Abstract

I have found the approximate analytical solution in explicit form for a vector soliton with an arbitrary component ratio. My solution describes the dependence of soliton intensity on polarization angle and also nonlinear polarization rotation. The analytical results agree well with the numerical simulations.

© 1995 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  5. S. G. Evangelides, L. F. Mollenauer, J. P. Gordon, N. S. Bergano, J. Lightwave Technol. 10, 28 (1992).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  13. V. V. Afanasjev, A. B. Grudinin, Sov. Lightwave Commun. 3, 77 (1993).
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  22. V. V. Afanasjev, A. B. Grudinin, in Conference on Lasers and Electro-Optics, Vol. 11 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), paper CWJ100.
  23. N. N. Akhmediev, J. M. Soto-Crespo, Phys. Rev. E 49, 5742 (1994).
    [CrossRef]

1994 (3)

1993 (5)

D. J. Kaup, B. A. Malomed, R. S. Tasgal, Phys. Rev. E 48, 3049 (1993).
[CrossRef]

R. P. Davey, N. Langford, A. I. Ferguson, Electron. Lett. 29, 758 (1993).
[CrossRef]

M. Nakazawa, E. Yoshida, T. Sugawa, Y. Kimura, Electron. Lett. 29, 1327 (1993).
[CrossRef]

A. B. Grudinin, D. J. Richardson, D. N. Payne, Electron Lett. 29, 1860 (1993).
[CrossRef]

V. V. Afanasjev, A. B. Grudinin, Sov. Lightwave Commun. 3, 77 (1993).

1992 (4)

F. Fontana, G. Grasso, N. Manfredini, M. Romagnoli, B. Daino, Electron. Lett. 28, 1291 (1992).
[CrossRef]

V. J. Matsas, T. P. Newson, D. J. Richardson, D. N. Payne, Electron. Lett. 28, 1391 (1992); V. J. Matsas, D. J. Richardson, T. P. Newson, D. N. Payne, Opt. Lett. 18, 358 (1993); V. J. Matsas, W. H. Loh, D. J. Richardson, IEEE Photon. Technol. Lett. 5, 492 (1993).
[CrossRef] [PubMed]

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

C. J. Chen, P. K. A. Wai, C. R. Menyuk, Opt. Lett. 17, 417 (1992).
[CrossRef] [PubMed]

1991 (2)

1990 (3)

1988 (1)

1987 (2)

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

C. R. Menyuk, IEEE J. Quantum Electron. 23, 174 (1987); Opt. Lett. 12, 614 (1987); J. Opt. Soc. Am. B 5, 392 (1988).
[CrossRef] [PubMed]

1982 (1)

1973 (1)

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

Afanasjev, V. V.

W. H. Loh, A. B. Grudinin, V. V. Afanasjev, D. N. Payne, Opt. Lett. 19, 698 (1994).
[CrossRef] [PubMed]

V. V. Afanasjev, V. A. Vysloukh, J. Opt. Soc. Am. B 11, 2385 (1994).
[CrossRef]

V. V. Afanasjev, A. B. Grudinin, Sov. Lightwave Commun. 3, 77 (1993).

V. V. Afanasjev, A. B. Grudinin, in Conference on Lasers and Electro-Optics, Vol. 11 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), paper CWJ100.

Akhmediev, N. N.

N. N. Akhmediev, J. M. Soto-Crespo, Phys. Rev. E 49, 5742 (1994).
[CrossRef]

Anderson, D.

Ashkin, A.

Bergano, N. S.

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

Blow, K. J.

Botineau, J.

Chen, C. J.

Chen, H. H.

Christodoulides, D. N.

Daino, B.

F. Fontana, G. Grasso, N. Manfredini, M. Romagnoli, B. Daino, Electron. Lett. 28, 1291 (1992).
[CrossRef]

Davey, R. P.

R. P. Davey, N. Langford, A. I. Ferguson, Electron. Lett. 29, 758 (1993).
[CrossRef]

Doran, N. J.

Evangelides, S. G.

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

Ferguson, A. I.

R. P. Davey, N. Langford, A. I. Ferguson, Electron. Lett. 29, 758 (1993).
[CrossRef]

Fontana, F.

F. Fontana, G. Grasso, N. Manfredini, M. Romagnoli, B. Daino, Electron. Lett. 28, 1291 (1992).
[CrossRef]

Gordon, J. P.

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

M. N. Islam, C. E. Soccolich, J. P. Gordon, U. C. Paek, Opt. Lett. 15, 21 (1990).
[CrossRef] [PubMed]

Grasso, G.

F. Fontana, G. Grasso, N. Manfredini, M. Romagnoli, B. Daino, Electron. Lett. 28, 1291 (1992).
[CrossRef]

Grudinin, A. B.

W. H. Loh, A. B. Grudinin, V. V. Afanasjev, D. N. Payne, Opt. Lett. 19, 698 (1994).
[CrossRef] [PubMed]

V. V. Afanasjev, A. B. Grudinin, Sov. Lightwave Commun. 3, 77 (1993).

A. B. Grudinin, D. J. Richardson, D. N. Payne, Electron Lett. 29, 1860 (1993).
[CrossRef]

V. V. Afanasjev, A. B. Grudinin, in Conference on Lasers and Electro-Optics, Vol. 11 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), paper CWJ100.

Höök, A.

Islam, M. N.

Joseph, R. I.

Kaup, D. J.

D. J. Kaup, B. A. Malomed, R. S. Tasgal, Phys. Rev. E 48, 3049 (1993).
[CrossRef]

Kimura, Y.

M. Nakazawa, E. Yoshida, T. Sugawa, Y. Kimura, Electron. Lett. 29, 1327 (1993).
[CrossRef]

Kivshar, Yu. S.

Langford, N.

R. P. Davey, N. Langford, A. I. Ferguson, Electron. Lett. 29, 758 (1993).
[CrossRef]

Lisak, M.

Loh, W. H.

Malomed, B. A.

D. J. Kaup, B. A. Malomed, R. S. Tasgal, Phys. Rev. E 48, 3049 (1993).
[CrossRef]

Manakov, S. V.

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

Manassah, J. T.

Manfredini, N.

F. Fontana, G. Grasso, N. Manfredini, M. Romagnoli, B. Daino, Electron. Lett. 28, 1291 (1992).
[CrossRef]

Matsas, V. J.

V. J. Matsas, T. P. Newson, D. J. Richardson, D. N. Payne, Electron. Lett. 28, 1391 (1992); V. J. Matsas, D. J. Richardson, T. P. Newson, D. N. Payne, Opt. Lett. 18, 358 (1993); V. J. Matsas, W. H. Loh, D. J. Richardson, IEEE Photon. Technol. Lett. 5, 492 (1993).
[CrossRef] [PubMed]

Menyuk, C. R.

Mollenauer, L. F.

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

Nakazawa, M.

M. Nakazawa, E. Yoshida, T. Sugawa, Y. Kimura, Electron. Lett. 29, 1327 (1993).
[CrossRef]

Newson, T. P.

V. J. Matsas, T. P. Newson, D. J. Richardson, D. N. Payne, Electron. Lett. 28, 1391 (1992); V. J. Matsas, D. J. Richardson, T. P. Newson, D. N. Payne, Opt. Lett. 18, 358 (1993); V. J. Matsas, W. H. Loh, D. J. Richardson, IEEE Photon. Technol. Lett. 5, 492 (1993).
[CrossRef] [PubMed]

Paek, U. C.

Payne, D. N.

W. H. Loh, A. B. Grudinin, V. V. Afanasjev, D. N. Payne, Opt. Lett. 19, 698 (1994).
[CrossRef] [PubMed]

A. B. Grudinin, D. J. Richardson, D. N. Payne, Electron Lett. 29, 1860 (1993).
[CrossRef]

V. J. Matsas, T. P. Newson, D. J. Richardson, D. N. Payne, Electron. Lett. 28, 1391 (1992); V. J. Matsas, D. J. Richardson, T. P. Newson, D. N. Payne, Opt. Lett. 18, 358 (1993); V. J. Matsas, W. H. Loh, D. J. Richardson, IEEE Photon. Technol. Lett. 5, 492 (1993).
[CrossRef] [PubMed]

Richardson, D. J.

A. B. Grudinin, D. J. Richardson, D. N. Payne, Electron Lett. 29, 1860 (1993).
[CrossRef]

V. J. Matsas, T. P. Newson, D. J. Richardson, D. N. Payne, Electron. Lett. 28, 1391 (1992); V. J. Matsas, D. J. Richardson, T. P. Newson, D. N. Payne, Opt. Lett. 18, 358 (1993); V. J. Matsas, W. H. Loh, D. J. Richardson, IEEE Photon. Technol. Lett. 5, 492 (1993).
[CrossRef] [PubMed]

Romagnoli, M.

F. Fontana, G. Grasso, N. Manfredini, M. Romagnoli, B. Daino, Electron. Lett. 28, 1291 (1992).
[CrossRef]

Soccolich, C. E.

Soto-Crespo, J. M.

N. N. Akhmediev, J. M. Soto-Crespo, Phys. Rev. E 49, 5742 (1994).
[CrossRef]

Stolen, R. H.

Sugawa, T.

M. Nakazawa, E. Yoshida, T. Sugawa, Y. Kimura, Electron. Lett. 29, 1327 (1993).
[CrossRef]

Tasgal, R. S.

D. J. Kaup, B. A. Malomed, R. S. Tasgal, Phys. Rev. E 48, 3049 (1993).
[CrossRef]

Vysloukh, V. A.

Wai, P. K. A.

Wood, D.

Yoshida, E.

M. Nakazawa, E. Yoshida, T. Sugawa, Y. Kimura, Electron. Lett. 29, 1327 (1993).
[CrossRef]

Electron Lett. (1)

A. B. Grudinin, D. J. Richardson, D. N. Payne, Electron Lett. 29, 1860 (1993).
[CrossRef]

Electron. Lett. (4)

F. Fontana, G. Grasso, N. Manfredini, M. Romagnoli, B. Daino, Electron. Lett. 28, 1291 (1992).
[CrossRef]

V. J. Matsas, T. P. Newson, D. J. Richardson, D. N. Payne, Electron. Lett. 28, 1391 (1992); V. J. Matsas, D. J. Richardson, T. P. Newson, D. N. Payne, Opt. Lett. 18, 358 (1993); V. J. Matsas, W. H. Loh, D. J. Richardson, IEEE Photon. Technol. Lett. 5, 492 (1993).
[CrossRef] [PubMed]

R. P. Davey, N. Langford, A. I. Ferguson, Electron. Lett. 29, 758 (1993).
[CrossRef]

M. Nakazawa, E. Yoshida, T. Sugawa, Y. Kimura, Electron. Lett. 29, 1327 (1993).
[CrossRef]

IEEE J. Quantum Electron. (1)

C. R. Menyuk, IEEE J. Quantum Electron. 23, 174 (1987); Opt. Lett. 12, 614 (1987); J. Opt. Soc. Am. B 5, 392 (1988).
[CrossRef] [PubMed]

J. Lightwave Technol. (1)

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

J. Opt. Soc. Am. B (3)

Opt. Lett. (8)

Phys. Rev. E (2)

N. N. Akhmediev, J. M. Soto-Crespo, Phys. Rev. E 49, 5742 (1994).
[CrossRef]

D. J. Kaup, B. A. Malomed, R. S. Tasgal, Phys. Rev. E 48, 3049 (1993).
[CrossRef]

Sov. Lightwave Commun. (1)

V. V. Afanasjev, A. B. Grudinin, Sov. Lightwave Commun. 3, 77 (1993).

Zh. Eksp. Teor. Fiz. (1)

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

Other (1)

V. V. Afanasjev, A. B. Grudinin, in Conference on Lasers and Electro-Optics, Vol. 11 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), paper CWJ100.

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Figures (4)

Fig. 1
Fig. 1

Soliton intensity I versus polarization angle α at γ = 2/3 and γ = 2. Solid curves, analytical result [Eq. (9)]; circles, numerical simulations.

Fig. 2
Fig. 2

Polarization components |ψ1(τ)|2 and |ψ2(τ)|2 at z = 0 (solid curves) and at z = 50 (dashed curves); α = π/6, γ = 2/3.

Fig. 3
Fig. 3

Ratio W1/W2 as a function of polarization angle (numerical result).

Fig. 4
Fig. 4

Length of polarization switch LS: analytical approximation (solid curves) and numerical data (circles).

Equations (11)

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i ( ψ 1 z + δ ψ 1 τ ) + 1 2 2 ψ 1 τ 2 + ( ψ 1 2 + γ ψ 2 2 ) ψ 1 + μ ψ 2 2 ψ 1 * exp ( - i R δ z ) = 0 ,
i ( ψ 2 z - δ ψ 2 τ ) + 1 2 2 ψ 2 τ 2 + ( ψ 2 2 + γ ψ 1 2 ) ψ 2 + μ ψ 1 2 ψ 2 * exp ( + i R δ z ) = 0 ,
ψ 1 ( z , τ ) = I ( α ) cos α sech ( τ ) exp [ i Γ 1 ( α ) z ] , ψ 2 ( z , τ ) = I ( α ) sin α sech ( τ ) exp [ i Γ 2 ( α ) z ] ,
I ( 0 ) = I ( π / 2 ) = 1 ,             I ( π / 4 ) = 2 / ( 1 + γ ) ,
I ( α + π / 2 ) = I ( α ) ,             I ( π / 2 - α ) = I ( α ) .
L = L 1 + L 2 + L CPM ,
L i = i 2 ( ψ i * ψ i z - ψ i ψ i * z ) - 1 2 | ψ i τ | 2 + 1 2 ψ i 4 , L CPM = γ ψ 1 2 ψ 2 2 .
L = - + L d τ = - 2 I ( Γ 1 cos 2 α + Γ 2 sin 2 α ) - ( 1 / 3 ) I + ( 2 / 3 ) I 2 ( cos 4 α + sin 4 α ) + ( 4 / 3 ) γ I 2 cos 2 α sin 2 α .
Γ i ( α ) = I ( α ) N i ( α ) - 1 / 2 ,
N 1 ( α ) = cos 2 α + γ sin 2 α , N 2 ( α ) = sin 2 α + γ cos 2 α .
I ( α ) = [ 3 ( N 1 cos 2 α + N 2 sin 2 α ) - 2 ( cos 4 α + sin 4 α ) - 4 γ cos 2 α sin 2 α ] - 1 .

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