lett. 19, 864-866 (2007).
[CrossRef]

Li, J.

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

Lin, C.

K. K. Chow, C. Shu, C. Lin and A. Bjarklev, "Polarization-insensitive widely tunable wavelength converter based on four-wave mixing in a dispersion-flattened nonlinear photonic crystal fiber," IEEE Photon. Technol. Lett. 17, 624-626 (2005).
[CrossRef]

R. H. Stolen, M. A. Bosch and C. Lin, "Phase matching in birefringent fibers," Opt. Lett. 6, 213-215 (1981).
[CrossRef] [PubMed]

Luther, G. G.

McKinstrie, C. J.

C. J. McKinstrie, R. O. Moore, S. Radic and R. Jiang, "Phase-sensitive amplification of chirped optical pulses in fibers," Opt. Express 15, 3737-3758 (2007).
[CrossRef] [PubMed]

C. J. McKinstrie, S. Radic, M. G. Raymer and L. Schenato, "Unimpaired phase-sensitive amplification by vector four-wave mixing near the zero-dispersion frequency," Opt. Express 15, 2178-2189 (2007).
[CrossRef] [PubMed]

C. J. McKinstrie, H. Kogelnik, G. G. Luther and L. Schenato, "Stokes-space derivations of generalized Schr¨odinger equations for wave propagation in various fibers," Opt. Express 15, 10964-10983 (2007).
[CrossRef] [PubMed]

C. J. McKinstrie, S. Radic and A. H. Gnauck, "All-optical signal processing by fiber-based parametric devices," Opt. Photonics News 18, 34-40 (2007).
[CrossRef]

C. J. McKinstrie, H. Kogelnik and L. Schenato, "Four-wave mixing in a rapidly-spun fiber," Opt. Express 14, 8516-8534 (2006).
[CrossRef] [PubMed]

C. J. McKinstrie and M. G. Raymer, "Four-wave-mixing cascades near the zero-dispersion frequency," Opt. Express 14, 9600-9610 (2006).
[CrossRef] [PubMed]

C. J. McKinstrie, J. D. Harvey, S. Radic and M. G. Raymer, "Translation of quantum states by four-wave mixing in fibers," Opt. Express 13, 9131-9142 (2005).
[CrossRef] [PubMed]

C. J. McKinstrie and S. Radic, "Phase-sensitive amplification in a fiber," Opt. Express 12, 4973-4979 (2004).
[CrossRef] [PubMed]

C. J. McKinstrie, H. Kogelnik, R. M. Jopson, S. Radic and A. V. Kanaev, "Four-wave mixing in fibers with random birefringence," Opt. Express 12, 2033-2055 (2004).
[CrossRef] [PubMed]

S. Radic and C. J. McKinstrie, "Two-pump fiber parametric amplifiers," Opt. Fiber Technol. 9, 7-23 (2003).
[CrossRef]

C. J. McKinstrie, S. Radic and C. Xie, "Parametric instabilities driven by orthogonal pump waves in birefringent fibers," Opt. Express 11, 2619-2633 (2003).
[CrossRef] [PubMed]

C. J. McKinstrie, S. Radic and C. Xie, "Phase conjugation driven by orthogonal pump waves in birefringent fibers," J. Opt. Soc. Am. B 20, 1437-1446 (2003).
[CrossRef]

C. J. McKinstrie and S. Radic, "Parametric amplifiers driven by two pumps with dissimilar frequencies," Opt. Lett. 27, 1138-1140 (2002).
[CrossRef]

Menyuk, C. R.

C. R. Menyuk, "Nonlinear pulse propagation in birefringent optical fibers," IEEE J. Quantum Electron. 23, 174-176 (1987).
[CrossRef]

Moore, R. O.

Oda, K.

T. Hasegawa, K. Inoue and K. Oda, "Polarization independent frequency conversion by fiber four-wave mixing with a polarization diversity technique," IEEE Photon. Technol. Lett. 5, 947-949 (1993).
[CrossRef]

Radic, S.

C. J. McKinstrie, S. Radic and A. H. Gnauck, "All-optical signal processing by fiber-based parametric devices," Opt. Photonics News 18, 34-40 (2007).
[CrossRef]

C. J. McKinstrie, R. O. Moore, S. Radic and R. Jiang, "Phase-sensitive amplification of chirped optical pulses in fibers," Opt. Express 15, 3737-3758 (2007).
[CrossRef] [PubMed]

C. J. McKinstrie, S. Radic, M. G. Raymer and L. Schenato, "Unimpaired phase-sensitive amplification by vector four-wave mixing near the zero-dispersion frequency," Opt. Express 15, 2178-2189 (2007).
[CrossRef] [PubMed]

C. J. McKinstrie, J. D. Harvey, S. Radic and M. G. Raymer, "Translation of quantum states by four-wave mixing in fibers," Opt. Express 13, 9131-9142 (2005).
[CrossRef] [PubMed]

C. J. McKinstrie, H. Kogelnik, R. M. Jopson, S. Radic and A. V. Kanaev, "Four-wave mixing in fibers with random birefringence," Opt. Express 12, 2033-2055 (2004).
[CrossRef] [PubMed]

C. J. McKinstrie and S. Radic, "Phase-sensitive amplification in a fiber," Opt. Express 12, 4973-4979 (2004).
[CrossRef] [PubMed]

C. J. McKinstrie, S. Radic and C. Xie, "Parametric instabilities driven by orthogonal pump waves in birefringent fibers," Opt. Express 11, 2619-2633 (2003).
[CrossRef] [PubMed]

S. Radic and C. J. McKinstrie, "Two-pump fiber parametric amplifiers," Opt. Fiber Technol. 9, 7-23 (2003).
[CrossRef]

C. J. McKinstrie, S. Radic and C. Xie, "Phase conjugation driven by orthogonal pump waves in birefringent fibers," J. Opt. Soc. Am. B 20, 1437-1446 (2003).
[CrossRef]

C. J. McKinstrie and S. Radic, "Parametric amplifiers driven by two pumps with dissimilar frequencies," Opt. Lett. 27, 1138-1140 (2002).
[CrossRef]

Raymer, M. G.

Rothenberg, J.

J. Rothenberg, "Modulational instability for normal dispersion," Phys. Rev. A 42, 682-685 (1990).
[CrossRef] [PubMed]

Schenato, L.

Shu, C.

K. K. Chow, C. Shu, C. Lin and A. Bjarklev, "Polarization-insensitive widely tunable wavelength converter based on four-wave mixing in a dispersion-flattened nonlinear photonic crystal fiber," IEEE Photon. Technol. Lett. 17, 624-626 (2005).
[CrossRef]

Stolen, R. H.

Tang, R.

R. Tang, P. Devgan, P. L. Voss, V. S. Grigoryan and P. Kumar, "In-line frequency-nondegenerate phase-sensitive fibre parametric amplifer for fibre-optic communication," IEEE Photon. Technol. Lett. 17, 1845-1847 (2005).
[CrossRef]

R. Tang, J. Lasri, P. S. Devgan, V. Grigoryan, P. Kumar and M. Vasilyev, "Gain characteristics of a frequency nondegenerate phase-sensitive fiber-optic parametric amplifier with phase self-stabilized input," Opt. Express 13, 10483-10493 (2005).
[CrossRef] [PubMed]

Vasilyev, M.

Voss, P. L.

R. Tang, P. Devgan, P. L. Voss, V. S. Grigoryan and P. Kumar, "In-line frequency-nondegenerate phase-sensitive fibre parametric amplifer for fibre-optic communication," IEEE Photon. Technol. Lett. 17, 1845-1847 (2005).
[CrossRef]

Westlund, M.

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

Xie, C.

IEEE J. Quantum Electron.

C. R. Menyuk, "Nonlinear pulse propagation in birefringent optical fibers," IEEE J. Quantum Electron. 23, 174-176 (1987).
[CrossRef]

IEEE Photon. Technol. Lett.

K. Croussore and G. Li, "Phase regeneration of NRZ-DPSK signals based on symmetric-pump phase-sensitive amplification," IEEE Photon. Technol. Lett. 19, 864-866 (2007).
[CrossRef]

T. Hasegawa, K. Inoue and K. Oda, "Polarization independent frequency conversion by fiber four-wave mixing with a polarization diversity technique," IEEE Photon. Technol. Lett. 5, 947-949 (1993).
[CrossRef]

K. K. Chow, C. Shu, C. Lin and A. Bjarklev, "Polarization-insensitive widely tunable wavelength converter based on four-wave mixing in a dispersion-flattened nonlinear photonic crystal fiber," IEEE Photon. Technol. Lett. 17, 624-626 (2005).
[CrossRef]

R. Tang, P. Devgan, P. L. Voss, V. S. Grigoryan and P. Kumar, "In-line frequency-nondegenerate phase-sensitive fibre parametric amplifer for fibre-optic communication," IEEE Photon. Technol. Lett. 17, 1845-1847 (2005).
[CrossRef]

J. Opt. Soc. Am. B

J. Sel. Top. Quantum Electron.

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

Opt. Commun.

P. D. Drummond, T. A. B. Kennedy, J. M. Dudley, R. Leonhardt and J. D. Harvey, "Cross-phase modulational instability in high-birefringence fibers," Opt. Commun. 78, 137-142 (1990).
[CrossRef]

Opt. Express

R. Tang, J. Lasri, P. S. Devgan, V. Grigoryan, P. Kumar and M. Vasilyev, "Gain characteristics of a frequency nondegenerate phase-sensitive fiber-optic parametric amplifier with phase self-stabilized input," Opt. Express 13, 10483-10493 (2005).
[CrossRef] [PubMed]

C. J. McKinstrie, J. D. Harvey, S. Radic and M. G. Raymer, "Translation of quantum states by four-wave mixing in fibers," Opt. Express 13, 9131-9142 (2005).
[CrossRef] [PubMed]

C. J. McKinstrie, S. Radic and C. Xie, "Parametric instabilities driven by orthogonal pump waves in birefringent fibers," Opt. Express 11, 2619-2633 (2003).
[CrossRef] [PubMed]

C. J. McKinstrie, H. Kogelnik, R. M. Jopson, S. Radic and A. V. Kanaev, "Four-wave mixing in fibers with random birefringence," Opt. Express 12, 2033-2055 (2004).
[CrossRef] [PubMed]

C. J. McKinstrie, H. Kogelnik and L. Schenato, "Four-wave mixing in a rapidly-spun fiber," Opt. Express 14, 8516-8534 (2006).
[CrossRef] [PubMed]

C. J. McKinstrie, H. Kogelnik, G. G. Luther and L. Schenato, "Stokes-space derivations of generalized Schr¨odinger equations for wave propagation in various fibers," Opt. Express 15, 10964-10983 (2007).
[CrossRef] [PubMed]

C. J. McKinstrie and S. Radic, "Phase-sensitive amplification in a fiber," Opt. Express 12, 4973-4979 (2004).
[CrossRef] [PubMed]

C. J. McKinstrie, R. O. Moore, S. Radic and R. Jiang, "Phase-sensitive amplification of chirped optical pulses in fibers," Opt. Express 15, 3737-3758 (2007).
[CrossRef] [PubMed]

C. J. McKinstrie and M. G. Raymer, "Four-wave-mixing cascades near the zero-dispersion frequency," Opt. Express 14, 9600-9610 (2006).
[CrossRef] [PubMed]

C. J. McKinstrie, S. Radic, M. G. Raymer and L. Schenato, "Unimpaired phase-sensitive amplification by vector four-wave mixing near the zero-dispersion frequency," Opt. Express 15, 2178-2189 (2007).
[CrossRef] [PubMed]

Opt. Fiber Technol.

S. Radic and C. J. McKinstrie, "Two-pump fiber parametric amplifiers," Opt. Fiber Technol. 9, 7-23 (2003).
[CrossRef]

Opt. Lett.

Opt. Photonics News

C. J. McKinstrie, S. Radic and A. H. Gnauck, "All-optical signal processing by fiber-based parametric devices," Opt. Photonics News 18, 34-40 (2007).
[CrossRef]

Phys. Rev. A

J. Rothenberg, "Modulational instability for normal dispersion," Phys. Rev. A 42, 682-685 (1990).
[CrossRef] [PubMed]

Other

Z. Wang, N. Deng, C. Lin and C. K. Chan, "Polarization-insensitive widely tunable wavelength conversion based on four-wave mixing using dispersion-flatened high-nonlinearity photonic crystal fiber with residual birefringence," ECOC 2006, paper We3.P.18.

A. S. Lenihan and G. M. Carter, "Polarization-insensitive wavelength conversion at 40 Gb/s using birefringent nonlinear fiber," CLEO 2007, paper CThAA2.

G. B. Whitham, Linear and Nonlinear Waves (Wiley, 1974).

C. J. McKinstrie, S. Radic and A. R. Chraplyvy, "Parametric amplifiers driven by two pump waves," IEEE J. Sel. Top. Quantum Electron.  8, 538-547 and 956 (2002).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (22)

Fig. 1.
Fig. 1.

Normalized mode powers [Eq. (18)] plotted as functions of mode number for the case in which ρ0 =22.4, ρ 1x =0.283 and ρ 1y =0.141: (a) γsρ 2 0 z=0.0 and (b) γsρ 2 0 z=10.0.

Fig. 2.
Fig. 2.

(a) Simulated mode powers [Eqs. (1) and (2)] plotted as functions of frequency for the case in which the pump powers Px =Py =0.5 W and the signal powers Psx =0.08 and Psy =0.02 mW: (a) z=0 Km and (b) z=2.0 Km. Red bars denote x components, whereas blue bars denote y components.

Fig. 3.
Fig. 3.

Simulated gain [Eqs. (1) and (2)] of the signal (solid curve) and idler (dashed curve) plotted as functions of the signal polarization, for the same parameters as Fig. 2.

Fig. 4.
Fig. 4.

(a) Signal gain [Eq. (26)] plotted as a function of signal phase and distance (γsρ 2 z). Light and dark regions correspond to high and low gains, respectively. The contour spacing is 0.5. (b) Gain plotted as a function of phase for the case in which γsρ 2 z=2.0.

Fig. 5.
Fig. 5.

Input power plotted as a function of mode number (frequency) for the case in which there are two pumps and one signal. (a) ρ=22.4 and ρ 0=0.316. (b) P=0.5 W and P 0=0.1 mW. Red bars represent the odd harmonics (pumps), whereas blue bars represent the even harmonic (signal).

Fig. 6.
Fig. 6.

Normalized mode power [Eq. (24)] plotted as a function of mode number for cases in which ρ=22.4, ρ 0=0.316 and γsρ 2 z=2.0. (a) For ϕ 0=0.124 the signal is amplified by 10 dB. (b) For ϕ 0=1.69 the signal is attenuated by 35 dB. Red bars represent the odd harmonics (pumps), whereas blue bars represent the even harmonics (signal and idlers).

Fig. 7.
Fig. 7.

Simulated mode power [Eq. (1)] plotted as a function of mode frequency for cases in which P=0.5 W, P 0=0.1 mW and z=0.4 Km. (a) For ϕ 0=0.124 the signal is amplified by 10 dB. (b) For ϕ 0=1.69 the signal is attenuated by 20 dB.

Fig. 8.
Fig. 8.

(a) Simulated signal gain [Eq. (1)] plotted as a function of signal phase for the signal polarizations θ=0 (solid curve) and θ=π/4 (dashed curve). (b) Simulated gain [Eqs. (1) and (2)] plotted as a function of polarization for the phases ϕ=0.124 (solid curve) and ϕ=1.69 (dashed curve). The other parameters are the same as those of Fig. 7.

Fig. 9.
Fig. 9.

Signal gain plotted as a function of signal phase, for the fiber length l=0.46 Km, the pump powers P 1=P 3=0.25 Wand the signal power P 2=0.1 mW. The pump frequencies are -1.31 and 1.87 THz, and the signal frequency is 0.28 THz. The dashed curve denotes the theoretical prediction [Eq. (40)], whereas the solid curve denotes the simulation result [Eq. (1)].

Fig. 10.
Fig. 10.

Simulated mode power [Eq. (1)] plotted as a function of mode frequency (measured relative to the signal frequency), for the parameters of Fig. 9. (a) When the signal phase ϕ 2=0.78, the signal is amplified by 19.3 dB. (b) When ϕ 2=2.35, the signal is attenuated by 19.3 dB. Red bars denote odd harmonics (pumps), whereas blue bars denote even harmonics (signal and idlers).

Fig. 11.
Fig. 11.

Simulated signal gain [Eqs. (1) and (2)] plotted as a function of signal polarization, for the parameters of Fig. 9. The solid curve represents the signal phase ϕ 2=0.78, whereas the dashed curve represents ϕ 2=2.35.

Fig. 12.
Fig. 12.

Signal gain plotted as a function of the signal phase, for the fiber length l=0.46 Km, the pump powers P 1=P 3=0.25 W and the signal power P 2=0.1 mW. The solid, dot-dashed and dashed curves represent frequency differences of 0.16, 0.23 and 0.28 THz, respectively. (a) Theoretical predictions based on Eq. (40). (b) Simulation results based on Eq. (1).

Fig. 13.
Fig. 13.

Simulated mode power [Eq. (1)] plotted as a function of mode frequency, for the parameters of Fig. 12 and a frequency difference of 0.16 THz. (a) When the signal phase ϕ 2=0, the signal experiences little gain. (b) When ϕ 2=1.3, the signal experiences some gain. Red bars denote odd harmonics (pumps), whereas blue bars denote even harmonics (signal and idlers).

Fig. 14.
Fig. 14.

Simulated power [Eq. (1)] of a secondary pump plotted as a function of distance, for the parameters of Fig. 12. The solid, dot-dashed and dashed curves represent frequency differences of 0.16, 0.23 and 0.28 THz, respectively.

Fig. 15.
Fig. 15.

Simulated signal gain [Eq. (1)] plotted as a function of signal phase, for the parameters of Fig. 12 and a frequency difference of 0.23 THz. The dotted, dashed, dot-dashed and solid curves represent lengths of 0.2, 0.4, 0.6 and 0.8 Km, respectively.

Fig. 16.
Fig. 16.

Simulated mode power [Eq. (1)] plotted as a function of mode frequency, for the parameters of Fig. 12 and a frequency difference of 0.23 THz. Figures 16(a)–16(d) correspond to lengths of 0.2, 0.4, 0.6 and 0.8, respectively. Red bars denote odd harmonics (pumps), whereas blue bars denote even harmonics (signal and idlers).

Fig. 17.
Fig. 17.

Signal gain [Eqs. (38) and (41)] plotted as a function of signal frequency, for a fiber length of 1.0 Km. The pump frequencies are -3.35 and 3.65 THz (solid lines), and the (common) pump power is 0.25 W.

Fig. 18.
Fig. 18.

Simulated sideband power [Eqs. (1) and (2)] plotted as a function of frequency. The pump frequencies are -3.35 and 3.65 THz (solid lines), the (common) pump power is 0.25 W and the noise power is -50 dBmW. (a) Pumps and sidebands are x-polarized. (b) Pumps and sidebands are y-polarized.

Fig. 19.
Fig. 19.

Simulated sideband power [Eqs. (1) and (2)] plotted as a function of frequency. The pump frequencies are -3.35 and 3.65 THz (solid lines), the (common) pump power is 0.25 W in each polarization and the noise power is -50 dBmW in each polarization. (a) x-polarized power. (b) y-polarized power.

Fig. 20.
Fig. 20.

Signal-to-idler conversion efficiency [Eqs. (39) and (44)] plotted as a function of the lower pump frequency, for a fiber length of 0.31 Km. The signal frequency is -1.47 THz (dashed line), the higher pump frequency is 1.71 THz (solid line) and the (common) pump power is 0.25 W. The hollow circles denote lower pump and idler frequencies of -3.07 and 3.3 THz, respectively, whereas the solid circles denote frequencies of -4.66 and 4.89 THz.

Fig. 21.
Fig. 21.

Simulated mode power [Eq. (1)] plotted as a function of mode frequency. The signal frequency is -1.47 THz, the higher pump frequency is 1.71 THz and the (common) pump power is 0.25 W. (a) The lower pump (idler) frequency is -3.07 (3.30) THz. (b) The lower pump (idler) frequency is -4.66 (4.89) THz. Red bars denote pumps, whereas blue bars denote signal and idlers.

Fig. 22.
Fig. 22.

Simulated conversion efficiency [Eqs. (1) and (2)] plotted as a function of signal polarization. The signal frequency is -1.47 THz, the higher pump frequency is 1.71 THz and the (common) pump power is 0.25Win each polarization. The dashed curve represents a lower pump (idler) frequency of -3.07 (3.30) THz, whereas the solid curve represents a lower pump (idler) frequency of -4.66 (4.89) THz.

Equations (77)

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

z X = i β x ( i τ ) X + i ( γ s X 2 + γ c Y 2 ) X ,
z Y = i β y ( i τ ) Y + i ( γ c X 2 + γ s Y 2 ) Y ,
( z + β d t ) X = i ( γ s X 2 + γ c Y 2 ) X ,
( z β d t ) Y = i ( γ c X 2 + γ s Y 2 ) Y ,
( z + β d t ) P x = 0 ,
( z β d t ) P y = 0 ,
X ( τ x , z ) = X ( τ x , 0 ) exp { i γ s P x ( τ x , 0 ) z + i γ c 0 z P y ( τ x + 2 β d z , 0 ) d z } ,
Y ( τ y , z ) = Y ( τ y , 0 ) exp { i γ c 0 z P x ( τ y 2 β d z , 0 ) d z + i γ s P y ( τ y , 0 ) z } .
X ( τ , 0 ) = ρ 0 x exp ( i ϕ 0 x ) + ρ 1 x exp ( i ϕ 1 x ) ,
Y ( τ , 0 ) = ρ 0 y exp ( i ϕ 0 y ) + ρ 1 y exp ( i ϕ 1 y ) ,
P x ( τ x , 0 ) = ρ 0 x 2 + ρ 1 x 2 + 2 ρ 0 x ρ 1 x cos ( ϕ 0 x ϕ 1 x ) .
P y ( τ y , 0 ) = ρ 0 y 2 + ρ 1 y 2 + 2 ρ 0 y ρ 1 y cos ( ϕ 0 y ϕ 1 y ) .
0 z P x ( τ y 2 β d z , 0 ) d z = ( ρ 0 x 2 + ρ 1 x 2 ) z ρ 0 x ρ 1 x { sin [ ω d ( τ y 2 β d z ) ϕ d x ]
sin [ ω d τ y ϕ d x ] } / β d ω d .
0 z P y ( τ x + 2 β d z , 0 ) d z = ( ρ 0 y 2 + ρ 1 y 2 ) z + ρ 0 y ρ 1 y { sin [ ω d ( τ x + 2 β d z ) ϕ dy ]
sin [ ω d τ x ϕ dy ] } / β d ω d ,
X ( τ x , z ) = n X n ( z ) exp ( i ϕ n x + i ψ x ) ,
ϕ n x ( τ x ) = ϕ 0 x ( τ x ) + n [ ϕ 1 x ( τ x ) ϕ 0 x ( τ x ) ]
ψ x ( z ) = γ s ( ρ 0 x 2 + ρ 1 x 2 ) z + γ c ( ρ 0 y 2 + ρ 1 y 2 ) z .
X n ( z ) = i n ρ 0 x J n ( ζ x ) + i n 1 ρ 1 x J n 1 ( ζ x ) ,
X 1 ( 1 + i γ s ρ 0 2 z ) ρ 1 x , X 1 ( i γ s ρ 0 2 z ) ρ 1 x .
X ( τ , 0 ) = ρ exp ( i ϕ 1 ) + ρ 0 x exp ( i ϕ 0 ) + ρ exp ( i ϕ 1 ) .
X ( τ , 0 ) = ρ exp ( i ω d τ x ) + ρ 0 x exp ( i ϕ 0 ) + ρ exp ( i ω d τ x ) ,
X ( τ x , z ) = n X n ( z ) exp ( i n ω d τ x + i ψ x ) ,
ψ x = 2 ( γ s + γ c ) ρ 2 z + ( γ s ρ 0 x 2 + γ c ρ 0 y 2 ) z ,
X n ( ζ ) = m i n m J m ( ζ ) [ ρ 0 x exp ( i ϕ 0 ) J n 2 m ( ε x ζ ) 2 i ρ J n 2 m ( ε x ζ ) ] ,
X n ( ζ ) i n 2 ρ 0 x { J n 2 ( ζ ) [ exp ( i ϕ 0 ) + 2 i ζ cos ϕ 0 ] + J n 2 ( ζ ) 2 ζ cos ϕ 0 ] ,
X 0 ( ζ ) = ρ 0 [ μ ( ζ ) exp ( i ϕ 0 ) + ν ( ζ ) exp ( i ϕ 0 ) ] ,
2 ϕ m ( ζ ) = tan 1 { J 0 2 ( ζ ) ζ [ J 0 2 ( ζ ) + J 1 2 ( ζ ) ] J 0 ( ζ ) J 1 ( ζ ) } .
X ( t , z ) = j = 1 4 X j ( z ) exp ( i ω j t ) ,
Y ( t , z ) = j = 1 4 Y j ( z ) exp ( i ω j t )
z X 1 = i β x ( ω 1 ) X 1 + i γ s ( X 1 2 + 2 X 2 2 + 2 X 3 2 + 2 X 4 2 ) X 1
+ i γ s X 3 * X 2 2 + i 2 γ s X 4 * X 2 X 3
+ i γ c ( Y 1 2 + Y 2 2 + Y 3 2 + Y 4 2 ) X 1 + i γ c Y 1 ( Y 2 * X 2 + Y 3 * X 3 + Y 4 * X 4 )
+ i γ c Y 3 * Y 2 X 2 + i γ c Y 4 * ( Y 2 X 3 + Y 3 X 2 ) ,
z X 2 = i β x ( ω 2 ) X 2 + i γ s ( X 2 2 + 2 X 3 2 + 2 X 4 2 + 2 X 1 2 ) X 2
+ i 2 γ s X 2 * X 3 X 1 + i γ s X 4 * X 3 2 + i 2 γ s X 3 * X 4 X 1
+ i γ c ( Y 2 2 + Y 3 2 + Y 4 2 + Y 1 2 ) X 2 + i γ c Y 2 ( Y 3 * X 3 + Y 4 * X 4 + Y 1 * X 1 )
+ i γ c Y 2 * ( Y 3 X 1 + Y 1 X 3 ) + i γ c Y 4 * Y 3 X 3 + i γ c Y 3 * ( Y 4 X 1 + Y 1 X 4 ) .
z X 1 i β x ( ω 1 ) X 1 + i γ s ( X 1 2 + 2 X 2 2 + 2 X 3 2 + 2 X 4 2 ) X 1
i γ s X 3 * X 2 2 + i 2 γ s X 4 * X 2 X 3
+ i γ c ( Y 1 2 + Y 2 2 + Y 3 2 + Y 4 2 ) X 1 ,
z X 2 i β x ( ω 2 ) X 2 + i γ s ( X 2 2 + 2 X 3 2 + 2 X 4 2 + 2 X 1 2 ) X 2
i 2 γ s X 2 * X 3 X 1 + i γ s X 4 * X 3 2 + i 2 γ s X 3 * X 4 X 1
+ i γ c ( Y 2 2 + Y 3 2 + Y 4 2 + Y 1 2 ) X 2 .
z X 1 i β x ( ω 1 ) X 1 i γ s X 1 2 X 1 + i γ s X 3 * X 2 2 + i 2 γ s X 4 * X 2 X 3 ,
z X 2 i β x ( ω 2 ) X 2 i γ s X 2 2 X 2 + i 2 γ s X 2 * X 3 X 1 + i γ s X 4 * X 3 2 + i 2 γ s X 3 * X 4 X 1 ,
X 1 ( z ) = μ ( z ) X 1 ( 0 ) + ν ( z ) X 3 * ( 0 ) ,
X 3 * ( z ) = ν * ( z ) X 1 ( 0 ) + μ * ( z ) X 3 * ( 0 ) .
μ ( z ) = cos ( kz ) + i ( δ k ) sin ( kz ) ,
ν ( z ) = i ( γ ̅ k ) sin ( kz ) ,
X 2 ( z ) = μ ( z ) X 2 ( 0 ) + ν ( z ) X 2 * ( 0 ) ,
X 1 ( z ) = μ ( z ) X 1 ( 0 ) + ν ( z ) X 4 * ( 0 ) ,
X 4 * ( z ) = ν * ( z ) X 1 ( 0 ) + μ * ( z ) X 4 * ( 0 ) ,
X 2 ( z ) = μ ( z ) X 2 ( 0 ) + ν ( z ) X 4 ( 0 ) ,
X 4 ( z ) = ν * ( z ) X 2 ( 0 ) + μ * ( z ) X 4 ( 0 ) ,
d z X 1 2 = i γ s X 1 * X 2 2 X 3 * + i 2 γ s X 1 * X 2 X 3 X 4 * + c. c . ,
d z X 2 2 = i 2 γ s X 1 ( X 2 * ) 2 X 3 + i 2 γ s X 1 X 2 * X 3 * X 4 + i γ s X 2 * X 3 2 X 4 * + c . c . ,
d z X 3 2 = i γ s X 1 * X 2 2 X 3 * + i 2 γ s X 1 X 2 * X 3 * X 4 + i 2 γ s X 2 ( X 3 * ) 2 X 4 + c . c . ,
d z X 4 2 = i 2 γ s X 1 * X 2 X 3 X 4 * + i γ S X 2 * X 3 2 X 4 * + c. c .
d z ( P 1 x + P 2 x + P 3 x + P 4 x ) = 0 .
d z X 1 2 = i γ c X 1 * Y 1 X 2 Y 2 * + c. c . ,
d z Y 1 2 = i γ c X 1 Y 1 * X 2 * Y 2 + c. c . ,
d z X 2 2 = i γ c X 1 Y 1 * X 2 * Y 2 + c. c . ,
d z Y 2 2 = i γ c X 1 * Y 1 X 2 Y 2 * + c. c .
d z ( P 1 x + P 2 x ) = 0 = d z ( P 1 y + P 2 y ) ,
d z ( P 1 x + P 1 y ) = 0 = d z ( P 2 x + P 2 y ) .
d z X 1 2 = i γ c X 1 * X 2 Y 2 Y 3 * + c. c . ,
d z X 2 2 = i γ c X 1 X 2 * Y 2 * Y 3 + c. c . ,
d z Y 2 2 = i γ c X 1 X 2 * Y 2 * Y 3 + c. c . ,
d z Y 3 2 = i γ c X 1 * X 2 Y 2 Y 3 * + c. c .
d z ( P 1 x + P 2 x ) = 0 = d z ( P 2 y + P 3 y ) .
d z X 1 2 = i γ c X 1 * Y 2 X 3 Y 4 * + c. c . ,
d z Y 2 2 = i γ c X 1 Y 2 * X 3 * Y 4 + c. c . ,
d z X 3 2 = i γ c X 1 Y 2 * X 3 * Y 4 + c. c . ,
d z Y 4 2 = i γ c X 1 * Y 2 X 3 Y 4 * + c. c .
d z ( P 1 x + P 3 x ) = 0 = d z ( P 2 y + P 4 y ) .

Metrics