Abstract

The polarization properties of an electromagnetic field that propagates in a fiber with polarization-mode dispersion (PMD) and randomly varying birefringence are studied by resorting to the coupled nonlinear Schrödinger equations. It is shown that the concept of principal states of polarization (PSP’s), meant to be the states that allow undistorted pulse propagation to be achieved in the presence of PMD, may be defined even in the presence of dispersion and nonlinearity. Furthermore, nonlinear PSP’s are proved to coincide with linear PSP’s, as they are customarily defined through the frequency dependence of the fiber input/output relation. Finally, it is also shown that the propagation equations may be exactly reduced to the Manakov equations for any fixed realization of the random process accounting for the fiber PMD. As a result, a whole class of simulton pulses that preserve their shape in the presence of PMD is analytically found.

© 2000 Optical Society of America

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  24. N. S. Bergano, C. D. Poole, and R. E. Wagner, “Investigation of polarization dispersion in long lengths of single-mode fiber using multi-longitudinal mode laser,” J. Lightwave Technol. 5, 1618–1622 (1987).
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  26. F. Curti, B. Daino, Q. Mao, F. Matera, and C. G. Someda, “Concatenation of polarization-dispersion in single-mode fibers,” Electron. Lett. 25, 290–291 (1989).
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  27. C. D. Poole, “Measurement of polarization-mode dispersion in single-mode fibers with random mode coupling,” Opt. Lett. 14, 523–525 (1989).
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  28. F. Curti, B. Daino, G. De Marchis, and F. Matera, “Statistical treatment of the evolution of the principal states of polarization on a low-birefringence terrestrial fiber cable,” J. Lightwave Technol. 8, 1162–1166 (1990).
    [CrossRef]
  29. C. D. Poole, J. H. Winters, and J. A. Nagel, “Dynamical equation for polarization dispersion,” Opt. Lett. 16, 372–374 (1991).
    [CrossRef] [PubMed]
  30. S. Betti, F. Curti, G. De Marchis, E. Iannone, and F. Matera, “Evolution of the bandwidth of the principal states of polarization in single-mode fibers,” Opt. Lett. 16, 467–469 (1991).
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  31. G. J. Foschini and C. D. Poole, “Statistical theory of polarization dispersion in single mode fibers,” J. Lightwave Technol. 9, 1439–1456 (1991).
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  32. B. L. Heffner, “Automated measurement of polarization mode dispersion using Jones matrix eigenanalysis,” IEEE Photonics Technol. Lett. 4, 1066–1069 (1992).
    [CrossRef]
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    [CrossRef]

1997 (2)

S. K. Turitsyn, “Theory of averaged pulse propagation in high bit rate optical transmission systems with strong dispersion management,” JETP Lett. 65, 845–850 (1997).
[CrossRef]

P. K. A. Wai, W. L. Kath, C. R. Menyuk, and J. W. Zhang, “Nonlinear polarization-mode dispersion in optical fibers with randomly varying birefringence,” J. Opt. Soc. Am. B 14, 2967–2979 (1997).
[CrossRef]

1996 (5)

P. K. A. Wai and C. R. Menyuk, “Polarization mode dispersion, decorrelation and diffusion in optical fibers with randomly varying birefringence,” J. Lightwave Technol. 14, 148–157 (1996).
[CrossRef]

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, “Enhanced power solitons in optical fibers with periodic dispersion management,” Electron. Lett. 32, 54–55 (1996).
[CrossRef]

I. Gabitov and S. K. Turitsyn, “Average pulse dynamics in the cascaded transmission system based on passive compensating technique,” Opt. Lett. 21, 327–329 (1996).
[CrossRef]

I. Gabitov and S. K. Turitsyn, “Breathing solitons in optical fiber links,” JETP Lett. 63, 861–866 (1996).
[CrossRef]

N. J. Smith, N. J. Doran, F. M. Knox, and W. Forysiak, “Energy-scaling characteristics of solitons in strongly dispersion managed fibers,” Opt. Lett. 21, 1981–1983 (1996).
[CrossRef] [PubMed]

1995 (1)

N. S. Bergano and C. R. Davidson, “Circulating loop transmission experiments for the study of long-haul transmission systems using erbium-doped fiber amplifiers,” J. Lightwave Technol. 13, 879–888 (1995).
[CrossRef]

1993 (1)

M. Nakazawa, K. Suzuki, E. Yamada, H. Kubota, Y. Kimura, and M. Takaya, “Experimental demonstration of soliton data transmission over unlimited distance with soliton control in time and frequency domain,” Electron. Lett. 29, 729–730 (1993).
[CrossRef]

1992 (4)

Y. Kodama and A. Hasegawa, “Generation of asymptotically stable optical solitons and suppression of the Gordon–Haus effect,” Opt. Lett. 17, 31–33 (1992).
[CrossRef] [PubMed]

N. J. Smith, K. J. Blow, and I. Andonovic, “Sideband generation through perturbations to the average soliton model,” J. Lightwave Technol. 10, 1329–1333 (1992).
[CrossRef]

B. L. Heffner, “Automated measurement of polarization mode dispersion using Jones matrix eigenanalysis,” IEEE Photonics Technol. Lett. 4, 1066–1069 (1992).
[CrossRef]

C. De Angelis, A. Galtarossa, G. Gianello, F. Matera, and M. Schiano, “Time evolution of polarization mode dispersion in long terrestrial links,” J. Lightwave Technol. 10, 552–555 (1992).
[CrossRef]

1991 (6)

1990 (1)

F. Curti, B. Daino, G. De Marchis, and F. Matera, “Statistical treatment of the evolution of the principal states of polarization on a low-birefringence terrestrial fiber cable,” J. Lightwave Technol. 8, 1162–1166 (1990).
[CrossRef]

1989 (3)

F. Curti, B. Daino, Q. Mao, F. Matera, and C. G. Someda, “Concatenation of polarization-dispersion in single-mode fibers,” Electron. Lett. 25, 290–291 (1989).
[CrossRef]

C. D. Poole, “Measurement of polarization-mode dispersion in single-mode fibers with random mode coupling,” Opt. Lett. 14, 523–525 (1989).
[CrossRef] [PubMed]

C. R. Menyuk, “Pulse propagation in elliptically birefringent Kerr medium,” IEEE J. Quantum Electron. 25, 2674–2682 (1989).
[CrossRef]

1988 (1)

1987 (3)

D. Andresciani, F. Curti, F. Matera, and B. Daino, “Measurement of the group-delay difference between the principal states of polarization on a low birefringence terrestrial fiber cable,” Opt. Lett. 12, 844–846 (1987).
[CrossRef] [PubMed]

N. S. Bergano, C. D. Poole, and R. E. Wagner, “Investigation of polarization dispersion in long lengths of single-mode fiber using multi-longitudinal mode laser,” J. Lightwave Technol. 5, 1618–1622 (1987).
[CrossRef]

C. R. Menyuk, “Nonlinear pulse propagation in birefringent optical fibers,” IEEE J. Quantum Electron. 23, 174–176 (1987).
[CrossRef]

1986 (3)

J. P. Gordon and H. A. Haus, “Random walk of coherently amplified solitons in optical fiber transmission,” Opt. Lett. 11, 665–667 (1986).
[CrossRef] [PubMed]

L. F. Mollenauer, J. P. Gordon, and M. N. Islam, “Soliton propagation in long fibers with periodically compensated loss,” IEEE J. Quantum Electron. 22, 157–173 (1986).
[CrossRef]

C. D. Poole and R. E. Wagner, “Phenomenological approach to polarization dispersion in long single-mode fibers,” Electron. Lett. 22, 1029–1030 (1986).
[CrossRef]

1985 (1)

1983 (1)

1973 (1)

A. Hasegawa and F. Tappert, “Transmission of stationary nonliner optical pulses in dispersive dielectric fibers. I. Anomalous dispersion,” Appl. Phys. Lett. 23, 142–144 (1973).
[CrossRef]

Andonovic, I.

N. J. Smith, K. J. Blow, and I. Andonovic, “Sideband generation through perturbations to the average soliton model,” J. Lightwave Technol. 10, 1329–1333 (1992).
[CrossRef]

Andresciani, D.

Bennion, I.

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, “Enhanced power solitons in optical fibers with periodic dispersion management,” Electron. Lett. 32, 54–55 (1996).
[CrossRef]

Bergano, N. S.

N. S. Bergano and C. R. Davidson, “Circulating loop transmission experiments for the study of long-haul transmission systems using erbium-doped fiber amplifiers,” J. Lightwave Technol. 13, 879–888 (1995).
[CrossRef]

N. S. Bergano, C. D. Poole, and R. E. Wagner, “Investigation of polarization dispersion in long lengths of single-mode fiber using multi-longitudinal mode laser,” J. Lightwave Technol. 5, 1618–1622 (1987).
[CrossRef]

Betti, S.

Blow, K. J.

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, “Enhanced power solitons in optical fibers with periodic dispersion management,” Electron. Lett. 32, 54–55 (1996).
[CrossRef]

N. J. Smith, K. J. Blow, and I. Andonovic, “Sideband generation through perturbations to the average soliton model,” J. Lightwave Technol. 10, 1329–1333 (1992).
[CrossRef]

Chen, H. H.

Curti, F.

S. Betti, F. Curti, G. De Marchis, E. Iannone, and F. Matera, “Evolution of the bandwidth of the principal states of polarization in single-mode fibers,” Opt. Lett. 16, 467–469 (1991).
[CrossRef] [PubMed]

F. Curti, B. Daino, G. De Marchis, and F. Matera, “Statistical treatment of the evolution of the principal states of polarization on a low-birefringence terrestrial fiber cable,” J. Lightwave Technol. 8, 1162–1166 (1990).
[CrossRef]

F. Curti, B. Daino, Q. Mao, F. Matera, and C. G. Someda, “Concatenation of polarization-dispersion in single-mode fibers,” Electron. Lett. 25, 290–291 (1989).
[CrossRef]

D. Andresciani, F. Curti, F. Matera, and B. Daino, “Measurement of the group-delay difference between the principal states of polarization on a low birefringence terrestrial fiber cable,” Opt. Lett. 12, 844–846 (1987).
[CrossRef] [PubMed]

Daino, B.

F. Curti, B. Daino, G. De Marchis, and F. Matera, “Statistical treatment of the evolution of the principal states of polarization on a low-birefringence terrestrial fiber cable,” J. Lightwave Technol. 8, 1162–1166 (1990).
[CrossRef]

F. Curti, B. Daino, Q. Mao, F. Matera, and C. G. Someda, “Concatenation of polarization-dispersion in single-mode fibers,” Electron. Lett. 25, 290–291 (1989).
[CrossRef]

D. Andresciani, F. Curti, F. Matera, and B. Daino, “Measurement of the group-delay difference between the principal states of polarization on a low birefringence terrestrial fiber cable,” Opt. Lett. 12, 844–846 (1987).
[CrossRef] [PubMed]

Davidson, C. R.

N. S. Bergano and C. R. Davidson, “Circulating loop transmission experiments for the study of long-haul transmission systems using erbium-doped fiber amplifiers,” J. Lightwave Technol. 13, 879–888 (1995).
[CrossRef]

De Angelis, C.

C. De Angelis, A. Galtarossa, G. Gianello, F. Matera, and M. Schiano, “Time evolution of polarization mode dispersion in long terrestrial links,” J. Lightwave Technol. 10, 552–555 (1992).
[CrossRef]

De Marchis, G.

S. Betti, F. Curti, G. De Marchis, E. Iannone, and F. Matera, “Evolution of the bandwidth of the principal states of polarization in single-mode fibers,” Opt. Lett. 16, 467–469 (1991).
[CrossRef] [PubMed]

F. Curti, B. Daino, G. De Marchis, and F. Matera, “Statistical treatment of the evolution of the principal states of polarization on a low-birefringence terrestrial fiber cable,” J. Lightwave Technol. 8, 1162–1166 (1990).
[CrossRef]

Doran, N. J.

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, “Enhanced power solitons in optical fibers with periodic dispersion management,” Electron. Lett. 32, 54–55 (1996).
[CrossRef]

N. J. Smith, N. J. Doran, F. M. Knox, and W. Forysiak, “Energy-scaling characteristics of solitons in strongly dispersion managed fibers,” Opt. Lett. 21, 1981–1983 (1996).
[CrossRef] [PubMed]

Forysiak, W.

Foschini, G. J.

G. J. Foschini and C. D. Poole, “Statistical theory of polarization dispersion in single mode fibers,” J. Lightwave Technol. 9, 1439–1456 (1991).
[CrossRef]

Gabitov, I.

Galtarossa, A.

C. De Angelis, A. Galtarossa, G. Gianello, F. Matera, and M. Schiano, “Time evolution of polarization mode dispersion in long terrestrial links,” J. Lightwave Technol. 10, 552–555 (1992).
[CrossRef]

Gianello, G.

C. De Angelis, A. Galtarossa, G. Gianello, F. Matera, and M. Schiano, “Time evolution of polarization mode dispersion in long terrestrial links,” J. Lightwave Technol. 10, 552–555 (1992).
[CrossRef]

Gordon, J. P.

J. P. Gordon and H. A. Haus, “Random walk of coherently amplified solitons in optical fiber transmission,” Opt. Lett. 11, 665–667 (1986).
[CrossRef] [PubMed]

L. F. Mollenauer, J. P. Gordon, and M. N. Islam, “Soliton propagation in long fibers with periodically compensated loss,” IEEE J. Quantum Electron. 22, 157–173 (1986).
[CrossRef]

Hasegawa, A.

Y. Kodama and A. Hasegawa, “Generation of asymptotically stable optical solitons and suppression of the Gordon–Haus effect,” Opt. Lett. 17, 31–33 (1992).
[CrossRef] [PubMed]

A. Hasegawa and Y. Kodama, “Guiding center soliton,” Phys. Rev. Lett. 66, 161–164 (1991).
[CrossRef] [PubMed]

A. Hasegawa, “Amplification and reshaping of optical solitons in glass fibers. IV. Use of stimulated Raman process,” Opt. Lett. 8, 650–652 (1983).
[CrossRef] [PubMed]

A. Hasegawa and F. Tappert, “Transmission of stationary nonliner optical pulses in dispersive dielectric fibers. I. Anomalous dispersion,” Appl. Phys. Lett. 23, 142–144 (1973).
[CrossRef]

Haus, H. A.

Heffner, B. L.

B. L. Heffner, “Automated measurement of polarization mode dispersion using Jones matrix eigenanalysis,” IEEE Photonics Technol. Lett. 4, 1066–1069 (1992).
[CrossRef]

Iannone, E.

Islam, M. N.

L. F. Mollenauer, J. P. Gordon, and M. N. Islam, “Soliton propagation in long fibers with periodically compensated loss,” IEEE J. Quantum Electron. 22, 157–173 (1986).
[CrossRef]

L. F. Mollenauer, R. H. Stolen, and M. N. Islam, “Experimental demonstration of soliton propagation in long fibers: loss compensated by Raman gain,” Opt. Lett. 10, 229–231 (1985).
[CrossRef] [PubMed]

Kath, W. L.

Kimura, Y.

M. Nakazawa, K. Suzuki, E. Yamada, H. Kubota, Y. Kimura, and M. Takaya, “Experimental demonstration of soliton data transmission over unlimited distance with soliton control in time and frequency domain,” Electron. Lett. 29, 729–730 (1993).
[CrossRef]

Knox, F. M.

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, “Enhanced power solitons in optical fibers with periodic dispersion management,” Electron. Lett. 32, 54–55 (1996).
[CrossRef]

N. J. Smith, N. J. Doran, F. M. Knox, and W. Forysiak, “Energy-scaling characteristics of solitons in strongly dispersion managed fibers,” Opt. Lett. 21, 1981–1983 (1996).
[CrossRef] [PubMed]

Kodama, Y.

Kubota, H.

M. Nakazawa, K. Suzuki, E. Yamada, H. Kubota, Y. Kimura, and M. Takaya, “Experimental demonstration of soliton data transmission over unlimited distance with soliton control in time and frequency domain,” Electron. Lett. 29, 729–730 (1993).
[CrossRef]

Lai, Y.

Mao, Q.

F. Curti, B. Daino, Q. Mao, F. Matera, and C. G. Someda, “Concatenation of polarization-dispersion in single-mode fibers,” Electron. Lett. 25, 290–291 (1989).
[CrossRef]

Matera, F.

C. De Angelis, A. Galtarossa, G. Gianello, F. Matera, and M. Schiano, “Time evolution of polarization mode dispersion in long terrestrial links,” J. Lightwave Technol. 10, 552–555 (1992).
[CrossRef]

S. Betti, F. Curti, G. De Marchis, E. Iannone, and F. Matera, “Evolution of the bandwidth of the principal states of polarization in single-mode fibers,” Opt. Lett. 16, 467–469 (1991).
[CrossRef] [PubMed]

F. Curti, B. Daino, G. De Marchis, and F. Matera, “Statistical treatment of the evolution of the principal states of polarization on a low-birefringence terrestrial fiber cable,” J. Lightwave Technol. 8, 1162–1166 (1990).
[CrossRef]

F. Curti, B. Daino, Q. Mao, F. Matera, and C. G. Someda, “Concatenation of polarization-dispersion in single-mode fibers,” Electron. Lett. 25, 290–291 (1989).
[CrossRef]

D. Andresciani, F. Curti, F. Matera, and B. Daino, “Measurement of the group-delay difference between the principal states of polarization on a low birefringence terrestrial fiber cable,” Opt. Lett. 12, 844–846 (1987).
[CrossRef] [PubMed]

Mecozzi, A.

Menyuk, C. R.

P. K. A. Wai, W. L. Kath, C. R. Menyuk, and J. W. Zhang, “Nonlinear polarization-mode dispersion in optical fibers with randomly varying birefringence,” J. Opt. Soc. Am. B 14, 2967–2979 (1997).
[CrossRef]

P. K. A. Wai and C. R. Menyuk, “Polarization mode dispersion, decorrelation and diffusion in optical fibers with randomly varying birefringence,” J. Lightwave Technol. 14, 148–157 (1996).
[CrossRef]

P. K. A. Wai, C. R. Menyuk, and H. H. Chen, “Stability of solitons in randomly varying birefringent fibers,” Opt. Lett. 16, 1231–1233 (1991).
[CrossRef] [PubMed]

C. R. Menyuk, “Pulse propagation in elliptically birefringent Kerr medium,” IEEE J. Quantum Electron. 25, 2674–2682 (1989).
[CrossRef]

C. R. Menyuk, “Nonlinear pulse propagation in birefringent optical fibers,” IEEE J. Quantum Electron. 23, 174–176 (1987).
[CrossRef]

Mollenauer, L. F.

L. F. Mollenauer, J. P. Gordon, and M. N. Islam, “Soliton propagation in long fibers with periodically compensated loss,” IEEE J. Quantum Electron. 22, 157–173 (1986).
[CrossRef]

L. F. Mollenauer, R. H. Stolen, and M. N. Islam, “Experimental demonstration of soliton propagation in long fibers: loss compensated by Raman gain,” Opt. Lett. 10, 229–231 (1985).
[CrossRef] [PubMed]

Moores, J. D.

Nagel, J. A.

Nakazawa, M.

M. Nakazawa, K. Suzuki, E. Yamada, H. Kubota, Y. Kimura, and M. Takaya, “Experimental demonstration of soliton data transmission over unlimited distance with soliton control in time and frequency domain,” Electron. Lett. 29, 729–730 (1993).
[CrossRef]

Poole, C. D.

C. D. Poole, J. H. Winters, and J. A. Nagel, “Dynamical equation for polarization dispersion,” Opt. Lett. 16, 372–374 (1991).
[CrossRef] [PubMed]

G. J. Foschini and C. D. Poole, “Statistical theory of polarization dispersion in single mode fibers,” J. Lightwave Technol. 9, 1439–1456 (1991).
[CrossRef]

C. D. Poole, “Measurement of polarization-mode dispersion in single-mode fibers with random mode coupling,” Opt. Lett. 14, 523–525 (1989).
[CrossRef] [PubMed]

C. D. Poole, “Statistical treatment of polarization dispersion in single-mode fibers,” Opt. Lett. 13, 687–689 (1988).
[CrossRef]

N. S. Bergano, C. D. Poole, and R. E. Wagner, “Investigation of polarization dispersion in long lengths of single-mode fiber using multi-longitudinal mode laser,” J. Lightwave Technol. 5, 1618–1622 (1987).
[CrossRef]

C. D. Poole and R. E. Wagner, “Phenomenological approach to polarization dispersion in long single-mode fibers,” Electron. Lett. 22, 1029–1030 (1986).
[CrossRef]

Schiano, M.

C. De Angelis, A. Galtarossa, G. Gianello, F. Matera, and M. Schiano, “Time evolution of polarization mode dispersion in long terrestrial links,” J. Lightwave Technol. 10, 552–555 (1992).
[CrossRef]

Smith, N. J.

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, “Enhanced power solitons in optical fibers with periodic dispersion management,” Electron. Lett. 32, 54–55 (1996).
[CrossRef]

N. J. Smith, N. J. Doran, F. M. Knox, and W. Forysiak, “Energy-scaling characteristics of solitons in strongly dispersion managed fibers,” Opt. Lett. 21, 1981–1983 (1996).
[CrossRef] [PubMed]

N. J. Smith, K. J. Blow, and I. Andonovic, “Sideband generation through perturbations to the average soliton model,” J. Lightwave Technol. 10, 1329–1333 (1992).
[CrossRef]

Someda, C. G.

F. Curti, B. Daino, Q. Mao, F. Matera, and C. G. Someda, “Concatenation of polarization-dispersion in single-mode fibers,” Electron. Lett. 25, 290–291 (1989).
[CrossRef]

Stolen, R. H.

Suzuki, K.

M. Nakazawa, K. Suzuki, E. Yamada, H. Kubota, Y. Kimura, and M. Takaya, “Experimental demonstration of soliton data transmission over unlimited distance with soliton control in time and frequency domain,” Electron. Lett. 29, 729–730 (1993).
[CrossRef]

Takaya, M.

M. Nakazawa, K. Suzuki, E. Yamada, H. Kubota, Y. Kimura, and M. Takaya, “Experimental demonstration of soliton data transmission over unlimited distance with soliton control in time and frequency domain,” Electron. Lett. 29, 729–730 (1993).
[CrossRef]

Tappert, F.

A. Hasegawa and F. Tappert, “Transmission of stationary nonliner optical pulses in dispersive dielectric fibers. I. Anomalous dispersion,” Appl. Phys. Lett. 23, 142–144 (1973).
[CrossRef]

Turitsyn, S. K.

S. K. Turitsyn, “Theory of averaged pulse propagation in high bit rate optical transmission systems with strong dispersion management,” JETP Lett. 65, 845–850 (1997).
[CrossRef]

I. Gabitov and S. K. Turitsyn, “Breathing solitons in optical fiber links,” JETP Lett. 63, 861–866 (1996).
[CrossRef]

I. Gabitov and S. K. Turitsyn, “Average pulse dynamics in the cascaded transmission system based on passive compensating technique,” Opt. Lett. 21, 327–329 (1996).
[CrossRef]

Wagner, R. E.

N. S. Bergano, C. D. Poole, and R. E. Wagner, “Investigation of polarization dispersion in long lengths of single-mode fiber using multi-longitudinal mode laser,” J. Lightwave Technol. 5, 1618–1622 (1987).
[CrossRef]

C. D. Poole and R. E. Wagner, “Phenomenological approach to polarization dispersion in long single-mode fibers,” Electron. Lett. 22, 1029–1030 (1986).
[CrossRef]

Wai, P. K. A.

Winters, J. H.

Yamada, E.

M. Nakazawa, K. Suzuki, E. Yamada, H. Kubota, Y. Kimura, and M. Takaya, “Experimental demonstration of soliton data transmission over unlimited distance with soliton control in time and frequency domain,” Electron. Lett. 29, 729–730 (1993).
[CrossRef]

Zhang, J. W.

Appl. Phys. Lett. (1)

A. Hasegawa and F. Tappert, “Transmission of stationary nonliner optical pulses in dispersive dielectric fibers. I. Anomalous dispersion,” Appl. Phys. Lett. 23, 142–144 (1973).
[CrossRef]

Electron. Lett. (4)

M. Nakazawa, K. Suzuki, E. Yamada, H. Kubota, Y. Kimura, and M. Takaya, “Experimental demonstration of soliton data transmission over unlimited distance with soliton control in time and frequency domain,” Electron. Lett. 29, 729–730 (1993).
[CrossRef]

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, “Enhanced power solitons in optical fibers with periodic dispersion management,” Electron. Lett. 32, 54–55 (1996).
[CrossRef]

C. D. Poole and R. E. Wagner, “Phenomenological approach to polarization dispersion in long single-mode fibers,” Electron. Lett. 22, 1029–1030 (1986).
[CrossRef]

F. Curti, B. Daino, Q. Mao, F. Matera, and C. G. Someda, “Concatenation of polarization-dispersion in single-mode fibers,” Electron. Lett. 25, 290–291 (1989).
[CrossRef]

IEEE J. Quantum Electron. (3)

C. R. Menyuk, “Nonlinear pulse propagation in birefringent optical fibers,” IEEE J. Quantum Electron. 23, 174–176 (1987).
[CrossRef]

C. R. Menyuk, “Pulse propagation in elliptically birefringent Kerr medium,” IEEE J. Quantum Electron. 25, 2674–2682 (1989).
[CrossRef]

L. F. Mollenauer, J. P. Gordon, and M. N. Islam, “Soliton propagation in long fibers with periodically compensated loss,” IEEE J. Quantum Electron. 22, 157–173 (1986).
[CrossRef]

IEEE Photonics Technol. Lett. (1)

B. L. Heffner, “Automated measurement of polarization mode dispersion using Jones matrix eigenanalysis,” IEEE Photonics Technol. Lett. 4, 1066–1069 (1992).
[CrossRef]

J. Lightwave Technol. (7)

F. Curti, B. Daino, G. De Marchis, and F. Matera, “Statistical treatment of the evolution of the principal states of polarization on a low-birefringence terrestrial fiber cable,” J. Lightwave Technol. 8, 1162–1166 (1990).
[CrossRef]

G. J. Foschini and C. D. Poole, “Statistical theory of polarization dispersion in single mode fibers,” J. Lightwave Technol. 9, 1439–1456 (1991).
[CrossRef]

N. S. Bergano, C. D. Poole, and R. E. Wagner, “Investigation of polarization dispersion in long lengths of single-mode fiber using multi-longitudinal mode laser,” J. Lightwave Technol. 5, 1618–1622 (1987).
[CrossRef]

P. K. A. Wai and C. R. Menyuk, “Polarization mode dispersion, decorrelation and diffusion in optical fibers with randomly varying birefringence,” J. Lightwave Technol. 14, 148–157 (1996).
[CrossRef]

N. J. Smith, K. J. Blow, and I. Andonovic, “Sideband generation through perturbations to the average soliton model,” J. Lightwave Technol. 10, 1329–1333 (1992).
[CrossRef]

N. S. Bergano and C. R. Davidson, “Circulating loop transmission experiments for the study of long-haul transmission systems using erbium-doped fiber amplifiers,” J. Lightwave Technol. 13, 879–888 (1995).
[CrossRef]

C. De Angelis, A. Galtarossa, G. Gianello, F. Matera, and M. Schiano, “Time evolution of polarization mode dispersion in long terrestrial links,” J. Lightwave Technol. 10, 552–555 (1992).
[CrossRef]

J. Opt. Soc. Am. B (1)

JETP Lett. (2)

S. K. Turitsyn, “Theory of averaged pulse propagation in high bit rate optical transmission systems with strong dispersion management,” JETP Lett. 65, 845–850 (1997).
[CrossRef]

I. Gabitov and S. K. Turitsyn, “Breathing solitons in optical fiber links,” JETP Lett. 63, 861–866 (1996).
[CrossRef]

Opt. Lett. (13)

N. J. Smith, N. J. Doran, F. M. Knox, and W. Forysiak, “Energy-scaling characteristics of solitons in strongly dispersion managed fibers,” Opt. Lett. 21, 1981–1983 (1996).
[CrossRef] [PubMed]

P. K. A. Wai, C. R. Menyuk, and H. H. Chen, “Stability of solitons in randomly varying birefringent fibers,” Opt. Lett. 16, 1231–1233 (1991).
[CrossRef] [PubMed]

I. Gabitov and S. K. Turitsyn, “Average pulse dynamics in the cascaded transmission system based on passive compensating technique,” Opt. Lett. 21, 327–329 (1996).
[CrossRef]

J. P. Gordon and H. A. Haus, “Random walk of coherently amplified solitons in optical fiber transmission,” Opt. Lett. 11, 665–667 (1986).
[CrossRef] [PubMed]

A. Mecozzi, J. D. Moores, H. A. Haus, and Y. Lai, “Soliton transmission control,” Opt. Lett. 16, 1841–1843 (1991).
[CrossRef] [PubMed]

Y. Kodama and A. Hasegawa, “Generation of asymptotically stable optical solitons and suppression of the Gordon–Haus effect,” Opt. Lett. 17, 31–33 (1992).
[CrossRef] [PubMed]

A. Hasegawa, “Amplification and reshaping of optical solitons in glass fibers. IV. Use of stimulated Raman process,” Opt. Lett. 8, 650–652 (1983).
[CrossRef] [PubMed]

L. F. Mollenauer, R. H. Stolen, and M. N. Islam, “Experimental demonstration of soliton propagation in long fibers: loss compensated by Raman gain,” Opt. Lett. 10, 229–231 (1985).
[CrossRef] [PubMed]

C. D. Poole, J. H. Winters, and J. A. Nagel, “Dynamical equation for polarization dispersion,” Opt. Lett. 16, 372–374 (1991).
[CrossRef] [PubMed]

S. Betti, F. Curti, G. De Marchis, E. Iannone, and F. Matera, “Evolution of the bandwidth of the principal states of polarization in single-mode fibers,” Opt. Lett. 16, 467–469 (1991).
[CrossRef] [PubMed]

D. Andresciani, F. Curti, F. Matera, and B. Daino, “Measurement of the group-delay difference between the principal states of polarization on a low birefringence terrestrial fiber cable,” Opt. Lett. 12, 844–846 (1987).
[CrossRef] [PubMed]

C. D. Poole, “Statistical treatment of polarization dispersion in single-mode fibers,” Opt. Lett. 13, 687–689 (1988).
[CrossRef]

C. D. Poole, “Measurement of polarization-mode dispersion in single-mode fibers with random mode coupling,” Opt. Lett. 14, 523–525 (1989).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

A. Hasegawa and Y. Kodama, “Guiding center soliton,” Phys. Rev. Lett. 66, 161–164 (1991).
[CrossRef] [PubMed]

Other (5)

F. Matera and C. G. Someda, “Random birefringence and polarization dispersion in long single-mode optical fibers,” in Anisotropic and Nonlinear Optical Waveguides, C. G. Someda and G. Stegeman, eds. (Elsevier, Amsterdam, 1992), pp. 1–38.

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

A. Hasegawa and Y. Kodama, Solitons in Optical Communications (Oxford University, New York, 1995).

T. Georges and F. Favre, “Transmission systems based on dispersion managed solitons: theory and experiment,” in Proceedings of the Second Research Group for Optical Soliton Communications Meeting, A. Hasegawa, ed. (Kluwer Academic, Dordrecht, The Netherlands, 1998); paper 2-A-2.

M. K. Simon, S. M. Hinedi, and W. C. Lindsey, Digital Communication Techniques (Prentice-Hall, Englewood Cliffs, N.J., 1995).

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Figures (2)

Fig. 1
Fig. 1

Power profile of a sech-like pulse traveling in a 300-km-long fiber affected by PMD, in the linear nondispersive regime [(a) and (b)] and in the presence of GVD and nonlinearity [(c) and (d)]. (a) The solid curve is the input pulse shape. The dashed and dotted curves are the output profiles when the input state of polarization coincides with the PSP’s ˆ- and ˆ+, respectively. (b) Broadening of a pulse having its initial power equally split between ˆ- and ˆ+. Solid curve, input pulse; dashed curve, numerically evaluated output profile; circles, theoretically evaluated output profile. (c) Solid curve, input profile; dashed and dotted curves, output pulses for an initial state of polarization coinciding with each of the linear PSP’s. (d) Nonlinear evolution of a pulse having half of its initial power in each PSP. Solid curve, input pulse; dashed curve, numerically computed output pulse; circles, output pulse in the absence of GVD and nonlinearity.

Fig. 2
Fig. 2

Performance of a dispersion-managed (DM) system versus the corresponding linear system in the presence of PMD for pulses having the initial state of polarization chosen either at random or accordingly to the PSP’s.

Equations (51)

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i ϕ1z+bϕ1-i2dθdzϕ2+ib ϕ1t+122ϕ1t2
+|ϕ1|2+23|ϕ2|2ϕ1=13N1,
i ϕ2z+i2dθdzϕ1-bϕ2-ib ϕ2t+122ϕ2t2
+23|ϕ1|2+|ϕ2|2ϕ2=13N2,
ϕ1(t, z)ϕ2(t, z)=H(z)Φ1(t, z)Φ2(t, z),
i Hz=b-i2dθdzi2dθdz-b=H(z),H(0)=1001,
i Φ1z+122Φ1t2+89(|Φ1|2+|Φ2|2)Φ1
=-iba1(z) Φ1t-iba4(z) Φ2t,
i Φ2z+122Φ2t2+89(|Φ1|2+|Φ2|2)Φ2
=-iba4*(z) Φt+iba1(z) Φ2t,
ddzx1x2x3=x2-x10 dθdz+0-2bx3-2bx2.
i zuv+122t2uv+(|u|2+|v|2)uv=-ibM tuv,
M=k1k4k4*-k1,
k1=1L0La1(ξ)dξ,k4=1L0La4(ξ)dξ,
ψ1(t, z)ψ2(t, z)=T-1u(t, z)v(t, z),T-1=11+|a|21-αα*1,
u(t, z)v(t, z)=Tψ1(t, z)ψ2(t, z),T=11+|α|21α-α*1,
α=k1-λk4*,λ=k12+|k4|2.
i ψ1z+122ψ1t2+(|ψ1|2+|ψ2|2)ψ1=-ibλ ψ1t,
i ψ2z+122ψ2t2+(|ψ1|2+|ψ2|2)ψ2=ibλ ψ2t.
ψ1z=-bλ ψ1t,ψ2z=bλ ψ2t,
ψ1(t, z)=ψ1(t+bλz),ψ2(t, z)=ψ2(t-bλz).
u(t, z=0)v(t, z=0)=11+|α|21-α*f(t)ˆ+f(t)
u(t, z=0)v(t, z=0)=11+|α|2α1g(t)ˆ-g(t),
q1(t, z)=ψ1(t, z)exp(+ibλt)exp[-12i(bλ)2z],
q2(t, z)=ψ2(t, z)exp(-ibλt)exp[-12i(bλ)2z].
i q1z+122q1t2+(|q1|2+|q2|2)q1=0,
i q2z+122q2t2+(|q1|2+|q2|2)q2=0,
u(t, z)v(t, z)=[ˆ+ cos(θ)exp(-ibλt)+ˆ- sin(θ)exp(ibλt+iϕ)]η sech(ηt)×expi2|η2+(bλ)2|z,
u(t, z)v(t, z)=ˆ± exp(ibλt)η sech(ηt)×expi2[η2+(bλ)2]z.
ηˆin+ˆ+,ηˆin-ˆ-.
zuˆvˆ=iωbk1k4k4*-k1uˆvˆiωbMuˆvˆ,
Eˆout=uˆ(z, ω)vˆ(z, ω)=R(ω, z)Eˆin=R(ω, z)uˆ(z=0, ω)vˆ(z=0, ω),
R(ω, z)=exp(iωbMz).
RωR-1=izbMTiλbz00-iλbzT-1.
ηˆout+ˆ+,witheigenvalue+iλbz;
ηˆout-ˆ-,witheigenvalue-iλbz.
ηˆin+R-1ηˆout+=Texp(-iωbλz)00exp(+iωbλz)T-1ηˆout+=Texp(-iωbλz)00exp(+iωbλz)10,
u(t, z=0)v(t, z=0)=cos(θ)sin(θ)exp(iϕ)f(t),
y=cos2(θ)+|α|2 sin(θ)2-2|α|cos(θ)sin(θ)cos(ϕ+ϕα)1+|α|2,
|α|=1+k12|k4|2-k1|k4|.
f|k4|(b)b{Prob.[|k4|<b]}=bσ2exp-12b2σ2,b>0.
Prob.[χ<b]=121+b1+b2;
fχ(b)=121(1+b2)3/2,bR.
Prob.[|α|<b]=Prob.[1+χ2-χ<b]=12-121-b22b1-b22b2.
f|α|(b)=2b(1+b2)2,b>0.
yp=l=0Ppl[cos2(θ)+|α|2 sin2(θ)]p-l[-|α|sin(2θ)cos(ϕ-ϕα)]l(1+|α|2)p
ypϕ=l=0levenppl 22l|α|lπ2(1+|α|2)pΓl+124[Γ(l+1)]2×[cos2(θ)+|α|2 sin2(θ)]p-l.
y-pϕ,θ=l=0levenppl 22l|α|lπ3(1+|α|2)pΓl+124[Γ(l+1)]2×j=0p-lp-lj|α|2jp-l+1j+1/2-1.
0+ am2a(1+a2)N+2da=Γ(1+m/2)Γ(1+N-m/2)Γ(N+2).
yp=l=0levenppl 22lπ3Γl+124[Γ(l+1)]2j=0p-lp-lj×p-l+1j+1/2-1p+2j+1+l/2-1.
yp=1p+1,

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