Abstract

We present a vector theory of four-wave mixing and use it to study the polarization-dependent nature of four-wave mixing and the conditions under which the gain of a dual-pump fiber-optic parametric amplifier becomes polarization independent. We find that in the absence of self- and cross-phase modulations, any pair of orthogonally polarized pumps can provide polarization-independent gain, but this gain is minimum for linearly polarized pumps and becomes maximum when the two pumps are circularly polarized. Self- and cross-phase modulations induce nonlinear polarization rotation and change the orthogonality between the two pump polarizations. We discuss the general case of elliptically polarized cases and show that only linearly and circularly polarized pumps can maintain their orthogonality along the fiber. A stability analysis shows that the case of linearly polarized pumps is more stable than the circular one against small deviations from the ideal case but that the latter provides much more amplification.

© 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, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. 8, 506–520 (2002).
    [CrossRef]
  2. M. N. Islam and Ö. Boyraz, “Fiber parametric amplifiers for wavelength band conversion,” IEEE J. Sel. Top. Quantum Electron. 8, 527–537 (2002).
    [CrossRef]
  3. G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, San Diego, Calif. 2001).
  4. 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 (2002).
    [CrossRef]
  5. S. Radic, C. J. McKinstrie, A. R. Chraplyvy, G. Raybon, J. C. Centanni, C. G. Jorgensen, K. Brar, and C. Headley, “Continuous-wave parametric gain synthesis using nondegenerate pump four-wave mixing,” IEEE Photon. Technol. Lett. 14, 1406–1408 (2002).
    [CrossRef]
  6. S. Radic and C. J. McKinstrie, “Two-pump fiber parametric amplifiers,” Opt. Fiber Technol. 9, 7–23 (2003).
    [CrossRef]
  7. S. Radic, C. J. McKinstrie, R. M. Jopson, J. C. Centanni, Q. Lin, and G. P. Agrawal, “Record performance of parametric amplifier constructed with highly nonlinear fiber,” Electron. Lett. 39, 838–840 (2003).
    [CrossRef]
  8. 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]
  9. K. K. Y. Wong, M. E. Marhic, K. Uesaka, and L. G. Kazovsky, “Polarization-independent one-pump fiber-optical parametric amplifier,” IEEE Photon. Technol. Lett. 14, 1506–1508 (2002).
    [CrossRef]
  10. 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]
  11. 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]
  12. M. E. Marhic, K. K. Y. Wong, and L. G. Kazovsky, “Fiber optical parametric amplifiers with circularly-polarized pumps,” Electron. Lett. 39, 350–351 (2003).
    [CrossRef]
  13. R. W. Boyd, Nonlinear Optics, 2nd ed. (Academic, San Diego, Calif. 2003).
  14. J. P. Gordon and H. Kogelnik, “PMD fundamentals: polarization mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. U.S.A. 97, 4541–4550 (2000).
    [CrossRef] [PubMed]
  15. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, New York, 1995), Chap. 10.
  16. S. Huard, Polarization of Light (Wiley, New York, 1997).
  17. A. V. Mikhailov and S. Wabnitz, “Polarization dynamics of counterpropagating beams in optical fibers,” Opt. Lett. 15, 1055–1057 (1990).
    [CrossRef] [PubMed]
  18. S. Wabnitz and B. Daino, “Polarization domains and instabilities in nonlinear optical fibers,” Phys. Rev. A 182, 289–293 (1993).
  19. Q. Lin and G. P. Agrawal, “Effects of polarization-mode dispersion on fiber-based parametric amplification and wavelength conversion,” Opt. Lett. 29, 1114–1116 (2004).
    [CrossRef] [PubMed]
  20. F. Yaman, Q. Lin, and G. P. Agrawal, “Effects of polarization-mode dispersion in dual-pump fiber-optic parametric amplifiers,” IEEE Photon. Technol. Lett. 16, 431–433 (2004).
    [CrossRef]

2004 (2)

F. Yaman, Q. Lin, and G. P. Agrawal, “Effects of polarization-mode dispersion in dual-pump fiber-optic parametric amplifiers,” IEEE Photon. Technol. Lett. 16, 431–433 (2004).
[CrossRef]

Q. Lin and G. P. Agrawal, “Effects of polarization-mode dispersion on fiber-based parametric amplification and wavelength conversion,” Opt. Lett. 29, 1114–1116 (2004).
[CrossRef] [PubMed]

2003 (3)

M. E. Marhic, K. K. Y. Wong, and L. G. Kazovsky, “Fiber optical parametric amplifiers with circularly-polarized pumps,” Electron. Lett. 39, 350–351 (2003).
[CrossRef]

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

S. Radic, C. J. McKinstrie, R. M. Jopson, J. C. Centanni, Q. Lin, and G. P. Agrawal, “Record performance of parametric amplifier constructed with highly nonlinear fiber,” Electron. Lett. 39, 838–840 (2003).
[CrossRef]

2002 (6)

K. K. Y. Wong, M. E. Marhic, K. Uesaka, and L. G. Kazovsky, “Polarization-independent one-pump fiber-optical parametric amplifier,” IEEE Photon. Technol. Lett. 14, 1506–1508 (2002).
[CrossRef]

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

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 (2002).
[CrossRef]

S. Radic, C. J. McKinstrie, A. R. Chraplyvy, G. Raybon, J. C. Centanni, C. G. Jorgensen, K. Brar, and C. Headley, “Continuous-wave parametric gain synthesis using nondegenerate pump four-wave mixing,” IEEE Photon. Technol. Lett. 14, 1406–1408 (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]

2000 (1)

J. P. Gordon and H. Kogelnik, “PMD fundamentals: polarization mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. U.S.A. 97, 4541–4550 (2000).
[CrossRef] [PubMed]

1994 (1)

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 (2)

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]

S. Wabnitz and B. Daino, “Polarization domains and instabilities in nonlinear optical fibers,” Phys. Rev. A 182, 289–293 (1993).

1990 (1)

Agrawal, G. P.

Q. Lin and G. P. Agrawal, “Effects of polarization-mode dispersion on fiber-based parametric amplification and wavelength conversion,” Opt. Lett. 29, 1114–1116 (2004).
[CrossRef] [PubMed]

F. Yaman, Q. Lin, and G. P. Agrawal, “Effects of polarization-mode dispersion in dual-pump fiber-optic parametric amplifiers,” IEEE Photon. Technol. Lett. 16, 431–433 (2004).
[CrossRef]

S. Radic, C. J. McKinstrie, R. M. Jopson, J. C. Centanni, Q. Lin, and G. P. Agrawal, “Record performance of parametric amplifier constructed with highly nonlinear fiber,” Electron. Lett. 39, 838–840 (2003).
[CrossRef]

Andrekson, P. A.

J. Hansryd, P. A. 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]

Boyraz, Ö.

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

Brar, K.

S. Radic, C. J. McKinstrie, A. R. Chraplyvy, G. Raybon, J. C. Centanni, C. G. Jorgensen, K. Brar, and C. Headley, “Continuous-wave parametric gain synthesis using nondegenerate pump four-wave mixing,” IEEE Photon. Technol. Lett. 14, 1406–1408 (2002).
[CrossRef]

Centanni, J. C.

S. Radic, C. J. McKinstrie, R. M. Jopson, J. C. Centanni, Q. Lin, and G. P. Agrawal, “Record performance of parametric amplifier constructed with highly nonlinear fiber,” Electron. Lett. 39, 838–840 (2003).
[CrossRef]

S. Radic, C. J. McKinstrie, A. R. Chraplyvy, G. Raybon, J. C. Centanni, C. G. Jorgensen, K. Brar, and C. Headley, “Continuous-wave parametric gain synthesis using nondegenerate pump four-wave mixing,” IEEE Photon. Technol. Lett. 14, 1406–1408 (2002).
[CrossRef]

Chraplyvy, A. R.

S. Radic, C. J. McKinstrie, A. R. Chraplyvy, G. Raybon, J. C. Centanni, C. G. Jorgensen, K. Brar, and C. Headley, “Continuous-wave parametric gain synthesis using nondegenerate pump four-wave mixing,” IEEE Photon. Technol. Lett. 14, 1406–1408 (2002).
[CrossRef]

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 (2002).
[CrossRef]

Daino, B.

S. Wabnitz and B. Daino, “Polarization domains and instabilities in nonlinear optical fibers,” Phys. Rev. A 182, 289–293 (1993).

Gordon, J. P.

J. P. Gordon and H. Kogelnik, “PMD fundamentals: polarization mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. U.S.A. 97, 4541–4550 (2000).
[CrossRef] [PubMed]

Hansryd, J.

J. Hansryd, P. A. 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]

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]

Headley, C.

S. Radic, C. J. McKinstrie, A. R. Chraplyvy, G. Raybon, J. C. Centanni, C. G. Jorgensen, K. Brar, and C. Headley, “Continuous-wave parametric gain synthesis using nondegenerate pump four-wave mixing,” IEEE Photon. Technol. Lett. 14, 1406–1408 (2002).
[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,” IEEE J. Sel. Top. Quantum Electron. 8, 506–520 (2002).
[CrossRef]

Inoue, K.

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]

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]

Islam, M. N.

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

Jopson, R. M.

S. Radic, C. J. McKinstrie, R. M. Jopson, J. C. Centanni, Q. Lin, and G. P. Agrawal, “Record performance of parametric amplifier constructed with highly nonlinear fiber,” Electron. Lett. 39, 838–840 (2003).
[CrossRef]

Jorgensen, C. G.

S. Radic, C. J. McKinstrie, A. R. Chraplyvy, G. Raybon, J. C. Centanni, C. G. Jorgensen, K. Brar, and C. Headley, “Continuous-wave parametric gain synthesis using nondegenerate pump four-wave mixing,” IEEE Photon. Technol. Lett. 14, 1406–1408 (2002).
[CrossRef]

Kazovsky, L. G.

M. E. Marhic, K. K. Y. Wong, and L. G. Kazovsky, “Fiber optical parametric amplifiers with circularly-polarized pumps,” Electron. Lett. 39, 350–351 (2003).
[CrossRef]

K. K. Y. Wong, M. E. Marhic, K. Uesaka, and L. G. Kazovsky, “Polarization-independent one-pump fiber-optical parametric amplifier,” IEEE Photon. Technol. Lett. 14, 1506–1508 (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]

Kogelnik, H.

J. P. Gordon and H. Kogelnik, “PMD fundamentals: polarization mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. U.S.A. 97, 4541–4550 (2000).
[CrossRef] [PubMed]

Li, J.

J. Hansryd, P. A. 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]

Lin, Q.

Q. Lin and G. P. Agrawal, “Effects of polarization-mode dispersion on fiber-based parametric amplification and wavelength conversion,” Opt. Lett. 29, 1114–1116 (2004).
[CrossRef] [PubMed]

F. Yaman, Q. Lin, and G. P. Agrawal, “Effects of polarization-mode dispersion in dual-pump fiber-optic parametric amplifiers,” IEEE Photon. Technol. Lett. 16, 431–433 (2004).
[CrossRef]

S. Radic, C. J. McKinstrie, R. M. Jopson, J. C. Centanni, Q. Lin, and G. P. Agrawal, “Record performance of parametric amplifier constructed with highly nonlinear fiber,” Electron. Lett. 39, 838–840 (2003).
[CrossRef]

Marhic, M. E.

M. E. Marhic, K. K. Y. Wong, and L. G. Kazovsky, “Fiber optical parametric amplifiers with circularly-polarized pumps,” Electron. Lett. 39, 350–351 (2003).
[CrossRef]

K. K. Y. Wong, M. E. Marhic, K. Uesaka, and L. G. Kazovsky, “Polarization-independent one-pump fiber-optical parametric amplifier,” IEEE Photon. Technol. Lett. 14, 1506–1508 (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]

McKinstrie, C. J.

S. Radic, C. J. McKinstrie, R. M. Jopson, J. C. Centanni, Q. Lin, and G. P. Agrawal, “Record performance of parametric amplifier constructed with highly nonlinear fiber,” Electron. Lett. 39, 838–840 (2003).
[CrossRef]

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

S. Radic, C. J. McKinstrie, A. R. Chraplyvy, G. Raybon, J. C. Centanni, C. G. Jorgensen, K. Brar, and C. Headley, “Continuous-wave parametric gain synthesis using nondegenerate pump four-wave mixing,” IEEE Photon. Technol. Lett. 14, 1406–1408 (2002).
[CrossRef]

Mikhailov, A. V.

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.

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

S. Radic, C. J. McKinstrie, R. M. Jopson, J. C. Centanni, Q. Lin, and G. P. Agrawal, “Record performance of parametric amplifier constructed with highly nonlinear fiber,” Electron. Lett. 39, 838–840 (2003).
[CrossRef]

S. Radic, C. J. McKinstrie, A. R. Chraplyvy, G. Raybon, J. C. Centanni, C. G. Jorgensen, K. Brar, and C. Headley, “Continuous-wave parametric gain synthesis using nondegenerate pump four-wave mixing,” IEEE Photon. Technol. Lett. 14, 1406–1408 (2002).
[CrossRef]

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 (2002).
[CrossRef]

Raybon, G.

S. Radic, C. J. McKinstrie, A. R. Chraplyvy, G. Raybon, J. C. Centanni, C. G. Jorgensen, K. Brar, and C. Headley, “Continuous-wave parametric gain synthesis using nondegenerate pump four-wave mixing,” IEEE Photon. Technol. Lett. 14, 1406–1408 (2002).
[CrossRef]

Uesaka, K.

K. K. Y. Wong, M. E. Marhic, K. Uesaka, and L. G. Kazovsky, “Polarization-independent one-pump fiber-optical parametric amplifier,” IEEE Photon. Technol. Lett. 14, 1506–1508 (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]

Wabnitz, S.

S. Wabnitz and B. Daino, “Polarization domains and instabilities in nonlinear optical fibers,” Phys. Rev. A 182, 289–293 (1993).

A. V. Mikhailov and S. Wabnitz, “Polarization dynamics of counterpropagating beams in optical fibers,” Opt. Lett. 15, 1055–1057 (1990).
[CrossRef] [PubMed]

Westlund, M.

J. Hansryd, P. A. 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, K. K. Y.

M. E. Marhic, K. K. Y. Wong, and L. G. Kazovsky, “Fiber optical parametric amplifiers with circularly-polarized pumps,” Electron. Lett. 39, 350–351 (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]

K. K. Y. Wong, M. E. Marhic, K. Uesaka, and L. G. Kazovsky, “Polarization-independent one-pump fiber-optical parametric amplifier,” IEEE Photon. Technol. Lett. 14, 1506–1508 (2002).
[CrossRef]

Yaman, F.

F. Yaman, Q. Lin, and G. P. Agrawal, “Effects of polarization-mode dispersion in dual-pump fiber-optic parametric amplifiers,” IEEE Photon. Technol. Lett. 16, 431–433 (2004).
[CrossRef]

Electron. Lett. (2)

S. Radic, C. J. McKinstrie, R. M. Jopson, J. C. Centanni, Q. Lin, and G. P. Agrawal, “Record performance of parametric amplifier constructed with highly nonlinear fiber,” Electron. Lett. 39, 838–840 (2003).
[CrossRef]

M. E. Marhic, K. K. Y. Wong, and L. G. Kazovsky, “Fiber optical parametric amplifiers with circularly-polarized pumps,” Electron. Lett. 39, 350–351 (2003).
[CrossRef]

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

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

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 (2002).
[CrossRef]

IEEE Photon. Technol. Lett. (5)

S. Radic, C. J. McKinstrie, A. R. Chraplyvy, G. Raybon, J. C. Centanni, C. G. Jorgensen, K. Brar, and C. Headley, “Continuous-wave parametric gain synthesis using nondegenerate pump four-wave mixing,” IEEE Photon. Technol. Lett. 14, 1406–1408 (2002).
[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. Y. Wong, M. E. Marhic, K. Uesaka, and L. G. Kazovsky, “Polarization-independent one-pump fiber-optical parametric amplifier,” IEEE Photon. Technol. Lett. 14, 1506–1508 (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]

F. Yaman, Q. Lin, and G. P. Agrawal, “Effects of polarization-mode dispersion in dual-pump fiber-optic parametric amplifiers,” IEEE Photon. Technol. Lett. 16, 431–433 (2004).
[CrossRef]

J. Lightwave Technol. (1)

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]

Opt. Fiber Technol. (1)

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

Opt. Lett. (2)

Phys. Rev. A (1)

S. Wabnitz and B. Daino, “Polarization domains and instabilities in nonlinear optical fibers,” Phys. Rev. A 182, 289–293 (1993).

Proc. Natl. Acad. Sci. U.S.A. (1)

J. P. Gordon and H. Kogelnik, “PMD fundamentals: polarization mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. U.S.A. 97, 4541–4550 (2000).
[CrossRef] [PubMed]

Other (4)

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, New York, 1995), Chap. 10.

S. Huard, Polarization of Light (Wiley, New York, 1997).

R. W. Boyd, Nonlinear Optics, 2nd ed. (Academic, San Diego, Calif. 2003).

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, San Diego, Calif. 2001).

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Figures (6)

Fig. 1
Fig. 1

Normalized parametric gain as a function of pump ellipticity angle. The two pumps are assumed to be orthogonally polarized. The solid curve shows the case in which the phase-matching condition is perfectly satisfied. The dotted curve shows the case of a finite phase mismatch for Δβ=η=4γP1P2/3.

Fig. 2
Fig. 2

Evolution of the SOP of one of the pumps on the Poincaré sphere over a long propagation distance. The two pumps are orthogonal initially. The four trajectories correspond to a pump ellipticity angle θ=2°, 15°, 30°, and 43°, beginning from the inside.

Fig. 3
Fig. 3

(a) Pump SOP evolution for the same four values of θ for a 500-m-long fiber with γ=10 W-1/km. The two pumps have equal powers of 0.5 W. (b) The inner product ρ as a function of propagation distance for the same fiber. Pumps are orthogonally polarized when ρ=-1.

Fig. 4
Fig. 4

Gain as a function of signal detuning from the zero-dispersion wavelength (λ0=1580 nm) for a 500-m-long FOPA pumped by use of two 0.5-W pumps located at 1535 and 1628 nm. Pumps are orthogonally polarized for the middle two curves for which gain does not depend on the state of signal polarization. The thin solid and dotted curves show the dependence of gain on signal polarization in the case of linearly copolarized pumps.

Fig. 5
Fig. 5

Gain as a function of signal detuning from the zero-dispersion wavelength under different pump polarizations. Other parameters are the same as Fig. 4(a) Solid curves show the cases in which the signal is linearly polarized (ϕ=45°) such that it experiences minimum gain. (b) Solid curves show the cases in which the signal is linearly polarized (ϕ=135°) such that it experiences maximum gain. The two dotted curves show the cases in which the two pumps are linearly or circularly polarized.

Fig. 6
Fig. 6

(a) Gain as a function of signal polarization angle ϕ for the same FOPA under different pumping configurations. (b) The maximum and minimum gains (solid curves) and the amount of PDG (dotted curve) as a function of pump ellipticity angle for the FOPA of Fig. 4.

Equations (22)

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

P(3)(r, t)=0χ(3)E(r, t)E(r, t)E(r, t),
E=Re[E1 exp(-iω1t)+E2 exp(-iω2t)+Es exp(-iωst)+Ei exp(-iωit)],
P(3)=Re[P1 exp(-iω1t)+P2 exp(-iω2t)+Ps exp(-iωst)+Pi exp(-iωit)],
Pj(ωj)=0χ111(3)4[(Ej·Ej)Ej*+2(Ej*·Ej)Ej+2(Em*·Em)Ej+2(Em·Ej)Em*+2(Em*·Ej)Em],
Pj(ωj)=0χ1111(3)2[(E1*·E1)Ej+(E1·Ej)E1*+(E1*·Ej)E1+(E2*·E2)Ej+(E2·Ej)E2*+(E2*·Ej)E2+(Em*·E1)E2+(Em*·E2)E1+(E1·E2)Em*],
Ej(r)=Fj(x, y)|Aj(z)exp(iβjz),
d|Ajdz=iβj|Aj+iγ3(2Aj|Aj+2Am|Am+|Aj*Aj*|+2|AmAm|+2|Am*Am*|)|Aj,
d|Ajdz=iβj|Aj+2iγ3(A1|A1+A2|A2+|A1A1|+|A2A2|+|A1*A1*|+|A2*A2*|)|Aj+2iγ3(Am|A1|A2+Am|A2|A1+A1*|A2|Am*),
γn2k0/aeff=3k0χ1111(3)/(8n¯aeff),
dUidz=iβiUi+4iγ3[U1U2Us*+(U1D2+D1U2)Ds*],
dDidz=iβiDi+4iγ3[D1D2Ds*+(U1D2+D1U2)Us*].
|A1(z)=P1cos θi sin θexp(iβ1z),
|A2(z)=P2i sin θcos θexp(iβ2z),
d|Bsdz=2iγ3 P1P2 exp(-iΔβz)(2i sin 2θσ0+cos 2θσ2)|Bi*,
d|Bidz=2iγ3 P1P2 exp(-iΔβz)(2i sin 2θσ0+cos 2θσ2)|Bs*,
σ1=100-1,σ2=0110,σ3=0-ii0.
|Bs(z)=|Bs(0)×cosh(gz)+iΔβ2g sinh(gz)exp(-iΔβz/2),
g(θ)=[(2γ/3)2P1P2(1+3 sin2 2θ)-(Δβ/2)2]1/2.
Sp1=A1|σ|A1,Sp2=A2|σ|A2,
dSp1dz=2γ3[(Sp1+2Sp2)3eˆ3-2Sp2]×Sp1,
dSp2dz=2γ3[(Sp2+2Sp1)3eˆ3-2Sp1]×Sp2,
GAs(L)|As(L)As(0)|As(0)=1+[1+κ2/(4g2)]sinh2 (gL),

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