Comptes Rendus
Optical telecommunications/Les télécommunications optiques
Physics and mathematics of dispersion-managed optical solitons
Comptes Rendus. Physique, Volume 4 (2003) no. 1, pp. 145-161.

We review the main physical and mathematical properties of dispersion-managed (DM) optical solitons. Theory of DM solitons can be presented at two levels of accuracy: first, simple, but nevertheless, quantitative models based on ordinary differential equations governing evolution of the soliton width and phase parameter (the so-called chirp); and second, a comprehensive path-average theory that is capable of describing in detail both the fine structure of DM soliton form and its evolution along the fiber line. An analogy between DM soliton and a macroscopic nonlinear quantum oscillator model is also discussed.

Nous passons en revue les principales propriétés physiques et mathématiques des solitons dits managés par la dispersion (DM). La théorie des solitions DM peut être développée selon deux niveaux de précision : le premier relève de modèles simples, mais toutefois quantitatifs, tels que basés sur des équations différentielles ordinaires gouvernant les deux paramètres solitons que sont la largeur temporelle et la phase (le soit-disant ‘chirp’ ou dérive temporelle de fréquence) ; le deuxième relève d'une théorie poussée de cheminement-moyen, laquelle est en mesure de décrire en détail et la structure fine de l'enveloppe du soliton DM, et son évolution tout au long de la ligne de fibre. Nous présentons également une discussion sur une analogie entre le DM soliton et un modèle d'oscillateur quantique non-linéaire à l'échelle macroscopique.

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Published online:
DOI: 10.1016/S1631-0705(03)00008-2
Keywords: Optical soliton, Fiber communications, Dispersion-management
Mot clés : Solitons optiques, Communications à fibres optiques, Management de dispersion

Sergei K. Turitsyn 1; Elena G. Shapiro 2; Sergei B. Medvedev 3; Mikhail P. Fedoruk 3; Vladimir K. Mezentsev 1

1 Photonics Research group, Aston University, Birmingham, B4 7ET, UK
2 Institute of Automation and Electrometry, SB Russian Academy of Science, 630090, Novosibirsk, Russia
3 Institute of Computational Technologies, SB Russian Academy of Science, 630090, Novosibirsk, Russia
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Sergei K. Turitsyn; Elena G. Shapiro; Sergei B. Medvedev; Mikhail P. Fedoruk; Vladimir K. Mezentsev. Physics and mathematics of dispersion-managed optical solitons. Comptes Rendus. Physique, Volume 4 (2003) no. 1, pp. 145-161. doi : 10.1016/S1631-0705(03)00008-2. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/S1631-0705(03)00008-2/

[1] V.E. Zakharov; S.V. Manakov; S.P. Novikov; L.P. Pitaevskii Theory of Solitons. The Inverse Scattering Method, Plenum, New York, 1984

[2] M.J. Ablowitz; H. Segur Solitons and the Inverse Scattering Transform, SIAM, Philadelphia, 1981

[3] F. Calogero; A. Degasperis Spectral Transform and Solitons I, North-Holland, Amsterdam, 1982

[4] A.C. Newell Solitons in Mathematics and Physics, SIAM, Philadelphia, 1985

[5] M.J. Ablowitz; P.A. Clarkson Solitons, Nonlinear Evolution Equations and Inverse Scattering, London Math. Soc. Lecture Note Ser., 149, Cambridge University Press, 1991

[6] Solitons in Action (K. Lonngren; A. Scott, eds.), Academic Press, London, 1978

[7] R.K. Dodd; J.C. Eilbeck; J.D. Gibbon; H.C. Morris Solitons and Nonlinear Waves, Academic Press, London, 1982

[8] Solitons (S.E. Trullinger; V.E. Zakharov; V.L. Pokrovsky, eds.), Elsevier, Amstredam, 1986

[9] A. Hasegawa; Y. Kodama Solitons in Optical Communications, Claredon Press, Oxford, 1995

[10] A. Scott Nonlinear Science. Emergence and Dynamics of Coherent Structures, Oxford University Press, Oxford, 1999

[11] E. Desurvire Erbium-Doped Fiber Amplifiers: Principles and Applications, Wiley, New York, 1994

[12] C. Lin; H. Kogelnik; L.G. Cohen Optical-pulse equalization of low-dispersion transmission in single-mode fibers in the 1.3–1.7 μm spectral region, Opt. Lett., Volume 5 (1980), pp. 476-480

[13] A. Hasegawa; F. Tappert Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion, Appl. Phys. Lett., Volume 23 (1991), pp. 142-144

[14] V.E. Zakharov; A.B. Shabat Exact theory of two-dimensional self focusing and one dimensional modulation of waves in nonlinear media, Sov. Phys. JETP, Volume 33 (1971), pp. 77-83

[15] L.F. Mollenauer; R. Stolen; J. Gordon Experimental observation of picosecond pulse narrowing and solitons in optical fibers, Phys. Rev. Lett., Volume 45 (1980), pp. 1095-1097

[16] L.F. Mollenauer; S.G. Evangelides; H.A. Haus Long-distance soliton propagation using lumped amplifiers and dispersion-shifted fiber, IEEE J. Lightwave Technol., Volume 9 (1991), pp. 194-197

[17] A. Hasegawa; Y. Kodama Guiding-center soliton in optical fibers, Opt. Lett., Volume 15 (1991), pp. 1443-1444

[18] K.J. Blow; N.J. Doran Average soliton dynamics and the operation of soliton systems with lumped amplifiers, IEEE Photon. Technol. Lett., Volume 3 (1991), pp. 369-379

[19] L.F. Mollenauer; J.P. Gordon; P.V. Mamyshev Optical Fiber Telecommunications, Vol. IIIA (I.P. Kaminow; T.L. Koch, eds.), Academic Press, 1997, p. 373 (Chapter 12)

[20] A. Mecozzi; J.D. Moores; H.A. Haus; Y. Lai Soliton transmission control, Opt. Lett., Volume 16 (1991), pp. 1841-1843

[21] A. Mecozzi; J.D. Moores; H.A. Haus; Y. Lai Modulation and filtering control of soliton transmission, J. Opt. Soc. Am. B, Volume 9 (1992), pp. 1350-1364

[22] J.P. Gordon; H.A. Haus Random walk of coherently amplified solitons in optical fiber transmission, Opt. Lett., Volume 11 (1986), pp. 665-666

[23] F.M. Knox; W. Forysiak; N.J. Doran 10 Gbit/s soliton communication systems over standard fiber at 1.55 μm and the use of dispersion compensation, IEEE J. Lightwave Technol., Volume 13 (1995), pp. 1960-1995

[24] M. Suzuki; I. Morita; N. Edagawa; S. Yamamoto; H. Taga; S. Akiba Reduction of Gordon–Haus timing jitter bz periodic dispersion compensation in soliton transmission, Electron. Lett., Volume 31 (1995), pp. 2027-2035

[25] D. Le Guen; F. Favre; M.L. Moulinard; M. Henry; F. Devaux; T. Georges 320 Gbit/s soliton WDM transmission over 1100 km with 100 km dispersion-compensated spans of standard fiber, ECOC '97, Edinburgh, 1997, pp. 25-30 (post deadline paper V.5)

[26] N.S. Bergano et al. 320 Gb/s WDM transmission (64×5 Gb/s) over 7200 km using large mode fiber spans and chirped return-to-zero signals, OFC '98, San Jose, USA, 1998 (post deadline presentation, PD12-1)

[27] N. Robinson et al. 4×SONET OC-192 field installed dispersion managed soliton system over 450 km of standard fiber in the 1550 nm erbium band, OFC '98, San Jose, USA, 1998 (post deadline presentation, PD19-1)

[28] H.A. Haus; K. Tamura; L.E. Nelson; E.P. Ippen Stretched-pulse additive pulse mode-locking in fiber ring lasers: Theory and Experiment, IEEE J. Quantum Electron., Volume 31 (1995), pp. 591-595

[29] N. Smith; F.M. Knox; N.J. Doran; K.J. Blow; I. Bennion Enhanced power solitons in optical fiber transmission line, Electron. Lett., Volume 32 (1996), pp. 54-60

[30] I. Gabitov; S.K. Turitsyn Averaged pulse dynamics in a cascaded transmission system with passive dispersion compensation, Opt. Lett., Volume 21 (1996), pp. 327-328

[31] I. Gabitov; S.K. Turitsyn Breathing solitons in optical fiber links, JETP Lett., Volume 63 (1996), pp. 861-864

[32] N.J. Smith; N.J. Doran; F.M. Knox; W. Forysiak Energy scaling characteristics of solitons in strongly dispersion-managed fibers, Opt. Lett., Volume 21 (1997), pp. 1981-1983

[33] I. Gabitov; E.G. Shapiro; S.K. Turitsyn Optical pulse dynamics in fiber links with dispersion compensation, Opt. Commun., Volume 134 (1997), pp. 317-335

[34] I. Gabitov; E.G. Shapiro; S.K. Turitsyn Asymptotic breathing pulse in optical transmission systems with dispersion compensation, Phys. Rev. E, Volume 55 (1997), pp. 3624-3630

[35] M.J. Ablowitz; G. Biondini Multiscale pulse dynamics in communication systems with strong dispersion management, Opt. Lett., Volume 23 (1998), pp. 384-386

[36] S.K. Turitsyn; V.K. Mezentsev On the theory of chirped optical soliton in fiber lines with varying dispersion, JETP Lett., Volume 68 (1998) no. 11, pp. 830-836

[37] S. Medvedev; S.K. Turitsyn Hamiltonian averaging and integrability in nonlinear systems with periodically varying dispersion, JETP Lett., Volume 69 (1999) no. 7, pp. 499-506

[38] A.F. Evans Novel fibers for soliton communications, Optical Fiber Communication Conference, Vol. 2, OSA, Washington, DC, 1998, OSA Technical Digest Series, 1998, p. 22

[39] S.K. Turitsyn; M. Fedoruk; A. Gornakova Opt. Lett., 24 (1999), p. 869

[40] I. Gabitov; T. Schäfer; S.K. Turitsyn Lie-transform averaging in nonlinear optical transmission systems with strong and rapid periodic variations, Phys. Lett. A, Volume 265 (2000), pp. 274-281

[41] V.E. Zakharov; S.V. Manakov On propagation of short pulses in strong dispersion managed optical lines, JETP Lett., Volume 70 (1999) no. 9, pp. 573-578

[42] V.E. Zakharov Propagation of optical pulses in nonlinear systems with varying dispersion (V.E. Zakharov; S. Wabnitz, eds.), Optical Solitons. Theoretical Challenges and Industrial Perspectives, EDP Sciences, Springer, 1999

[43] T. Georges; B. Charbonnier Reduction of the dispersive wave in periodically amplified links with initially chirped solitons, IEEE Photon. Technol. Lett., Volume 9 (1997), pp. 127-133

[44] M. Matsumoto; H.A. Haus Stretched-pulse optical fiber communications, IEEE Photon. Technol. Lett., Volume 9 (1997), pp. 785-790

[45] T.S. Yang; W.L. Kath Analysis of enhanced-power solitons in dispersion-managed optical fibers, Opt. Lett., Volume 22 (1997), pp. 985-987

[46] J.N. Kutz; P. Holmes; S.G. Evangelides; J.P. Gordon Hamiltonian dynamics of dispersion managed breathers, JOSA B, Volume 15 (1998), pp. 87-90

[47] M. Wald; I.M. Uzunov; F. Lederer; S. Wabnitz Optimization of periodically dispersion compensated breathing soliton transmissions, Photon. Technol. Lett., Volume 9 (1997), pp. 1670-1673

[48] E. Shapiro; S.K. Turitsyn; E. Shapiro; S.K. Turitsyn Enhanced power breathing soliton in communication systems with dispersion management, Phys. Rev. E, Volume 22 (1997), pp. 1544-1546

[49] J.H.B. Nijhof; N.J. Doran; W. Forysiak; F.M. Knox Stable soliton-like propagation in dispersion managed systems with net anomalous, zero and normal dispersion, Electron. Lett., Volume 33 (1997), pp. 1726-1727

[50] A. Hasegawa; Y. Kodama; A. Maruta Recent progress in dispersion-managed soliton transmission technologies, Opt. Fiber Technol., Volume 3 (1997), pp. 197-200

[51] T. Georges; F. Favre Transmission systems based on dispersion-managed solitons: Theory and experiment, Proc. of II International Symposium on Physics and Applications of Optical Solitons in Fibers, Kyoto, 1997 (paper 2-A-2)

[52] S.K. Turitsyn; V.K. Mezentsev Dynamics of self-similar dispersion-managed soliton presented in the basis of chirped Gauss–Hermite functions, JETP Lett., Volume 67 (1998), pp. 640-643

[53] T. Lakoba; D.J. Kaup Hermite–Gaussian expansion for pulse propagation in strongly dispersion managed fibers, Phys. Rev. E, Volume 34 (1998), pp. 1124-1125

[54] S.K. Turitsyn; T. Schäfer; V.K. Mezentsev Self-similar core and oscillatory tails of a path-averaged chirped dispersion-managed optical pulse, Opt. Lett., Volume 23 (1998), pp. 1351-1353

[55] S.K. Turitsyn; A.B. Aceves; C.K.R.T. Jones; V. Zharnitsky; V.K. Mezentsev Hamiltonian averaging in soliton-bearing systems with periodically varying dispersion, Phys. Rev. E, Volume 59 (1999), p. R3843-R3846

[56] S.K. Turitsyn Self-similar dynamics and oscillatory tails of a breathing soliton in systems with varying dispersion, Phys. Rev. E, Volume 58 (1998)

[57] P.A. Belanger; N. Belanger Rms characteristics of pulses in nonlinear dispersive lossy fibers, Opt. Commun., Volume 117 (1995), pp. 56-60

[58] P.A. Bélanger; C. Paré Dispersion management in optical fiber links: self-consistent solution for the RMS pulse parameters, IEEE J. Lightwave Technol., Volume 17 (1999), pp. 445-458

[59] T.S. Yang; W.L. Kath; S.K. Turitsyn Optimal dispersion maps for wavelength-division-multiplexed soliton transmission, Opt. Lett., Volume 23 (1998), pp. 597-599

[60] S.K. Turitsyn; T. Shafer; K.H. Spatschek; V.K. Mezentsev Path-average theory of chirped dispersion-managed soliton, Opt. Commun., Volume 163 (1999), pp. 122-158

[61] P.M. Lushnikov Dispersion-managed soliton in a strong dispersion map limit, Opt. Lett., Volume 26 (2001), pp. 1535-1537

[62] P.M. Lushnikov Dispersion-managed soliton in optical fibers with zero average dispersion, Opt. Lett., Volume 25 (2000), pp. 1144-1146

[63] I.R. Gabitov; P.M. Lushnikov Nonlinearity management in dispersion managed system, Opt. Lett., Volume 27 (2002), pp. 113-115

[64] D.E. Pelinovsky Instabilities of dispersion-managed solitons in the normal dispersion regime, Phys. Rev. E, Volume 62 (1998), pp. 4283-4293

[65] S.K. Turitsyn; E.G. Turitsyna; S.B. Medvedev; M.P. Fedoruk Averaged model and integrable limits in nonlinear double-periodic Hamiltonian systems, Phys. Rev. E, Volume 61 (2000), pp. 3127-3132

[66] S. Turitsyn; N. Doran; E. Turitsyna; E. Shapiro; M. Fedoruk; S. Medvedev Averaged model and integrable limits in nonlinear double-periodic Hamiltonian systems, Massive WDM and TDM Solution Transmission Systems, Kluwer Academic, 2000

[67] S.K. Turitsyn; E.G. Shapiro; V.K. Mezentsev Dispersion-managed solitons and optimization of the dispersion management, Opt. Fiber Technol., Volume 4 (1998), pp. 384-402

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