Abstract

In this paper, Raman induced polarization dependent gain (PDG) in orthogonally pumped optical parametric amplifiers is investigated. Based on the Manakov Eqs., complete coupled Eqs. are derived and numerically solved. Analytical approximate solutions are derived. The simulation results show that in orthogonally pumped optical parametric amplifiers, the Raman effect between the pump and the signal contributes more prominently to the PDG than that induced by asymmetrical pump depletion.

© 2006 Optical Society of America

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  1. J. Hansryd, P. A. Anderson, M. Westland, 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]
  2. C. J. Mckinstric, S. Radic, and A. R. Chraplyvy. “Parametric amplifier driven by two pump waves,” IEEE J. Sel. Top. Quantum Electron. 8, 538–547 (2002).
    [CrossRef]
  3. R. M. Jopson and R. E. Tench, “Polarisation-independent phase conjugation of lightwave signals,” Electron. Lett. 29, 2216–2217 (1993).
    [CrossRef]
  4. K. Inoue, “Polarization independent wavelength conversion using fiber four-wave mixing with two orthogonal pump lights of different frequencies,” J. Lightwave Technol. 12, 1916–1920 (1994).
    [CrossRef]
  5. K. K. Y. Wong, M. E. Marhic, K. Uesaka, and L. G. Kazovsky. “Polarization-independent two-pump fiber optical parametric amplifier,” IEEE Photon. Technol. Lett. 14, 911–913 (2002).
    [CrossRef]
  6. S. Radic, C. J. McKinstrie, R. M. Jopson, Q. Lin, and G. P. Agrawal, “Record performance of a parametric amplifier constructed with highly-nonlinear fiber,” Electron. Lett. 39, 838–839 (2003).
    [CrossRef]
  7. T. Tanemura and K. Kikuchi, “Polarization-independent broad-band wavelength conversion using two-pump fiber optical parametric amplification without idler spectral broadening,” IEEE Photon. Technol. Lett. 15, 1573–1575 (2003).
    [CrossRef]
  8. 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]
  9. 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]
  10. M. E. Marhic, K. K. Y. Wong, M. C. Ho, and L. G Kazovsky, “92% pump depletion in a CW one-pump fiber OPA,” Opt. Lett. 26, 620–622 (2001).
    [CrossRef]
  11. K. Inoue and T. Mukai, “Signal wavelength dependence of gain saturation in a fiber optical parametric amplifier,” Opt. Lett. 26, 10–12 (2001).
    [CrossRef]
  12. J. M. C. Boggio, P. Dainese, F. Karlsson, and H. L. Fragnito, “Broadband efficient two-pump fiber optical parametric. amplifier,” IEEE Photon. Technol. Lett. 15, 1528–1530 (2003).
    [CrossRef]
  13. X. Zhang and B. F. Jorgensen, “Analysis of polarization-insensitive optical phase conjugation in a dispersion-shifted fiber,” Opt. Lett. 21, 791–793 (1996)
    [CrossRef] [PubMed]
  14. M.-C. Ho, K. Uesaka, M. E. Marhic, Y. Akasaka, and L. G. Kazovsky, “200-nm-bandwidth fiber optical amplifier combining parametric and Raman gain”, J. Lightwave Technol. 19, 977–982 (2001).
    [CrossRef]
  15. C. J. S. de Matos, D. A. Chestnut, and J. R. Taylor, “Continuous-wave 1664.7nm fiber source utilizing four-wave mixing and stimulated Raman scattering,” Applied Phys. Lett. 81, 1390–1392 (2002).
    [CrossRef]
  16. D. A. Chestnut, C. J. S. de Matos, and J. R. Taylor, “Raman-assisted fiber optical parametric amplifier and wavelength converter in highly nonlinear fiber,” J. Opt. Soc. Am. B 19, 1901–1904 (2002).
    [CrossRef]
  17. R. Stolen, “Parametric amplification and frequency conversion in optical fibers,” IEEE J. Quantum Electron. 18, 1062–1072 (1982).
    [CrossRef]
  18. R. W. Boyd, Nonlinear Optics (Academic Press, 1992).
  19. P. L. Voss and P. Kumar, “Raman-noise-induced noise-figure limit for chi χ(3) parametric amplifiers,” Opt. Lett. 29, 445 (2004).
    [CrossRef] [PubMed]
  20. R. Tang, P. L Voss, J. Lasri, P. Devgan, and P. Kumar, “Noise-figure limit of fiber-optical parametric amplifiers and wavelength converters: experimental investigation,” Opt. Lett. 29, 2372 (2004).
    [CrossRef] [PubMed]
  21. K. Inoue, K. Nakanishi, K. Oda, and H. Toba, “Crosstalk and power penalty due to fiber four-wave mixing in multi-channel transmissions,” J. Lightwave Technol. 12, 1423–1439 (1994).
    [CrossRef]
  22. R. W. Tkach, A. R. Chraplyvy, F. Forghieri, A. H. Gnauck, and R. M. Derosier, “Four-photon mixing and high-speed WDM systems,” J. Lightwave Technol. 13, 841–849 (1995).
    [CrossRef]
  23. F. A. Callegari, J. M. C. Boggio, and H. L. Fragnito,”Spurious four-wave mixing in two-pump fiberoptic parametric amplifiers,” IEEE Photon. Technol. Lett. 16, 434–436 (2004).
    [CrossRef]
  24. J. L. Blows and P. F. Hu, “Cross-talk-induced limitations of two-pump optical fiber parametric amplifiers,” J. Opt. Soc. Am. B 21, 989–995 (2004).
    [CrossRef]
  25. P. K. A. Wai, C. R. Menyuk, and H. H. Chen, “Stability of solitons in randomly varying birefringent fibers,” Opt. Lett. 16, 1231–1233 (1991).
    [CrossRef] [PubMed]
  26. S. G. Evanglides, L. F. Mollenauer, J. P. Gordon, and N. S. Bergano, “Polarization multiplexing with solitons,” J. Lightwave Technol. 10, 28–35 (1992).
    [CrossRef]
  27. P. K. A. Wai and C. R. Menyuk, “Polarization mode dispersion, decorrelation and diffusion in optical fibers with randomly varying birefringence,” J. Lightwave Technol. 14, 148–157 (1996).
    [CrossRef]
  28. T. I. Lakoba, “Concerning the equations governing nonlinear pulse propagation in randomly birefringent fibers,” J. Opt. Soc. Am. B 13, 2006–2011 (1996).
    [CrossRef]
  29. M. E. Marhic, K. K. Y. Wong, and L. G. Kazovsky,”Parametric amplification in optical fibers with random birefringence,” OFC 2004  1, 23–27 (2004).
  30. R. Stolen,“Polarization effects in fiber Raman and Brillouin lasers,” IEEE J. Quantum Electron. 15, 1157–1160 (1979).
    [CrossRef]
  31. J. Bromage, “Raman amplification for fiber communication systems,” J. Lightwave Technol. 22, 79–93 (2004).
    [CrossRef]

2004 (7)

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]

P. L. Voss and P. Kumar, “Raman-noise-induced noise-figure limit for chi χ(3) parametric amplifiers,” Opt. Lett. 29, 445 (2004).
[CrossRef] [PubMed]

R. Tang, P. L Voss, J. Lasri, P. Devgan, and P. Kumar, “Noise-figure limit of fiber-optical parametric amplifiers and wavelength converters: experimental investigation,” Opt. Lett. 29, 2372 (2004).
[CrossRef] [PubMed]

F. A. Callegari, J. M. C. Boggio, and H. L. Fragnito,”Spurious four-wave mixing in two-pump fiberoptic parametric amplifiers,” IEEE Photon. Technol. Lett. 16, 434–436 (2004).
[CrossRef]

J. L. Blows and P. F. Hu, “Cross-talk-induced limitations of two-pump optical fiber parametric amplifiers,” J. Opt. Soc. Am. B 21, 989–995 (2004).
[CrossRef]

M. E. Marhic, K. K. Y. Wong, and L. G. Kazovsky,”Parametric amplification in optical fibers with random birefringence,” OFC 2004  1, 23–27 (2004).

J. Bromage, “Raman amplification for fiber communication systems,” J. Lightwave Technol. 22, 79–93 (2004).
[CrossRef]

2003 (4)

J. M. C. Boggio, P. Dainese, F. Karlsson, and H. L. Fragnito, “Broadband efficient two-pump fiber optical parametric. amplifier,” IEEE Photon. Technol. Lett. 15, 1528–1530 (2003).
[CrossRef]

S. Radic, C. J. McKinstrie, R. M. Jopson, Q. Lin, and G. P. Agrawal, “Record performance of a parametric amplifier constructed with highly-nonlinear fiber,” Electron. Lett. 39, 838–839 (2003).
[CrossRef]

T. Tanemura and K. Kikuchi, “Polarization-independent broad-band wavelength conversion using two-pump fiber optical parametric amplification without idler spectral broadening,” IEEE Photon. Technol. Lett. 15, 1573–1575 (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]

2002 (5)

J. Hansryd, P. A. Anderson, M. Westland, 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]

C. J. Mckinstric, S. Radic, and A. R. Chraplyvy. “Parametric amplifier driven by two pump waves,” IEEE J. Sel. Top. Quantum Electron. 8, 538–547 (2002).
[CrossRef]

K. K. Y. Wong, M. E. Marhic, K. Uesaka, and L. G. Kazovsky. “Polarization-independent two-pump fiber optical parametric amplifier,” IEEE Photon. Technol. Lett. 14, 911–913 (2002).
[CrossRef]

C. J. S. de Matos, D. A. Chestnut, and J. R. Taylor, “Continuous-wave 1664.7nm fiber source utilizing four-wave mixing and stimulated Raman scattering,” Applied Phys. Lett. 81, 1390–1392 (2002).
[CrossRef]

D. A. Chestnut, C. J. S. de Matos, and J. R. Taylor, “Raman-assisted fiber optical parametric amplifier and wavelength converter in highly nonlinear fiber,” J. Opt. Soc. Am. B 19, 1901–1904 (2002).
[CrossRef]

2001 (3)

1996 (3)

1995 (1)

R. W. Tkach, A. R. Chraplyvy, F. Forghieri, A. H. Gnauck, and R. M. Derosier, “Four-photon mixing and high-speed WDM systems,” J. Lightwave Technol. 13, 841–849 (1995).
[CrossRef]

1994 (2)

K. Inoue, K. Nakanishi, K. Oda, and H. Toba, “Crosstalk and power penalty due to fiber four-wave mixing in multi-channel transmissions,” J. Lightwave Technol. 12, 1423–1439 (1994).
[CrossRef]

K. Inoue, “Polarization independent wavelength conversion using fiber four-wave mixing with two orthogonal pump lights of different frequencies,” J. Lightwave Technol. 12, 1916–1920 (1994).
[CrossRef]

1993 (1)

R. M. Jopson and R. E. Tench, “Polarisation-independent phase conjugation of lightwave signals,” Electron. Lett. 29, 2216–2217 (1993).
[CrossRef]

1992 (1)

S. G. Evanglides, L. F. Mollenauer, J. P. Gordon, and N. S. Bergano, “Polarization multiplexing with solitons,” J. Lightwave Technol. 10, 28–35 (1992).
[CrossRef]

1991 (1)

1982 (1)

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

1979 (1)

R. Stolen,“Polarization effects in fiber Raman and Brillouin lasers,” IEEE J. Quantum Electron. 15, 1157–1160 (1979).
[CrossRef]

Agrawal, G. P.

S. Radic, C. J. McKinstrie, R. M. Jopson, Q. Lin, and G. P. Agrawal, “Record performance of a parametric amplifier constructed with highly-nonlinear fiber,” Electron. Lett. 39, 838–839 (2003).
[CrossRef]

Akasaka, Y.

Anderson, P. A.

J. Hansryd, P. A. Anderson, M. Westland, 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]

Bergano, N. S.

S. G. Evanglides, L. F. Mollenauer, J. P. Gordon, and N. S. Bergano, “Polarization multiplexing with solitons,” J. Lightwave Technol. 10, 28–35 (1992).
[CrossRef]

Blows, J. L.

Boggio, J. M. C.

F. A. Callegari, J. M. C. Boggio, and H. L. Fragnito,”Spurious four-wave mixing in two-pump fiberoptic parametric amplifiers,” IEEE Photon. Technol. Lett. 16, 434–436 (2004).
[CrossRef]

J. M. C. Boggio, P. Dainese, F. Karlsson, and H. L. Fragnito, “Broadband efficient two-pump fiber optical parametric. amplifier,” IEEE Photon. Technol. Lett. 15, 1528–1530 (2003).
[CrossRef]

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic Press, 1992).

Bromage, J.

Callegari, F. A.

F. A. Callegari, J. M. C. Boggio, and H. L. Fragnito,”Spurious four-wave mixing in two-pump fiberoptic parametric amplifiers,” IEEE Photon. Technol. Lett. 16, 434–436 (2004).
[CrossRef]

Chen, H. H.

Chestnut, D. A.

C. J. S. de Matos, D. A. Chestnut, and J. R. Taylor, “Continuous-wave 1664.7nm fiber source utilizing four-wave mixing and stimulated Raman scattering,” Applied Phys. Lett. 81, 1390–1392 (2002).
[CrossRef]

D. A. Chestnut, C. J. S. de Matos, and J. R. Taylor, “Raman-assisted fiber optical parametric amplifier and wavelength converter in highly nonlinear fiber,” J. Opt. Soc. Am. B 19, 1901–1904 (2002).
[CrossRef]

Chraplyvy, A. R.

C. J. Mckinstric, S. Radic, and A. R. Chraplyvy. “Parametric amplifier driven by two pump waves,” IEEE J. Sel. Top. Quantum Electron. 8, 538–547 (2002).
[CrossRef]

R. W. Tkach, A. R. Chraplyvy, F. Forghieri, A. H. Gnauck, and R. M. Derosier, “Four-photon mixing and high-speed WDM systems,” J. Lightwave Technol. 13, 841–849 (1995).
[CrossRef]

Dainese, P.

J. M. C. Boggio, P. Dainese, F. Karlsson, and H. L. Fragnito, “Broadband efficient two-pump fiber optical parametric. amplifier,” IEEE Photon. Technol. Lett. 15, 1528–1530 (2003).
[CrossRef]

de Matos, C. J. S.

D. A. Chestnut, C. J. S. de Matos, and J. R. Taylor, “Raman-assisted fiber optical parametric amplifier and wavelength converter in highly nonlinear fiber,” J. Opt. Soc. Am. B 19, 1901–1904 (2002).
[CrossRef]

C. J. S. de Matos, D. A. Chestnut, and J. R. Taylor, “Continuous-wave 1664.7nm fiber source utilizing four-wave mixing and stimulated Raman scattering,” Applied Phys. Lett. 81, 1390–1392 (2002).
[CrossRef]

Derosier, R. M.

R. W. Tkach, A. R. Chraplyvy, F. Forghieri, A. H. Gnauck, and R. M. Derosier, “Four-photon mixing and high-speed WDM systems,” J. Lightwave Technol. 13, 841–849 (1995).
[CrossRef]

Devgan, P.

Evanglides, S. G.

S. G. Evanglides, L. F. Mollenauer, J. P. Gordon, and N. S. Bergano, “Polarization multiplexing with solitons,” J. Lightwave Technol. 10, 28–35 (1992).
[CrossRef]

Forghieri, F.

R. W. Tkach, A. R. Chraplyvy, F. Forghieri, A. H. Gnauck, and R. M. Derosier, “Four-photon mixing and high-speed WDM systems,” J. Lightwave Technol. 13, 841–849 (1995).
[CrossRef]

Fragnito, H. L.

F. A. Callegari, J. M. C. Boggio, and H. L. Fragnito,”Spurious four-wave mixing in two-pump fiberoptic parametric amplifiers,” IEEE Photon. Technol. Lett. 16, 434–436 (2004).
[CrossRef]

J. M. C. Boggio, P. Dainese, F. Karlsson, and H. L. Fragnito, “Broadband efficient two-pump fiber optical parametric. amplifier,” IEEE Photon. Technol. Lett. 15, 1528–1530 (2003).
[CrossRef]

Gnauck, A. H.

R. W. Tkach, A. R. Chraplyvy, F. Forghieri, A. H. Gnauck, and R. M. Derosier, “Four-photon mixing and high-speed WDM systems,” J. Lightwave Technol. 13, 841–849 (1995).
[CrossRef]

Gordon, J. P.

S. G. Evanglides, L. F. Mollenauer, J. P. Gordon, and N. S. Bergano, “Polarization multiplexing with solitons,” J. Lightwave Technol. 10, 28–35 (1992).
[CrossRef]

Hansryd, J.

J. Hansryd, P. A. Anderson, M. Westland, 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]

Hedekvist, P.-O.

J. Hansryd, P. A. Anderson, M. Westland, 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]

Ho, M. C.

Ho, M.-C.

Hu, P. F.

Inoue, K.

K. Inoue and T. Mukai, “Signal wavelength dependence of gain saturation in a fiber optical parametric amplifier,” Opt. Lett. 26, 10–12 (2001).
[CrossRef]

K. Inoue, “Polarization independent wavelength conversion using fiber four-wave mixing with two orthogonal pump lights of different frequencies,” J. Lightwave Technol. 12, 1916–1920 (1994).
[CrossRef]

K. Inoue, K. Nakanishi, K. Oda, and H. Toba, “Crosstalk and power penalty due to fiber four-wave mixing in multi-channel transmissions,” J. Lightwave Technol. 12, 1423–1439 (1994).
[CrossRef]

Jopson, R. M.

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, C. J. McKinstrie, R. M. Jopson, Q. Lin, and G. P. Agrawal, “Record performance of a parametric amplifier constructed with highly-nonlinear fiber,” Electron. Lett. 39, 838–839 (2003).
[CrossRef]

R. M. Jopson and R. E. Tench, “Polarisation-independent phase conjugation of lightwave signals,” Electron. Lett. 29, 2216–2217 (1993).
[CrossRef]

Jorgensen, B. F.

Kanaev, A. V.

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]

Karlsson, F.

J. M. C. Boggio, P. Dainese, F. Karlsson, and H. L. Fragnito, “Broadband efficient two-pump fiber optical parametric. amplifier,” IEEE Photon. Technol. Lett. 15, 1528–1530 (2003).
[CrossRef]

Kazovsky, L. G

Kazovsky, L. G.

M. E. Marhic, K. K. Y. Wong, and L. G. Kazovsky,”Parametric amplification in optical fibers with random birefringence,” OFC 2004  1, 23–27 (2004).

K. K. Y. Wong, M. E. Marhic, K. Uesaka, and L. G. Kazovsky. “Polarization-independent two-pump fiber optical parametric amplifier,” IEEE Photon. Technol. Lett. 14, 911–913 (2002).
[CrossRef]

M.-C. Ho, K. Uesaka, M. E. Marhic, Y. Akasaka, and L. G. Kazovsky, “200-nm-bandwidth fiber optical amplifier combining parametric and Raman gain”, J. Lightwave Technol. 19, 977–982 (2001).
[CrossRef]

Kikuchi, K.

T. Tanemura and K. Kikuchi, “Polarization-independent broad-band wavelength conversion using two-pump fiber optical parametric amplification without idler spectral broadening,” IEEE Photon. Technol. Lett. 15, 1573–1575 (2003).
[CrossRef]

Kogelnik, H.

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]

Kumar, P.

Lakoba, T. I.

Lasri, J.

Li, J.

J. Hansryd, P. A. Anderson, M. Westland, 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]

Lin, Q.

S. Radic, C. J. McKinstrie, R. M. Jopson, Q. Lin, and G. P. Agrawal, “Record performance of a parametric amplifier constructed with highly-nonlinear fiber,” Electron. Lett. 39, 838–839 (2003).
[CrossRef]

Marhic, M. E.

M. E. Marhic, K. K. Y. Wong, and L. G. Kazovsky,”Parametric amplification in optical fibers with random birefringence,” OFC 2004  1, 23–27 (2004).

K. K. Y. Wong, M. E. Marhic, K. Uesaka, and L. G. Kazovsky. “Polarization-independent two-pump fiber optical parametric amplifier,” IEEE Photon. Technol. Lett. 14, 911–913 (2002).
[CrossRef]

M. E. Marhic, K. K. Y. Wong, M. C. Ho, and L. G Kazovsky, “92% pump depletion in a CW one-pump fiber OPA,” Opt. Lett. 26, 620–622 (2001).
[CrossRef]

M.-C. Ho, K. Uesaka, M. E. Marhic, Y. Akasaka, and L. G. Kazovsky, “200-nm-bandwidth fiber optical amplifier combining parametric and Raman gain”, J. Lightwave Technol. 19, 977–982 (2001).
[CrossRef]

Mckinstric, C. J.

C. J. Mckinstric, S. Radic, and A. R. Chraplyvy. “Parametric amplifier driven by two pump waves,” IEEE J. Sel. Top. Quantum Electron. 8, 538–547 (2002).
[CrossRef]

McKinstrie, C. J.

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, C. J. McKinstrie, R. M. Jopson, Q. Lin, and G. P. Agrawal, “Record performance of a parametric amplifier constructed with highly-nonlinear fiber,” Electron. Lett. 39, 838–839 (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]

Menyuk, C. R.

P. K. A. Wai and C. R. Menyuk, “Polarization mode dispersion, decorrelation and diffusion in optical fibers with randomly varying birefringence,” J. Lightwave Technol. 14, 148–157 (1996).
[CrossRef]

P. K. A. Wai, C. R. Menyuk, and H. H. Chen, “Stability of solitons in randomly varying birefringent fibers,” Opt. Lett. 16, 1231–1233 (1991).
[CrossRef] [PubMed]

Mollenauer, L. F.

S. G. Evanglides, L. F. Mollenauer, J. P. Gordon, and N. S. Bergano, “Polarization multiplexing with solitons,” J. Lightwave Technol. 10, 28–35 (1992).
[CrossRef]

Mukai, T.

Nakanishi, K.

K. Inoue, K. Nakanishi, K. Oda, and H. Toba, “Crosstalk and power penalty due to fiber four-wave mixing in multi-channel transmissions,” J. Lightwave Technol. 12, 1423–1439 (1994).
[CrossRef]

Oda, K.

K. Inoue, K. Nakanishi, K. Oda, and H. Toba, “Crosstalk and power penalty due to fiber four-wave mixing in multi-channel transmissions,” J. Lightwave Technol. 12, 1423–1439 (1994).
[CrossRef]

Radic, S.

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, 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]

S. Radic, C. J. McKinstrie, R. M. Jopson, Q. Lin, and G. P. Agrawal, “Record performance of a parametric amplifier constructed with highly-nonlinear fiber,” Electron. Lett. 39, 838–839 (2003).
[CrossRef]

C. J. Mckinstric, S. Radic, and A. R. Chraplyvy. “Parametric amplifier driven by two pump waves,” IEEE J. Sel. Top. Quantum Electron. 8, 538–547 (2002).
[CrossRef]

Stolen, R.

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

R. Stolen,“Polarization effects in fiber Raman and Brillouin lasers,” IEEE J. Quantum Electron. 15, 1157–1160 (1979).
[CrossRef]

Tanemura, T.

T. Tanemura and K. Kikuchi, “Polarization-independent broad-band wavelength conversion using two-pump fiber optical parametric amplification without idler spectral broadening,” IEEE Photon. Technol. Lett. 15, 1573–1575 (2003).
[CrossRef]

Tang, R.

Taylor, J. R.

D. A. Chestnut, C. J. S. de Matos, and J. R. Taylor, “Raman-assisted fiber optical parametric amplifier and wavelength converter in highly nonlinear fiber,” J. Opt. Soc. Am. B 19, 1901–1904 (2002).
[CrossRef]

C. J. S. de Matos, D. A. Chestnut, and J. R. Taylor, “Continuous-wave 1664.7nm fiber source utilizing four-wave mixing and stimulated Raman scattering,” Applied Phys. Lett. 81, 1390–1392 (2002).
[CrossRef]

Tench, R. E.

R. M. Jopson and R. E. Tench, “Polarisation-independent phase conjugation of lightwave signals,” Electron. Lett. 29, 2216–2217 (1993).
[CrossRef]

Tkach, R. W.

R. W. Tkach, A. R. Chraplyvy, F. Forghieri, A. H. Gnauck, and R. M. Derosier, “Four-photon mixing and high-speed WDM systems,” J. Lightwave Technol. 13, 841–849 (1995).
[CrossRef]

Toba, H.

K. Inoue, K. Nakanishi, K. Oda, and H. Toba, “Crosstalk and power penalty due to fiber four-wave mixing in multi-channel transmissions,” J. Lightwave Technol. 12, 1423–1439 (1994).
[CrossRef]

Uesaka, K.

K. K. Y. Wong, M. E. Marhic, K. Uesaka, and L. G. Kazovsky. “Polarization-independent two-pump fiber optical parametric amplifier,” IEEE Photon. Technol. Lett. 14, 911–913 (2002).
[CrossRef]

M.-C. Ho, K. Uesaka, M. E. Marhic, Y. Akasaka, and L. G. Kazovsky, “200-nm-bandwidth fiber optical amplifier combining parametric and Raman gain”, J. Lightwave Technol. 19, 977–982 (2001).
[CrossRef]

Voss, P. L

Voss, P. L.

Wai, P. K. A.

P. K. A. Wai and C. R. Menyuk, “Polarization mode dispersion, decorrelation and diffusion in optical fibers with randomly varying birefringence,” J. Lightwave Technol. 14, 148–157 (1996).
[CrossRef]

P. K. A. Wai, C. R. Menyuk, and H. H. Chen, “Stability of solitons in randomly varying birefringent fibers,” Opt. Lett. 16, 1231–1233 (1991).
[CrossRef] [PubMed]

Westland, M.

J. Hansryd, P. A. Anderson, M. Westland, 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, K. K. Y.

M. E. Marhic, K. K. Y. Wong, and L. G. Kazovsky,”Parametric amplification in optical fibers with random birefringence,” OFC 2004  1, 23–27 (2004).

K. K. Y. Wong, M. E. Marhic, K. Uesaka, and L. G. Kazovsky. “Polarization-independent two-pump fiber optical parametric amplifier,” IEEE Photon. Technol. Lett. 14, 911–913 (2002).
[CrossRef]

M. E. Marhic, K. K. Y. Wong, M. C. Ho, and L. G Kazovsky, “92% pump depletion in a CW one-pump fiber OPA,” Opt. Lett. 26, 620–622 (2001).
[CrossRef]

Xie, C.

Zhang, X.

Applied Phys. Lett. (1)

C. J. S. de Matos, D. A. Chestnut, and J. R. Taylor, “Continuous-wave 1664.7nm fiber source utilizing four-wave mixing and stimulated Raman scattering,” Applied Phys. Lett. 81, 1390–1392 (2002).
[CrossRef]

Electron. Lett. (2)

R. M. Jopson and R. E. Tench, “Polarisation-independent phase conjugation of lightwave signals,” Electron. Lett. 29, 2216–2217 (1993).
[CrossRef]

S. Radic, C. J. McKinstrie, R. M. Jopson, Q. Lin, and G. P. Agrawal, “Record performance of a parametric amplifier constructed with highly-nonlinear fiber,” Electron. Lett. 39, 838–839 (2003).
[CrossRef]

IEEE J. Quantum Electron. (2)

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

R. Stolen,“Polarization effects in fiber Raman and Brillouin lasers,” IEEE J. Quantum Electron. 15, 1157–1160 (1979).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (2)

J. Hansryd, P. A. Anderson, M. Westland, 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]

C. J. Mckinstric, S. Radic, and A. R. Chraplyvy. “Parametric amplifier driven by two pump waves,” IEEE J. Sel. Top. Quantum Electron. 8, 538–547 (2002).
[CrossRef]

IEEE Photon. Technol. Lett. (4)

T. Tanemura and K. Kikuchi, “Polarization-independent broad-band wavelength conversion using two-pump fiber optical parametric amplification without idler spectral broadening,” IEEE Photon. Technol. Lett. 15, 1573–1575 (2003).
[CrossRef]

J. M. C. Boggio, P. Dainese, F. Karlsson, and H. L. Fragnito, “Broadband efficient two-pump fiber optical parametric. amplifier,” IEEE Photon. Technol. Lett. 15, 1528–1530 (2003).
[CrossRef]

K. K. Y. Wong, M. E. Marhic, K. Uesaka, and L. G. Kazovsky. “Polarization-independent two-pump fiber optical parametric amplifier,” IEEE Photon. Technol. Lett. 14, 911–913 (2002).
[CrossRef]

F. A. Callegari, J. M. C. Boggio, and H. L. Fragnito,”Spurious four-wave mixing in two-pump fiberoptic parametric amplifiers,” IEEE Photon. Technol. Lett. 16, 434–436 (2004).
[CrossRef]

J. Lightwave Technol. (7)

J. Bromage, “Raman amplification for fiber communication systems,” J. Lightwave Technol. 22, 79–93 (2004).
[CrossRef]

K. Inoue, K. Nakanishi, K. Oda, and H. Toba, “Crosstalk and power penalty due to fiber four-wave mixing in multi-channel transmissions,” J. Lightwave Technol. 12, 1423–1439 (1994).
[CrossRef]

R. W. Tkach, A. R. Chraplyvy, F. Forghieri, A. H. Gnauck, and R. M. Derosier, “Four-photon mixing and high-speed WDM systems,” J. Lightwave Technol. 13, 841–849 (1995).
[CrossRef]

S. G. Evanglides, L. F. Mollenauer, J. P. Gordon, and N. S. Bergano, “Polarization multiplexing with solitons,” J. Lightwave Technol. 10, 28–35 (1992).
[CrossRef]

P. K. A. Wai and C. R. Menyuk, “Polarization mode dispersion, decorrelation and diffusion in optical fibers with randomly varying birefringence,” J. Lightwave Technol. 14, 148–157 (1996).
[CrossRef]

M.-C. Ho, K. Uesaka, M. E. Marhic, Y. Akasaka, and L. G. Kazovsky, “200-nm-bandwidth fiber optical amplifier combining parametric and Raman gain”, J. Lightwave Technol. 19, 977–982 (2001).
[CrossRef]

K. Inoue, “Polarization independent wavelength conversion using fiber four-wave mixing with two orthogonal pump lights of different frequencies,” J. Lightwave Technol. 12, 1916–1920 (1994).
[CrossRef]

J. Opt. Soc. Am. B (4)

Opt. Express. (1)

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]

Opt. Lett. (6)

Other (2)

M. E. Marhic, K. K. Y. Wong, and L. G. Kazovsky,”Parametric amplification in optical fibers with random birefringence,” OFC 2004  1, 23–27 (2004).

R. W. Boyd, Nonlinear Optics (Academic Press, 1992).

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Figures (6)

Fig. 1.
Fig. 1.

Relationship between the different polarization elements, ω0 is zeros dispersion wavelength

Fig. 2.
Fig. 2.

Gain spectra with/without Raman effect

Fig. 3.
Fig. 3.

Polarization dependent gain with/without Raman effect

Fig. 4.
Fig. 4.

Illustration of Raman process in orthogonally pumped OPA

Fig. 5.
Fig. 5.

PDG versus nonlinear coefficient

Fig. 6.
Fig. 6.

PDG versus dispersion slope

Equations (17)

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A ix z = ( jR ( A ix 2 + 2 j = 1 , j 1 4 A jx 2 + j = 1 4 A jy 2 ) + 1 2 j = 1 , j 1 4 ( g v j v i A jx 2 + g v j v i A jy 2 ) ) A ix + jR ( A 3 x A 4 y A 3 i , y * + A 4 x A 3 y A 3 i , y ) exp ( j Δ βz ) i = 1,2
A iy z = ( jR ( A iy 2 + 2 j = 1 , j 1 4 A jy 2 + j = 1 4 A jx 2 ) + 1 2 j = 1 , j 1 4 ( g v j v i A jy 2 + g v j v i A jx 2 ) ) A iy + jR ( A 3 x A 4 y A 3 i , x * + A 4 x A 3 y A 3 i , x ) exp ( j Δ βz )
A ix z = ( jR ( A ix 2 + 2 j = 1 , j 1 4 A jx 2 + j = 1 4 A jy 2 ) + 1 2 j = 1 , j 1 4 ( g v j v i A jx 2 + g v j v i A jy 2 ) ) A ix + jR ( A 1 x A 2 y A 7 i , y * + A 2 x A 1 y A 7 i , y ) exp ( j Δ βz ) i = 1,2
A iy z = ( jR ( A iy 2 + 2 j = 1 , j 1 4 A jy 2 + j = 1 4 A jx 2 ) + 1 2 j = 1 , j 1 4 ( g v j v i A jy 2 + g v j v i A jx 2 ) ) A iy + jR ( A 1 x A 2 y A 7 i , x * + A 2 x A 1 y A 7 i , x ) exp ( j Δ βz )
g ∥/⊥ ( v i , v j ) = { g ∥/⊥i ( v j v i ) A eff ( v i < v j ) ( v i v j ) g ∥/⊥i ( v i v j ) A eff ( v i > v j ) ,
A 1 x z = jR ( A 1 x 2 + A 1 y 2 ) A 1 x
A 2 y z = jR ( A 2 y 2 + A 1 x 2 ) A 2 y i = 3,4
A ix z = jR ( 2 A 1 x 2 + A 2 y 2 ) A ix + 1 2 [ g ( ω 1 , ω 3 ) A 1 x 2 + g ( ω 2 , ω 3 ) A 2 y 2 ] A ix + jR ( A 1 x A 2 y A 7 i , y * ) exp ( j Δ βz )
A iy z = ( 2 A 2 y 2 + A 1 x 2 ) A iy + 1 2 [ g ( ω 2 , ω 3 ) A 2 y 2 + g ( ω 1 , ω 3 ) A 1 x 2 ] A iy + jR ( A 1 x A 2 y A 7 i , x * ) exp ( j Δ βz )
A 3 x ( L ) = exp ( M 3 x L ) exp ( j κ x 2 L ) [ cosh ( g x L ) + j κ x 2 g x sinh ( g x L ) ] A 3 x ( 0 )
A 4 y ( L ) = exp ( M 4 y L ) exp ( j κ x 2 L ) P 1 x P 2 y g x * sinh ( g x L ) * A 3 x ( 0 )
M 3 x = jR ( 2 P 1 x + P 2 y ) + 1 2 g ( ω 1 , ω 3 ) P 1 x + 1 2 g ( ω 2 , ω 3 ) P 2 y
M 4 y = jR ( 2 P 2 y + P 1 x ) + 1 2 g ( ω 2 , ω 4 ) P 2 y + 1 2 g ( ω 1 , ω 4 ) P 1 x
κ x = Δ β + R ( P 1 x + P 2 y ) + j [ 1 2 g ( ω 2 , ω 3 ) P 2 y + 1 2 g ( ω 1 , ω 3 ) P 1 x 1 2 g ( ω 1 , ω 3 ) P 1 x 1 2 g ( ω 2 , ω 3 ) P 2 y ]
κ y = Δ β + R ( P 1 x + P 2 y ) + j [ 1 2 g ( ω 2 , ω 4 ) P 2 y + 1 2 g ( ω 1 , ω 4 ) P 1 x 1 2 g ( ω 1 , ω 4 ) P 1 x 1 2 g ( ω 2 , ω 4 ) P 2 y ]
g x 2 = R 2 P 1 x P 2 y ( κ x 2 ) 2
g y 2 = R 2 P 1 x P 2 y ( κ y 2 ) 2

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