Abstract

The effects of randomly varying birefringence on solitons are studied. It is shown analytically that the evolution equation can be reduced to the nonlinear Schrödinger equation if the variation length is much shorter than the soliton period. The soliton does not split at high values of the average birefringence, but it does undergo spreading and loss of polarization. A soliton with a temporally constant initial state of polarization is still largely polarized after 40z0 if the normalized birefringence is δ ≤ 1.3.

© 1991 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]

1991

L. F. Mollenauer, S. Evangelides, H. A. Haus, IEEE J. Lightwave Technol. 9, 194 (1991).
[CrossRef]

1990

1989

1988

P. K. A. Wai, C. R. Menyuk, H. H. Chen, Y. C. Lee, IEEE J. Quantum Electron. 24, 373 (1988).
[CrossRef]

C. R. Menyuk, J. Opt. Soc. Am. B 5, 392 (1988).
[CrossRef]

1987

1973

S. V. Manakov, Zh. Eksp. Teor. Fiz. 65, 505 (1973) [Sov. Phys. JETP 38, 248 (1974)].

Bom, M.

M. Bom, E. Wolf, Principles of Optics, 4th ed. (Pergamon, Oxford, 1970).

Chen, H. H.

P. K. A. Wai, C. R. Menyuk, H. H. Chen, Y. C. Lee, IEEE J. Quantum Electron. 24, 373 (1988).
[CrossRef]

Cohen, L. G.

Evangelides, S.

L. F. Mollenauer, S. Evangelides, H. A. Haus, IEEE J. Lightwave Technol. 9, 194 (1991).
[CrossRef]

Evangelides, S. V.

Gordon, J. P.

Gordon, J. R.

Hasegawa, A.

Haus, H. A.

L. F. Mollenauer, S. Evangelides, H. A. Haus, IEEE J. Lightwave Technol. 9, 194 (1991).
[CrossRef]

Kodama, Y.

Lee, Y. C.

P. K. A. Wai, C. R. Menyuk, H. H. Chen, Y. C. Lee, IEEE J. Quantum Electron. 24, 373 (1988).
[CrossRef]

Manakov, S. V.

S. V. Manakov, Zh. Eksp. Teor. Fiz. 65, 505 (1973) [Sov. Phys. JETP 38, 248 (1974)].

Menyuk, C. R.

Mollenauer, L. E.

Mollenauer, L. F.

Neubelt, M. J.

Simpson, J. R.

Smith, K.

Wai, P. K. A.

P. K. A. Wai, C. R. Menyuk, H. H. Chen, Y. C. Lee, IEEE J. Quantum Electron. 24, 373 (1988).
[CrossRef]

Wolf, E.

M. Bom, E. Wolf, Principles of Optics, 4th ed. (Pergamon, Oxford, 1970).

IEEE J. Lightwave Technol.

L. F. Mollenauer, S. Evangelides, H. A. Haus, IEEE J. Lightwave Technol. 9, 194 (1991).
[CrossRef]

IEEE J. Quantum Electron.

C. R. Menyuk, IEEE J. Quantum Electron. 25, 2674 (1989).
[CrossRef]

P. K. A. Wai, C. R. Menyuk, H. H. Chen, Y. C. Lee, IEEE J. Quantum Electron. 24, 373 (1988).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Lett.

Zh. Eksp. Teor. Fiz.

S. V. Manakov, Zh. Eksp. Teor. Fiz. 65, 505 (1973) [Sov. Phys. JETP 38, 248 (1974)].

Other

M. Bom, E. Wolf, Principles of Optics, 4th ed. (Pergamon, Oxford, 1970).

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Figures (4)

Fig. 1
Fig. 1

Pulse shape of the shadow from analytical (dotted curves) and numerical (solid curves) calculations after one soliton period z0. The birefringence axes rotate every z0/500; δ = 2.5.

Fig. 2
Fig. 2

Time delay of the soliton normalized by δ (solid curve) and the sequence zdz′ cos 2θ (dotted curve) as functions of distance traversed; δ = 2.5.

Fig. 3
Fig. 3

Normalized pulse width as a function of distance traversed for δ = 1.25 (circles), δ = 2.5 (squares), δ = 4 (diamonds), δ = 5 (triangles), and δ = 7.5 (crosses).

Fig. 4
Fig. 4

Normalized power in the plane of polarization of the input pulse for the same set of δ values as those in Fig. 3.

Equations (6)

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i U z + i δ U t + 1 2 2 U t 2 + ( | U | 2 + 2 3 | V | 2 ) U + 1 2 V 2 U * exp ( i R δ z ) = 0 , i V z i δ V t + 1 2 2 V t 2 + ( 2 3 | U | 2 + | V | 2 ) V + 1 3 U 2 V * exp ( i R δ z ) = 0 ,
[ U V ] = [ cos θ sin θ e i ϕ sin θ e i ϕ cos θ ] [ U V ] .
i U z + 1 2 2 U t 2 + 8 9 ( | U | 2 + | V | 2 ) U = 0 , i V z + 1 2 2 V t 2 + 8 9 ( | U | 2 + | V | 2 ) V = 0 .
i q z + 1 2 2 q t 2 + 8 9 | q | 2 q = 0 ,
U ( z , t ) = U ( 0 ) + i 1 12 [ z d z × ( cos 4 θ 1 3 ) ] | U ( 0 ) | 2 U ( 0 ) , V ( z , t ) = δ [ z d z sin 2 θ exp ( i ϕ ) ] U ( 0 ) t i 1 12 [ z d z sin 4 θ exp ( i ϕ ) ] | U ( 0 ) | 2 U ( 0 ) ,
U ( 0 ) = 9 8 A sech A ( t δ z d z cos 2 θ ) × exp ( i A 2 z / 2 ) .

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