Abstract

A detailed investigation of the coupled dynamics of the copropagating and counterpropagating polarization states in the optical loop fiber of a nonlinear amplifying loop mirror is performed. Analysis of the dynamics yields evidence for the existence of a polarization-insensitive configuration of the device.

© 1996 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  5. B. E. Olsson, P. A. Andrekson, presented at the European Conference on Optical Communications, Firenze, Italy, August 26–30, 1994.
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    [CrossRef]
  7. G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1989).
  8. P. D. Maker, R. W. Terhune, C. M. Savage, Phys. Rev. Lett. 12, 507 (1964).
    [CrossRef]

1995

K. Rottwitt, W. Margulis, J. R. Taylor, Electron. Lett. 31, 395 (1995).
[CrossRef]

1994

1992

S. Evangelides, L. F. Mollenauer, J. P. Gordon, N. S. Bergano, J. Lightwave Technol. 10, 28 (1992).
[CrossRef]

N. Finlayson, B. K. Nayar, N. J. Doran, Opt. Lett. 17, 112 (1992).
[CrossRef] [PubMed]

1990

1964

P. D. Maker, R. W. Terhune, C. M. Savage, Phys. Rev. Lett. 12, 507 (1964).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1989).

Andrekson, P. A.

B. E. Olsson, P. A. Andrekson, presented at the European Conference on Optical Communications, Firenze, Italy, August 26–30, 1994.

Bergano, N. S.

S. Evangelides, L. F. Mollenauer, J. P. Gordon, N. S. Bergano, J. Lightwave Technol. 10, 28 (1992).
[CrossRef]

Doran, N. J.

Evangelides, S.

S. Evangelides, L. F. Mollenauer, J. P. Gordon, N. S. Bergano, J. Lightwave Technol. 10, 28 (1992).
[CrossRef]

Fermann, M. E.

Finlayson, N.

Gordon, J. P.

S. Evangelides, L. F. Mollenauer, J. P. Gordon, N. S. Bergano, J. Lightwave Technol. 10, 28 (1992).
[CrossRef]

Haberl, F.

Hasegawa, A.

Hochreiter, H.

Hofer, M.

Kodama, Y.

Maker, P. D.

P. D. Maker, R. W. Terhune, C. M. Savage, Phys. Rev. Lett. 12, 507 (1964).
[CrossRef]

Margulis, W.

K. Rottwitt, W. Margulis, J. R. Taylor, Electron. Lett. 31, 395 (1995).
[CrossRef]

Matsumoto, M.

Mollenauer, L. F.

S. Evangelides, L. F. Mollenauer, J. P. Gordon, N. S. Bergano, J. Lightwave Technol. 10, 28 (1992).
[CrossRef]

Nayar, B. K.

Olsson, B. E.

B. E. Olsson, P. A. Andrekson, presented at the European Conference on Optical Communications, Firenze, Italy, August 26–30, 1994.

Rottwitt, K.

K. Rottwitt, W. Margulis, J. R. Taylor, Electron. Lett. 31, 395 (1995).
[CrossRef]

Savage, C. M.

P. D. Maker, R. W. Terhune, C. M. Savage, Phys. Rev. Lett. 12, 507 (1964).
[CrossRef]

Taylor, J. R.

K. Rottwitt, W. Margulis, J. R. Taylor, Electron. Lett. 31, 395 (1995).
[CrossRef]

Terhune, R. W.

P. D. Maker, R. W. Terhune, C. M. Savage, Phys. Rev. Lett. 12, 507 (1964).
[CrossRef]

Electron. Lett.

K. Rottwitt, W. Margulis, J. R. Taylor, Electron. Lett. 31, 395 (1995).
[CrossRef]

J. Lightwave Technol.

S. Evangelides, L. F. Mollenauer, J. P. Gordon, N. S. Bergano, J. Lightwave Technol. 10, 28 (1992).
[CrossRef]

Opt. Lett.

Phys. Rev. Lett.

P. D. Maker, R. W. Terhune, C. M. Savage, Phys. Rev. Lett. 12, 507 (1964).
[CrossRef]

Other

G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1989).

B. E. Olsson, P. A. Andrekson, presented at the European Conference on Optical Communications, Firenze, Italy, August 26–30, 1994.

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Figures (3)

Fig. 1
Fig. 1

Effect of XPM in a single fiber piece for two different initial polarization states of the copropagating field e+, which are indicated by filled circles on maps of the Poincaré sphere to the coordinates (ϕ, δ). The minimum of |α| was detected as a function of the initial polarization state of the counterpropagating field e. The results are presented as contour plots on the Poincaré sphere. Cases (i) and (ii) defined in the text are indicated by filled triangles and stars, respectively.

Fig. 2
Fig. 2

Period of |α| as a function of the power in the counterpropagating light. The solid curve is the analytical prediction, and the points with error bars are the numerically found averaged values and standard deviations. Inset: Variation of |α| as e+ propagates along the loop fiber. Each curve represents a random initial conditions.

Fig. 3
Fig. 3

Transmission coefficient (the ratio between output power and input power) for the NALM when the components fulfill the conditions for polarization insensitivity. Each curve correspond to a different polarization state of the incoming light. The power gain in the erbium-doped fiber amplifier is 14 dB.

Equations (6)

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z E + = ik [ n ¯ ¯ L + n ¯ ¯ ( E + ) SPM + n ¯ ¯ ( E ) XPM ] E + ,
n ¯ ¯ SPM = γ | E + | 2 [ | e x + | 2 + 2 3 | e y + | 2 1 3 e x + * e y + 1 3 e y + * e x + | e y + | 2 + 2 3 | e x + | 2 ] ,
n ¯ ¯ XPM = γ | E | 2 [ 2 | e x | 2 + 2 3 | e y | 2 4 3 Re { e x e y * } 4 3 Re { e y e x * } 2 | e y | 2 + 2 3 | e x | 2 ] ,
n SPM = e + * n ¯ ¯ SPM e + ,
n XPM = e + * n ¯ ¯ XPM e + ,
L α = 3 π 2 4 | E | 2 ,

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