Abstract

We present a vector theory of four-wave mixing in optical fibers and use it to discuss the effect of polarization-mode dispersion (PMD) on the performance of parametric amplifiers and wavelength converters. We show that PMD distorts the gain spectrum and makes it less uniform than that expected in the absence of residual birefringence. PMD also induces large fluctuations in the amplified or wavelength-converted signal.

© 2004 Optical Society of America

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References

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  1. J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. O. Hedekvist, IEEE J. Sel. Top. Quantum Electron. 8, 506 (2002).
    [CrossRef]
  2. M. N. Islam and Ö. Boyraz, IEEE J. Sel. Top. Quantum Electron. 8, 527 (2002).
    [CrossRef]
  3. S. Radic, C. McKinstrie, and R. Jopson, Opt. Fiber Technol. Mater. Devices Syst. 9, 7 (2003).
    [CrossRef]
  4. G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, New York, 2001).
  5. J. P. Gordon and H. Kogelnik, Proc. Natl. Acad. Sci. USA 97, 4541 (2000).
    [CrossRef]
  6. K. Inoue, IEEE J. Quantum Electron. 28, 883 (1992).
    [CrossRef]
  7. P. O. Hedekvist, M. Karlsson, and P. A. Andrekson, IEEE Photon. Technol. Lett. 8, 776 (1996).
    [CrossRef]
  8. O. Aso, S. Arai, T. Yagi, M. Tadakuma, Y. Suzuki, and S. Namiki, IEICE Trans. Electron. E83-C, 816 (2000).
  9. A. Galtarossa, L. Palmieri, M. Schiano, and T. Tambosso, Opt. Lett. 25, 384 (2000).
    [CrossRef]
  10. A. Galtarossa, L. Palmieri, M. Schiano, and T. Tambosso, Opt. Lett. 26, 962 (2001).
    [CrossRef]
  11. P. K. A. Wai and C. R. Menyuk, J. Lightwave Technol. 14, 148 (1996).
    [CrossRef]
  12. Q. Lin and G. P. Agrawal, J. Opt. Soc. Am. B 20, 1616 (2003).
    [CrossRef]

2003 (2)

S. Radic, C. McKinstrie, and R. Jopson, Opt. Fiber Technol. Mater. Devices Syst. 9, 7 (2003).
[CrossRef]

Q. Lin and G. P. Agrawal, J. Opt. Soc. Am. B 20, 1616 (2003).
[CrossRef]

2002 (2)

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. O. Hedekvist, IEEE J. Sel. Top. Quantum Electron. 8, 506 (2002).
[CrossRef]

M. N. Islam and Ö. Boyraz, IEEE J. Sel. Top. Quantum Electron. 8, 527 (2002).
[CrossRef]

2001 (1)

2000 (3)

J. P. Gordon and H. Kogelnik, Proc. Natl. Acad. Sci. USA 97, 4541 (2000).
[CrossRef]

O. Aso, S. Arai, T. Yagi, M. Tadakuma, Y. Suzuki, and S. Namiki, IEICE Trans. Electron. E83-C, 816 (2000).

A. Galtarossa, L. Palmieri, M. Schiano, and T. Tambosso, Opt. Lett. 25, 384 (2000).
[CrossRef]

1996 (2)

P. O. Hedekvist, M. Karlsson, and P. A. Andrekson, IEEE Photon. Technol. Lett. 8, 776 (1996).
[CrossRef]

P. K. A. Wai and C. R. Menyuk, J. Lightwave Technol. 14, 148 (1996).
[CrossRef]

1992 (1)

K. Inoue, IEEE J. Quantum Electron. 28, 883 (1992).
[CrossRef]

Agrawal, G. P.

Q. Lin and G. P. Agrawal, J. Opt. Soc. Am. B 20, 1616 (2003).
[CrossRef]

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, New York, 2001).

Andrekson, P. A.

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. O. Hedekvist, IEEE J. Sel. Top. Quantum Electron. 8, 506 (2002).
[CrossRef]

P. O. Hedekvist, M. Karlsson, and P. A. Andrekson, IEEE Photon. Technol. Lett. 8, 776 (1996).
[CrossRef]

Arai, S.

O. Aso, S. Arai, T. Yagi, M. Tadakuma, Y. Suzuki, and S. Namiki, IEICE Trans. Electron. E83-C, 816 (2000).

Aso, O.

O. Aso, S. Arai, T. Yagi, M. Tadakuma, Y. Suzuki, and S. Namiki, IEICE Trans. Electron. E83-C, 816 (2000).

Boyraz, Ö.

M. N. Islam and Ö. Boyraz, IEEE J. Sel. Top. Quantum Electron. 8, 527 (2002).
[CrossRef]

Galtarossa, A.

Gordon, J. P.

J. P. Gordon and H. Kogelnik, Proc. Natl. Acad. Sci. USA 97, 4541 (2000).
[CrossRef]

Hansryd, J.

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. O. Hedekvist, IEEE J. Sel. Top. Quantum Electron. 8, 506 (2002).
[CrossRef]

Hedekvist, P. O.

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. O. Hedekvist, IEEE J. Sel. Top. Quantum Electron. 8, 506 (2002).
[CrossRef]

P. O. Hedekvist, M. Karlsson, and P. A. Andrekson, IEEE Photon. Technol. Lett. 8, 776 (1996).
[CrossRef]

Inoue, K.

K. Inoue, IEEE J. Quantum Electron. 28, 883 (1992).
[CrossRef]

Islam, M. N.

M. N. Islam and Ö. Boyraz, IEEE J. Sel. Top. Quantum Electron. 8, 527 (2002).
[CrossRef]

Jopson, R.

S. Radic, C. McKinstrie, and R. Jopson, Opt. Fiber Technol. Mater. Devices Syst. 9, 7 (2003).
[CrossRef]

Karlsson, M.

P. O. Hedekvist, M. Karlsson, and P. A. Andrekson, IEEE Photon. Technol. Lett. 8, 776 (1996).
[CrossRef]

Kogelnik, H.

J. P. Gordon and H. Kogelnik, Proc. Natl. Acad. Sci. USA 97, 4541 (2000).
[CrossRef]

Li, J.

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. O. Hedekvist, IEEE J. Sel. Top. Quantum Electron. 8, 506 (2002).
[CrossRef]

Lin, Q.

McKinstrie, C.

S. Radic, C. McKinstrie, and R. Jopson, Opt. Fiber Technol. Mater. Devices Syst. 9, 7 (2003).
[CrossRef]

Menyuk, C. R.

P. K. A. Wai and C. R. Menyuk, J. Lightwave Technol. 14, 148 (1996).
[CrossRef]

Namiki, S.

O. Aso, S. Arai, T. Yagi, M. Tadakuma, Y. Suzuki, and S. Namiki, IEICE Trans. Electron. E83-C, 816 (2000).

Palmieri, L.

Radic, S.

S. Radic, C. McKinstrie, and R. Jopson, Opt. Fiber Technol. Mater. Devices Syst. 9, 7 (2003).
[CrossRef]

Schiano, M.

Suzuki, Y.

O. Aso, S. Arai, T. Yagi, M. Tadakuma, Y. Suzuki, and S. Namiki, IEICE Trans. Electron. E83-C, 816 (2000).

Tadakuma, M.

O. Aso, S. Arai, T. Yagi, M. Tadakuma, Y. Suzuki, and S. Namiki, IEICE Trans. Electron. E83-C, 816 (2000).

Tambosso, T.

Wai, P. K. A.

P. K. A. Wai and C. R. Menyuk, J. Lightwave Technol. 14, 148 (1996).
[CrossRef]

Westlund, M.

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. O. Hedekvist, IEEE J. Sel. Top. Quantum Electron. 8, 506 (2002).
[CrossRef]

Yagi, T.

O. Aso, S. Arai, T. Yagi, M. Tadakuma, Y. Suzuki, and S. Namiki, IEICE Trans. Electron. E83-C, 816 (2000).

IEEE J. Quantum Electron. (1)

K. Inoue, IEEE J. Quantum Electron. 28, 883 (1992).
[CrossRef]

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

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. O. Hedekvist, IEEE J. Sel. Top. Quantum Electron. 8, 506 (2002).
[CrossRef]

M. N. Islam and Ö. Boyraz, IEEE J. Sel. Top. Quantum Electron. 8, 527 (2002).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

P. O. Hedekvist, M. Karlsson, and P. A. Andrekson, IEEE Photon. Technol. Lett. 8, 776 (1996).
[CrossRef]

IEICE Trans. Electron. (1)

O. Aso, S. Arai, T. Yagi, M. Tadakuma, Y. Suzuki, and S. Namiki, IEICE Trans. Electron. E83-C, 816 (2000).

J. Lightwave Technol. (1)

P. K. A. Wai and C. R. Menyuk, J. Lightwave Technol. 14, 148 (1996).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Fiber Technol. Mater. Devices Syst. (1)

S. Radic, C. McKinstrie, and R. Jopson, Opt. Fiber Technol. Mater. Devices Syst. 9, 7 (2003).
[CrossRef]

Opt. Lett. (2)

Proc. Natl. Acad. Sci. USA (1)

J. P. Gordon and H. Kogelnik, Proc. Natl. Acad. Sci. USA 97, 4541 (2000).
[CrossRef]

Other (1)

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, New York, 2001).

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Figures (2)

Fig. 1
Fig. 1

Average FOPA gain as a function of signal detuning from the zero-dispersion wavelength for two values of Dp. Solid and dashed curves show the analytical and numerical results, respectively; two curves cannot be distinguished for Dp=0.05 ps/km1/2 on the scale used. The dotted curve shows for comparison the case without birefringence. The inset shows examples of FOPA gain spectra numerically obtained from Eqs. (1) and (2) for different realizations of residual birefringence.

Fig. 2
Fig. 2

Signal fluctuation level σs plotted as a function of signal detuning, under conditions of Fig. 1.

Equations (7)

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

d|Apdz=iβp-12ωpB·σ|Ap+iγ3(2Ap|Ap+|Ap*Ap*|)|Ap,
d|Asdz=iβs-12ωsB·σ|As+2iγ3(Ap|Ap+|ApAp+Ap*Ap*|)|As+iγ3(Ap*|Ap+2|ApAp*|)|Ai*,
d|Asdz=iΔβs-12Δωb·σ|As+iγe(Ap|As+Ai|Ap)|Ap,
d|Aidz=iΔβi+12Δωb·σ|Ai+iγe(Ap|Ai+As|Ap)|Ap,
dS0¯dz=dI0¯dz=γeP0U,
dUdz=-η/2+iκU+γeP0S0¯+I0¯+V,
dVdz=-ηV+2γeP0U,

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