Abstract

A simple theoretical formalism is developed to describe the effect of transmission on linearly polarized light through a fiber with random fluctuations of birefringence. We conclude that, for any optical fiber that does not experience polarization-dependent gain or loss, there exist two orientations for linearly polarized light input into the optical fiber that will also exit the fiber linearly polarized. We report experimental results that verify this prediction and also investigate its practical implications and limitations; in particular we investigate the stability of these linearly polarized output states in laboratory conditions.

© 1999 Optical Society of America

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References

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  1. S. C. Rashleigh, W. K. Burns, R. P. Moeller, R. Ulrich, “Polarization holding in birefringent single-mode fibers,” Opt. Lett. 7, 40–42 (1981).
    [CrossRef]
  2. H. G. Winful, A. Hu, “Intensity discrimination with twisted birefringent optical fibers,” Opt. Lett. 11, 668–670 (1986).
    [CrossRef] [PubMed]
  3. V. Ramaswamy, R. Standley, D. Sze, W. G. French, “Polarization effects in short length single mode fibers,” Bell Syst. Tech. J. 57, 635–651 (1978).
    [CrossRef]
  4. K. Okamoto, Y. Sasaki, T. Miya, M. Kawachi, T. Edahiro, “Polarisation characteristics in long length V.A.D. single-mode fibres,” Electron. Lett. 16, 768–769 (1980).
    [CrossRef]
  5. B. L. Heffner, “PMD measurement techniques—a consistent comparison,” in Optical Fiber Communication Conference, Vol. 2 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 292–293.
  6. C. D. Poole, R. E. Wagner, “Phenomenological approach to polarisation dispersion in long single-mode fibres,” Electron. Lett. 19, 1029–1030 (1986).
    [CrossRef]
  7. K. Inoue, “Polarization effect on four-wave mixing efficiency in a single-mode fiber,” IEEE J. Quantum. Electron. 28, 883–894 (1992).
    [CrossRef]
  8. S. C. Rashleigh, “Origins and control of polarization effects in single-mode fibers,” J. Lightwave Technol. LT-1, 312–331 (1983).
    [CrossRef]
  9. E. Hecht, Optics, 2nd ed. (Addison-Wesley, Reading, Mass., 1990), Chap. 8.
  10. R. Roy, C. Bracikowski, G. E. James, “Dynamics of a multimode laser with nonlinear birefringent intracavity elements,” in Recent Developments in Quantum Optics, R. Inguva, ed. (Plenum, New York, 1993), pp. 309–328.
    [CrossRef]
  11. G. E. James, “Models of intracavity frequency-doubled lasers,” Ph.D. dissertation (Georgia Institute of Technology, Atlanta, Ga., 1990).

1992 (1)

K. Inoue, “Polarization effect on four-wave mixing efficiency in a single-mode fiber,” IEEE J. Quantum. Electron. 28, 883–894 (1992).
[CrossRef]

1986 (2)

C. D. Poole, R. E. Wagner, “Phenomenological approach to polarisation dispersion in long single-mode fibres,” Electron. Lett. 19, 1029–1030 (1986).
[CrossRef]

H. G. Winful, A. Hu, “Intensity discrimination with twisted birefringent optical fibers,” Opt. Lett. 11, 668–670 (1986).
[CrossRef] [PubMed]

1983 (1)

S. C. Rashleigh, “Origins and control of polarization effects in single-mode fibers,” J. Lightwave Technol. LT-1, 312–331 (1983).
[CrossRef]

1981 (1)

1980 (1)

K. Okamoto, Y. Sasaki, T. Miya, M. Kawachi, T. Edahiro, “Polarisation characteristics in long length V.A.D. single-mode fibres,” Electron. Lett. 16, 768–769 (1980).
[CrossRef]

1978 (1)

V. Ramaswamy, R. Standley, D. Sze, W. G. French, “Polarization effects in short length single mode fibers,” Bell Syst. Tech. J. 57, 635–651 (1978).
[CrossRef]

Bracikowski, C.

R. Roy, C. Bracikowski, G. E. James, “Dynamics of a multimode laser with nonlinear birefringent intracavity elements,” in Recent Developments in Quantum Optics, R. Inguva, ed. (Plenum, New York, 1993), pp. 309–328.
[CrossRef]

Burns, W. K.

Edahiro, T.

K. Okamoto, Y. Sasaki, T. Miya, M. Kawachi, T. Edahiro, “Polarisation characteristics in long length V.A.D. single-mode fibres,” Electron. Lett. 16, 768–769 (1980).
[CrossRef]

French, W. G.

V. Ramaswamy, R. Standley, D. Sze, W. G. French, “Polarization effects in short length single mode fibers,” Bell Syst. Tech. J. 57, 635–651 (1978).
[CrossRef]

Hecht, E.

E. Hecht, Optics, 2nd ed. (Addison-Wesley, Reading, Mass., 1990), Chap. 8.

Heffner, B. L.

B. L. Heffner, “PMD measurement techniques—a consistent comparison,” in Optical Fiber Communication Conference, Vol. 2 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 292–293.

Hu, A.

Inoue, K.

K. Inoue, “Polarization effect on four-wave mixing efficiency in a single-mode fiber,” IEEE J. Quantum. Electron. 28, 883–894 (1992).
[CrossRef]

James, G. E.

G. E. James, “Models of intracavity frequency-doubled lasers,” Ph.D. dissertation (Georgia Institute of Technology, Atlanta, Ga., 1990).

R. Roy, C. Bracikowski, G. E. James, “Dynamics of a multimode laser with nonlinear birefringent intracavity elements,” in Recent Developments in Quantum Optics, R. Inguva, ed. (Plenum, New York, 1993), pp. 309–328.
[CrossRef]

Kawachi, M.

K. Okamoto, Y. Sasaki, T. Miya, M. Kawachi, T. Edahiro, “Polarisation characteristics in long length V.A.D. single-mode fibres,” Electron. Lett. 16, 768–769 (1980).
[CrossRef]

Miya, T.

K. Okamoto, Y. Sasaki, T. Miya, M. Kawachi, T. Edahiro, “Polarisation characteristics in long length V.A.D. single-mode fibres,” Electron. Lett. 16, 768–769 (1980).
[CrossRef]

Moeller, R. P.

Okamoto, K.

K. Okamoto, Y. Sasaki, T. Miya, M. Kawachi, T. Edahiro, “Polarisation characteristics in long length V.A.D. single-mode fibres,” Electron. Lett. 16, 768–769 (1980).
[CrossRef]

Poole, C. D.

C. D. Poole, R. E. Wagner, “Phenomenological approach to polarisation dispersion in long single-mode fibres,” Electron. Lett. 19, 1029–1030 (1986).
[CrossRef]

Ramaswamy, V.

V. Ramaswamy, R. Standley, D. Sze, W. G. French, “Polarization effects in short length single mode fibers,” Bell Syst. Tech. J. 57, 635–651 (1978).
[CrossRef]

Rashleigh, S. C.

S. C. Rashleigh, “Origins and control of polarization effects in single-mode fibers,” J. Lightwave Technol. LT-1, 312–331 (1983).
[CrossRef]

S. C. Rashleigh, W. K. Burns, R. P. Moeller, R. Ulrich, “Polarization holding in birefringent single-mode fibers,” Opt. Lett. 7, 40–42 (1981).
[CrossRef]

Roy, R.

R. Roy, C. Bracikowski, G. E. James, “Dynamics of a multimode laser with nonlinear birefringent intracavity elements,” in Recent Developments in Quantum Optics, R. Inguva, ed. (Plenum, New York, 1993), pp. 309–328.
[CrossRef]

Sasaki, Y.

K. Okamoto, Y. Sasaki, T. Miya, M. Kawachi, T. Edahiro, “Polarisation characteristics in long length V.A.D. single-mode fibres,” Electron. Lett. 16, 768–769 (1980).
[CrossRef]

Standley, R.

V. Ramaswamy, R. Standley, D. Sze, W. G. French, “Polarization effects in short length single mode fibers,” Bell Syst. Tech. J. 57, 635–651 (1978).
[CrossRef]

Sze, D.

V. Ramaswamy, R. Standley, D. Sze, W. G. French, “Polarization effects in short length single mode fibers,” Bell Syst. Tech. J. 57, 635–651 (1978).
[CrossRef]

Ulrich, R.

Wagner, R. E.

C. D. Poole, R. E. Wagner, “Phenomenological approach to polarisation dispersion in long single-mode fibres,” Electron. Lett. 19, 1029–1030 (1986).
[CrossRef]

Winful, H. G.

Bell Syst. Tech. J. (1)

V. Ramaswamy, R. Standley, D. Sze, W. G. French, “Polarization effects in short length single mode fibers,” Bell Syst. Tech. J. 57, 635–651 (1978).
[CrossRef]

Electron. Lett. (2)

K. Okamoto, Y. Sasaki, T. Miya, M. Kawachi, T. Edahiro, “Polarisation characteristics in long length V.A.D. single-mode fibres,” Electron. Lett. 16, 768–769 (1980).
[CrossRef]

C. D. Poole, R. E. Wagner, “Phenomenological approach to polarisation dispersion in long single-mode fibres,” Electron. Lett. 19, 1029–1030 (1986).
[CrossRef]

IEEE J. Quantum. Electron. (1)

K. Inoue, “Polarization effect on four-wave mixing efficiency in a single-mode fiber,” IEEE J. Quantum. Electron. 28, 883–894 (1992).
[CrossRef]

J. Lightwave Technol. (1)

S. C. Rashleigh, “Origins and control of polarization effects in single-mode fibers,” J. Lightwave Technol. LT-1, 312–331 (1983).
[CrossRef]

Opt. Lett. (2)

Other (4)

B. L. Heffner, “PMD measurement techniques—a consistent comparison,” in Optical Fiber Communication Conference, Vol. 2 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 292–293.

E. Hecht, Optics, 2nd ed. (Addison-Wesley, Reading, Mass., 1990), Chap. 8.

R. Roy, C. Bracikowski, G. E. James, “Dynamics of a multimode laser with nonlinear birefringent intracavity elements,” in Recent Developments in Quantum Optics, R. Inguva, ed. (Plenum, New York, 1993), pp. 309–328.
[CrossRef]

G. E. James, “Models of intracavity frequency-doubled lasers,” Ph.D. dissertation (Georgia Institute of Technology, Atlanta, Ga., 1990).

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Figures (4)

Fig. 1
Fig. 1

Experimental setup for measuring polarization of a test fiber. The extinction ratio results were obtained with the second polarizer and the power meter. The results shown in Figs. 24 were obtained with the polarization analyzer after the test fiber. P.C., polarization controller.

Fig. 2
Fig. 2

Polarization state paths (thicker curves) traced at the output of the fiber as the polarizer at the input is rotated through 180°. (a) 8-m test fiber. (b) 35-km test fiber.

Fig. 3
Fig. 3

Smear of points on the Poincaré sphere represent the evolution of the output polarization from an 8-m length of optical fiber during 32 h under typical laboratory conditions. (b) Same experiment showing the evolution of the output state of polarization of a 35-km length of fiber over only 4 h. Both experiments are intended to give some practical indication of the stability of the output polarization of a single-mode fiber when the input polarization is held constant.

Fig. 4
Fig. 4

(a) Polarization path traced by output light after experience of a small polarization-dependent gain in an EDFA. (b) Path traced by output light experiencing polarization-dependent loss.

Equations (15)

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Cδ=expiδ/200exp-iδ/2.
Rθ=cos θ-sin θsin θcos θ.
M=CδRθCRϕ.
M=ab-b*a*,
Σ=01-10.
Σ2=-I,
ΣRθΣ=-Rθ, ΣCΣ=-C¯,
M=abcd,
ΣMΣ=-d-c-ba.
ΣMΣ=ΣCδRθCRϕCγRψΣ =-ΣCδΣ2RθΣ2Σ2CγΣ2RψΣ =-C¯δRθC¯RϕC¯γRψ=-C¯δR¯θC¯R¯ϕC¯γR¯ψ =-M¯=-a*b*c*d*.
jout=M·jin.
ImExEy=0=aEx+bEy-b*Ex+a*Ey-c.c.,
r2-Ima2-b2Imab r-1=0.
Gc, d=c00d,
M=CδRθGc, dRϕCRψGe, fRζ.

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