Abstract

The effect of birefringence on soliton propagation in single-mode optical fibers is considered. Emphasis is on solitons with multipicosecond widths that are appropriate for communications applications. It is shown that while linear birefringence will lead to a substantial splitting of the two polarizations over 20 km, this effect can be eliminated by use of the Kerr nonlinearity. Above a certain amplitude threshold, the central frequency of each polarization shifts just enough to lock the two polarizations together.

© 1987 Optical Society of America

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  1. A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 142 (1973).
    [CrossRef]
  2. L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1045 (1980).
    [CrossRef]
  3. I. P. Kaminow, IEEE J. Quantum Electron. QE-17, 15 (1981).
    [CrossRef]
  4. R. H. Stolen, AT&T Bell Laboratories, Holmdel, New Jersey 07733 (personal communication).
  5. S. V. Manakov, Zh. Eksp. Teor. Fiz. 67, 543 (1974)[Sov. Phys. JETP 40, 269 (1975)].
  6. C. R. Menyuk, Phys. Rev. A 33, 4367 (1986);C. R. Menyuk, P. K. A. Wai, H. H. Chen, Y. C. Lee, “Hamiltonian deformations of integrable, nonlinear field equations (with applications to optical fibers),” in Transactions of the 4th Army Conference on Applied Mathematics and Computing, F. Dressel, ed., U.S. Army Research Office Rep. 87-1, pp. 373–386.
    [CrossRef] [PubMed]
  7. P. K. A. Wai, C. R. Menyuk, H. H. Chen, Y. C. Lee, Opt Lett. 12, 628 (1987).
    [CrossRef] [PubMed]
  8. A. Hasegawa, Y. Kodama, Proc. IEEE 69, 1145 (1981).
    [CrossRef]
  9. L. F. Mollenauer, J. P. Gordon, M. N. Islam, IEEE J. Quantum Electron. QE-22, 157 (1986).
    [CrossRef]
  10. C. R. Menyuk, IEEE J. Quantum Electron. QE-23, 174 (1987).
    [CrossRef]
  11. K. J. Blow, N. J. Doran, D. Wood, Opt. Lett 12, 202 (1987).
    [CrossRef] [PubMed]
  12. See, e.g., T. R. Taha, M. J. Ablowitz, J. Comput. Phys. 55, 203 (1984).
    [CrossRef]
  13. J. Satsuma, N. Yajima, Suppl. Prog. Theor. Phys. 55, 284 (1974).
    [CrossRef]

1987

P. K. A. Wai, C. R. Menyuk, H. H. Chen, Y. C. Lee, Opt Lett. 12, 628 (1987).
[CrossRef] [PubMed]

C. R. Menyuk, IEEE J. Quantum Electron. QE-23, 174 (1987).
[CrossRef]

K. J. Blow, N. J. Doran, D. Wood, Opt. Lett 12, 202 (1987).
[CrossRef] [PubMed]

1986

C. R. Menyuk, Phys. Rev. A 33, 4367 (1986);C. R. Menyuk, P. K. A. Wai, H. H. Chen, Y. C. Lee, “Hamiltonian deformations of integrable, nonlinear field equations (with applications to optical fibers),” in Transactions of the 4th Army Conference on Applied Mathematics and Computing, F. Dressel, ed., U.S. Army Research Office Rep. 87-1, pp. 373–386.
[CrossRef] [PubMed]

L. F. Mollenauer, J. P. Gordon, M. N. Islam, IEEE J. Quantum Electron. QE-22, 157 (1986).
[CrossRef]

1984

See, e.g., T. R. Taha, M. J. Ablowitz, J. Comput. Phys. 55, 203 (1984).
[CrossRef]

1981

A. Hasegawa, Y. Kodama, Proc. IEEE 69, 1145 (1981).
[CrossRef]

I. P. Kaminow, IEEE J. Quantum Electron. QE-17, 15 (1981).
[CrossRef]

1980

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1045 (1980).
[CrossRef]

1974

S. V. Manakov, Zh. Eksp. Teor. Fiz. 67, 543 (1974)[Sov. Phys. JETP 40, 269 (1975)].

J. Satsuma, N. Yajima, Suppl. Prog. Theor. Phys. 55, 284 (1974).
[CrossRef]

1973

A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 142 (1973).
[CrossRef]

Ablowitz, M. J.

See, e.g., T. R. Taha, M. J. Ablowitz, J. Comput. Phys. 55, 203 (1984).
[CrossRef]

Blow, K. J.

K. J. Blow, N. J. Doran, D. Wood, Opt. Lett 12, 202 (1987).
[CrossRef] [PubMed]

Chen, H. H.

P. K. A. Wai, C. R. Menyuk, H. H. Chen, Y. C. Lee, Opt Lett. 12, 628 (1987).
[CrossRef] [PubMed]

Doran, N. J.

K. J. Blow, N. J. Doran, D. Wood, Opt. Lett 12, 202 (1987).
[CrossRef] [PubMed]

Gordon, J. P.

L. F. Mollenauer, J. P. Gordon, M. N. Islam, IEEE J. Quantum Electron. QE-22, 157 (1986).
[CrossRef]

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1045 (1980).
[CrossRef]

Hasegawa, A.

A. Hasegawa, Y. Kodama, Proc. IEEE 69, 1145 (1981).
[CrossRef]

A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 142 (1973).
[CrossRef]

Islam, M. N.

L. F. Mollenauer, J. P. Gordon, M. N. Islam, IEEE J. Quantum Electron. QE-22, 157 (1986).
[CrossRef]

Kaminow, I. P.

I. P. Kaminow, IEEE J. Quantum Electron. QE-17, 15 (1981).
[CrossRef]

Kodama, Y.

A. Hasegawa, Y. Kodama, Proc. IEEE 69, 1145 (1981).
[CrossRef]

Lee, Y. C.

P. K. A. Wai, C. R. Menyuk, H. H. Chen, Y. C. Lee, Opt Lett. 12, 628 (1987).
[CrossRef] [PubMed]

Manakov, S. V.

S. V. Manakov, Zh. Eksp. Teor. Fiz. 67, 543 (1974)[Sov. Phys. JETP 40, 269 (1975)].

Menyuk, C. R.

P. K. A. Wai, C. R. Menyuk, H. H. Chen, Y. C. Lee, Opt Lett. 12, 628 (1987).
[CrossRef] [PubMed]

C. R. Menyuk, IEEE J. Quantum Electron. QE-23, 174 (1987).
[CrossRef]

C. R. Menyuk, Phys. Rev. A 33, 4367 (1986);C. R. Menyuk, P. K. A. Wai, H. H. Chen, Y. C. Lee, “Hamiltonian deformations of integrable, nonlinear field equations (with applications to optical fibers),” in Transactions of the 4th Army Conference on Applied Mathematics and Computing, F. Dressel, ed., U.S. Army Research Office Rep. 87-1, pp. 373–386.
[CrossRef] [PubMed]

Mollenauer, L. F.

L. F. Mollenauer, J. P. Gordon, M. N. Islam, IEEE J. Quantum Electron. QE-22, 157 (1986).
[CrossRef]

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1045 (1980).
[CrossRef]

Satsuma, J.

J. Satsuma, N. Yajima, Suppl. Prog. Theor. Phys. 55, 284 (1974).
[CrossRef]

Stolen, R. H.

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1045 (1980).
[CrossRef]

R. H. Stolen, AT&T Bell Laboratories, Holmdel, New Jersey 07733 (personal communication).

Taha, T. R.

See, e.g., T. R. Taha, M. J. Ablowitz, J. Comput. Phys. 55, 203 (1984).
[CrossRef]

Tappert, F.

A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 142 (1973).
[CrossRef]

Wai, P. K. A.

P. K. A. Wai, C. R. Menyuk, H. H. Chen, Y. C. Lee, Opt Lett. 12, 628 (1987).
[CrossRef] [PubMed]

Wood, D.

K. J. Blow, N. J. Doran, D. Wood, Opt. Lett 12, 202 (1987).
[CrossRef] [PubMed]

Yajima, N.

J. Satsuma, N. Yajima, Suppl. Prog. Theor. Phys. 55, 284 (1974).
[CrossRef]

Appl. Phys. Lett.

A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 142 (1973).
[CrossRef]

IEEE J. Quantum Electron.

I. P. Kaminow, IEEE J. Quantum Electron. QE-17, 15 (1981).
[CrossRef]

L. F. Mollenauer, J. P. Gordon, M. N. Islam, IEEE J. Quantum Electron. QE-22, 157 (1986).
[CrossRef]

C. R. Menyuk, IEEE J. Quantum Electron. QE-23, 174 (1987).
[CrossRef]

J. Comput. Phys.

See, e.g., T. R. Taha, M. J. Ablowitz, J. Comput. Phys. 55, 203 (1984).
[CrossRef]

Opt Lett.

P. K. A. Wai, C. R. Menyuk, H. H. Chen, Y. C. Lee, Opt Lett. 12, 628 (1987).
[CrossRef] [PubMed]

Opt. Lett

K. J. Blow, N. J. Doran, D. Wood, Opt. Lett 12, 202 (1987).
[CrossRef] [PubMed]

Phys. Rev. A

C. R. Menyuk, Phys. Rev. A 33, 4367 (1986);C. R. Menyuk, P. K. A. Wai, H. H. Chen, Y. C. Lee, “Hamiltonian deformations of integrable, nonlinear field equations (with applications to optical fibers),” in Transactions of the 4th Army Conference on Applied Mathematics and Computing, F. Dressel, ed., U.S. Army Research Office Rep. 87-1, pp. 373–386.
[CrossRef] [PubMed]

Phys. Rev. Lett.

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1045 (1980).
[CrossRef]

Proc. IEEE

A. Hasegawa, Y. Kodama, Proc. IEEE 69, 1145 (1981).
[CrossRef]

Suppl. Prog. Theor. Phys.

J. Satsuma, N. Yajima, Suppl. Prog. Theor. Phys. 55, 284 (1974).
[CrossRef]

Zh. Eksp. Teor. Fiz.

S. V. Manakov, Zh. Eksp. Teor. Fiz. 67, 543 (1974)[Sov. Phys. JETP 40, 269 (1975)].

Other

R. H. Stolen, AT&T Bell Laboratories, Holmdel, New Jersey 07733 (personal communication).

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Figures (3)

Fig. 1
Fig. 1

Variation of (a) the maximum location s max u and (b) the frequency centroid ω cent u with distance along the fiber measured in soliton periods (δ = 0.15, γ = 0.0).

Fig. 2
Fig. 2

Variation of (a) the maximum location s max u and (b) the frequency centroid ω cent u with distance along the fiber (δ = 0.5, γ = 0.0).

Fig. 3
Fig. 3

Details of the pulse evolution (A = 1.0, δ = 0.5, γ = 0.0). Solid lines indicate u and u ˜; dashed lines indicate υ and υ ˜. (A) u(s) and υ(s), ξ = 0; (B) u ˜(ω) and υ ˜(ω), ξ = 0; (C) u(s) and υ(s), ξ = 5π (10 soliton periods); (D) u ˜(ω) and υ ˜(ω), ξ = 5π.

Tables (1)

Tables Icon

Table 1 Threshold Values of A at Which the Kerr Nonlinearity Is Sufficient to Compensate for Linear Birefringence

Equations (9)

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i ( U z + k U t ) 1 2 k 2 U t 2 + χ 2 ( | U | 2 + 2 3 | V | 2 ) U = i Γ U ,
i ( V z + l V t ) 1 2 l 2 V t 2 + χ 2 ( 2 3 | U | 2 + | V | 2 ) V = i Γ V ,
k = l = λ 0 2 π c 2 D ( λ ) ,
ξ = π z 2 z 0 , z 0 = π 2 c 2 t 0 2 D ( λ ) λ 0 , t 0 = 0.568 τ , s = 1 t 0 ( t z υ ̅ g ) , υ ̅ g = 2 k + l , u = ( χ 2 ) 1 / 2 U , υ = ( χ 2 ) 1 / 2 V , δ = k l 2 | k | t 0 = π c Δ n D ( λ ) λ 0 t 0 , γ = 2 z 0 Γ π ,
i ( u ξ + δ u s ) + 1 2 2 u s 2 + ( | u | 2 + 2 3 | υ | 2 ) u = i γ u ,
i ( υ ξ δ υ s ) + 1 2 2 υ s 2 + ( 2 3 | u | 2 + | υ | 2 ) υ = i γ υ .
u ( ξ = 0 ) = A cos α sech s , υ ( ξ = 0 ) = A sin α sech s .
u ˜ ( ω , ξ ) = 1 2 π d s e i ω s u ( s , ξ ) , υ ˜ ( ω , ξ ) = 1 2 π d s e i ω s υ ( s , ξ ) ,
ω cent u ( ξ ) = d ω ω | u ˜ ( ω , ξ ) | 2 d ω | u ˜ ( ω , ξ ) | 2 , ω cent υ ( ξ ) = d ω ω | υ ˜ ( ω , ξ ) | 2 d ω | υ ˜ ( ω , ξ ) | 2 .

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