Advertisement

A Brief History of Fiber-Optic Soliton Transmission

  • Fedor MitschkeEmail author
Reference work entry

Abstract

This is a review of fiber-optic solitons, with an emphasis on their use for data transmission. The historic account begins with the first concept of nonlinear waves in the nineteenth century. In the 1980s satisfactory fibers became available, and research into fiber-optic solitons took off. Around the turn of the millennium, maturity of soliton transmission for commercial deployments was reached. Since then, various extensions and generalizations of the soliton concept have been found and investigated, and some of them have led to interesting new applications. This review outlines these developments and briefly touches upon current concepts and problems.

Keywords

Optical fiber Soliton Nonlinear Schrödinger equation 

References

  1. M.J. Ablowitz, T. Hirooka, T. Inoue, Higher-order asymptotic analysis of dispersion managed transmission systems: solutions and their characteristics. J. Opt. Soc. Am. B 19, 2876 (2002)CrossRefGoogle Scholar
  2. G.P. Agrawal, Nonlinear Fiber Optics, 5th edn. (Academic Press, Amsterdam, 2013)Google Scholar
  3. N. Akhmediev, A. Ankiewicz (eds.), Dissipative Solitons: From Optics to Biology and Medicine. Lecture Notes in Physics, vol. 751 (Springer, Berlin, 2008)Google Scholar
  4. N. Akhmediev, M. Karlsson, Cherenkov radiation emitted by solitons in optical fibers. Phys. Rev. A 51, 2602 (1995)CrossRefGoogle Scholar
  5. N.N. Akhmediev, V.I. Korneev, Modulation instability and periodic solutions of the nonlinear Schrödinger equation. Theor. Math. Phys. 69, 1089 (1986)CrossRefGoogle Scholar
  6. N. Akhmediev, E. Pelinovsky, Introductory remarks on “discussion & debate: rogue waves – towards a unifying concept?” Eur. Phys. J. Spec. Top. 185, 1 (2010)CrossRefGoogle Scholar
  7. N.N. Akhmediev, G. Town, S. Wabnitz, Soliton coding based on shape invariant interacting soliton packets: the three-soliton case. Opt. Commun. 104, 385 (1994)CrossRefGoogle Scholar
  8. N. Akhmediev, A. Ankiewicz, M. Taki, Waves that appear from nowhere and disappear without a trace. Phys. Lett. A 373, 675 (2009a)CrossRefGoogle Scholar
  9. N. Akhmediev, J.M. Soto-Crespo, A. Ankiewicz, Extreme waves that appear from nowhere: on the nature of rogue waves. Phys. Lett. A 373, 2137 (2009b)CrossRefGoogle Scholar
  10. U. Al Khawaja, Stability and dynamics of two-soliton molecules. Phys. Rev. E 81, 056603 (2010)CrossRefGoogle Scholar
  11. U. Al Khawaja, A. Boudjemâa, Binding energy of soliton molecules in time-dependent harmonic potential and nonlinear interaction. Phys. Rev. E 86, 036606 (2012)CrossRefGoogle Scholar
  12. S.M. Alamoudi, U. Al Khawaja, B.B. Baizakov, Averaged dynamics of soliton molecules in dispersion-managed optical fibers. Phys. Rev. A 89, 053817 (2014)CrossRefGoogle Scholar
  13. Alcatel-Lucent, 1625 Lambda Extreme Transport Brochure (2011). http://www.telecomnetworks.ru/datadocs/doc_1587tu.pdf
  14. Amcom IP1 (TM) Chooses Marconi’s Soliton-Based Technology for Ultra Long Haul Network: World’s Longest Overland Optical Transmission Without Regeneration, Marconi Corporation, press release 19 Mar 2002. Archived at: http://www.prnewswire.com/news-releases/amcom-ip1tm-chooses-marconis-soliton-based-technology-for-ultra-long-haul-network-76538107.html
  15. S. Amiranashvili, A. Demircan, Ultrashort optical pulse propagation in terms of analytic signal. Adv. Opt. Technol. 2011, 989515 (2011)CrossRefGoogle Scholar
  16. S. Amiranashvili, U. Bandelow, A. Mielke, Padé approximant for refractive index and nonlocal envelope equations. Opt. Commun. 283, 480 (2010)CrossRefGoogle Scholar
  17. D. Anderson, M. Lisak, Nonlinear asymmetric self-phase modulation and self-steepening of pulses in long optical waveguides. Phys. Rev. A 27, 1393 (1983)CrossRefGoogle Scholar
  18. D. Anderson, M. Lisak, Modulational instability of coherent optical-fiber transmission signals. Opt. Lett. 9, 468 (1984)CrossRefGoogle Scholar
  19. P. Andrekson, Solitons are near commercialization. LEOS Newslett. 13, 3 (1999)Google Scholar
  20. A. Ankiewicz, J.M. Soto-Crespo, A. Chowdhury, N. Akhmediev, Rogue waves in optical fibers in presence of third-order dispersion, self-steepening, and self-frequency shift. J. Opt. Soc. Am. B 30, 87 (2013)CrossRefGoogle Scholar
  21. A. Armaroli, C. Conti, F. Biancalana, Rogue solitons in optical fibers: a dynamical process in a complex energy landscape. Optica 2, 497 (2015)CrossRefGoogle Scholar
  22. J.R.M. Barr, D.W. Hughes, Coupled cavity modelocking of a Nd:YAG laser using second-harmonic generation. Appl. Phys. B 49, 323 (1989)CrossRefGoogle Scholar
  23. P.C. Becker, N.A. Olsson, J.R. Simpson, Erbium-Doped Fiber Amplifiers: Fundamentals and Technology (Academic Press, San Diego, 1999)Google Scholar
  24. R.F. Benson, A discussion of the theory of ionospheric cross modulation. Radio Sci. J. Res. NBS/USNC-URSI 68D, 10 (1964)Google Scholar
  25. S. Birkholz, C. Brée, I. Veselić, A. Demircan, G. Steinmeyer, Ocean rogue waves and their phase space dynamics in the limit of a linear interference model. Sci. Rep. 6, 35207 (2016)CrossRefGoogle Scholar
  26. K.J. Blow, N.J. Doran, The asymptotic dispersion of soliton pulses in lossy fibres. Opt. Commun. 52, 367 (1985)CrossRefGoogle Scholar
  27. K.J. Blow, B.P. Nelson, Improved mode locking of an F-center laser with a nonlinear nonsoliton external cavity. Opt. Lett. 13, 1026 (1988)CrossRefGoogle Scholar
  28. C. Bonatto, M. Feyereisen, S. Barland, M. Giudici, C. Masoller, Deterministic optical rogue waves. Phys. Rev. Lett. 107, 053901 (2011)CrossRefGoogle Scholar
  29. A. Boudjemâa, U. Al Khawaja, Stability of N-soliton molecules in dispersion-managed optical fibers. Phys. Rev. A 88, 045801 (2013)CrossRefGoogle Scholar
  30. J. Bromage, Raman amplification for fiber communications systems. J. Lightwave Technol. 22, 79 (2004)CrossRefGoogle Scholar
  31. Capacity Crunch: When, Where and What Can Be Done? Announcement for a Workshop at Optical Fiber Conference (2017). http://www.ofcconference.org/en-us/home/program-speakers/workshops/capacity-crunch/
  32. Y. Chen, H.A. Haus, Dispersion-managed solitons with net positive dispersion. Opt. Lett. 23, 1013 (1998)CrossRefGoogle Scholar
  33. C.-M. Chen, P.L. Kelley, Nonlinear pulse compression in optical fibers: scaling laws and numerical analysis. J. Opt. Soc. Am. B 19, 1961 (2002)CrossRefGoogle Scholar
  34. R.Y. Chiao, E. Garmire, C.H. Townes, Self-trapping of optical beams. Phys. Rev. Lett. 13, 479 (1964)CrossRefGoogle Scholar
  35. S.A. Chin, O.A. Ashour, M.R. Beli, Anatomy of the Akhmediev breather: cascading instability, first formation time, and Fermi-Pasta-Ulam recurrence. Phys. Rev. E 92, 063202 (2015)CrossRefGoogle Scholar
  36. S. Chouli, P. Grelu, Soliton rains in a fiber laser: an experimental study. Phys. Rev. A 81, 063829 (2010)CrossRefGoogle Scholar
  37. A. Chraplyvy, The coming capacity crunch, Plenary Paper 1.0.2, in Proceedings of 35th European Conference on Optical Communications ECOC (2009)Google Scholar
  38. A.R. Chraplyvy, A.H. Gnauck, R.W. Tkach, R.M. Derosier, 8 × 10 Gbit/s transmission through 280 km of dispersion-managed fiber. IEEE Photon. Technol. Lett. 5, 1233 (1993)CrossRefGoogle Scholar
  39. M. Conforti, A. Marini, T.X. Tran, D. Faccio, F. Biancalana, Interaction between optical fields and their conjugates in nonlinear media. Opt. Express 21, 31239 (2013)CrossRefGoogle Scholar
  40. B.A. Cumberland, J.C. Travers, S.V. Popov, J.R. Taylor, Toward visible CW-pumped supercontinua. Opt. Lett. 33, 2122 (2008)CrossRefGoogle Scholar
  41. E.M. de Jager, On the Origin of the Korteweg-de Vries Equation (2011). https://arxiv.org/pdf/math/0602661v1.pdf Google Scholar
  42. E.A. De Souza, C.E. Soccolich, W. Pleibel, R.H. Stolen, J.R. Simpson, D.J. DiGiovanni, Saturable absorber modelocked polarization maintaining Erbium-Doped fiber laser. Electron. Lett. 29, 447 (1993)CrossRefGoogle Scholar
  43. E. Desurvire, Erbium-Doped Fiber Amplifiers: Principles and Applications (Wiley, Hoboken, 1994)Google Scholar
  44. E. Desurvire, J.R. Simpson, P.C. Becker, High-gain erbium-doped traveling-wave fiber amplifier. Opt. Lett. 12, 888 (1987)CrossRefGoogle Scholar
  45. E.M. Dianov, A.Y. Karasik, P.V. Mamyshev, A.M. Prokhorov, V.N. Serkin, M.F. Stel’makh, A.A. Fomichev, Stimulated-Raman conversion of multisoliton pulses in quartz optical fibers. Pis’ma Zh. Eksp. Teor. Fiz. 41, 242 (1985); JETP Lett. 41, 294 (1985)Google Scholar
  46. F.J. Diaz-Otero, P. Chamorro-Posada, Propagation properties of strongly dispersion-managed soliton trains. Opt. Commun. 285, 162 (2012)CrossRefGoogle Scholar
  47. J.M. Dudley, G. Genty, S. Coen, Supercontinuum generation in photonic crystal fiber. Rev. Mod. Phys. 78, 1135 (2006)CrossRefGoogle Scholar
  48. J.M. Dudley, G. Genty, F. Dias, B. Kibler, N. Akhmediev, Modulation instability, Akhmediev Breathers and continuous wave supercontinuum generation. Opt. Express 17, 21497 (2009)Google Scholar
  49. I.N. Duling III, All-fiber ring soliton laser mode locked with a nonlinear mirror. Opt. Lett. 16, 539 (1991a)CrossRefGoogle Scholar
  50. I.N. Duling III, Subpicosecond all-fiber erbium laser. Electron. Lett. 27, 544 (1991b)CrossRefGoogle Scholar
  51. A.D. Ellis, N. MacSuibhne, D. Saad, D.N. Payne, Communication networks beyond the capacity crunch. Phil. Trans. R. Soc. A 374, 20150191 (2016)CrossRefGoogle Scholar
  52. P. Emplit, J.P. Hamaide, F. Reynaud, C. Froehly, A. Barthelemy, Picosecond steps and dark pulses through nonlinear single mode fibers. Opt. Commun. 62, 374 (1987)CrossRefGoogle Scholar
  53. M. Erkintalo, G. Genty, J.M. Dudley, Giant dispersive wave generation through soliton collision. Opt. Lett. 35, 658 (2010)CrossRefGoogle Scholar
  54. R.-J. Essiambre, R.W. Tkach, Capacity trends and limits of optical communication networks. Proc. IEEE 100, 1035 (2012)CrossRefGoogle Scholar
  55. S.G. Evangelides, L.F. Mollenauer, J.P. Gordon, N.S. Bergano, Polarization multiplexing with solitons. J. Lightwave Technol. 10, 28 (1992)CrossRefGoogle Scholar
  56. I.L. Fabelinskii, Molecular scattering of light (Nauka Press, Moscow, 1965); transl. (Plenum Press, New York, 1968)CrossRefGoogle Scholar
  57. F. Fedele, J. Brennan, S. Ponce de León, J. Dudley, F. Dias, Real world ocean rogue waves explained without the modulational instability. Sci. Rep. 6, 27715 (2016)CrossRefGoogle Scholar
  58. B.-F. Feng, B.A. Malomed, Antisymmetric solitons and their interactions in strongly dispersion-managed fiber-optic systems. Opt. Commun. 229, 173 (2004)CrossRefGoogle Scholar
  59. E. Fermi, J. Pasta, S. Ulam, Studies of Non Linear Problems. Document LA-1940 (May 1955) Los Alamos Report LA-1940 (1955) Reprinted in E. Fermi, Collected Papers Vol. II (ed. E. Segrè) 978, University of Chicago Press, 1965Google Scholar
  60. M.E. Fermann, V.I. Kruglov, B.C. Thomsen, J.M. Dudley, J.D. Harvey, Self-similar propagation and amplification of parabolic pulses in optical fibers. Phys. Rev. Lett. 84, 6010 (2000)CrossRefGoogle Scholar
  61. C. Finot, G. Millot, J.M. Dudley, Asymptotic characteristics of parabolic similariton pulses in optical fiber amplifiers. Opt. Lett. 29, 2533 (2004)CrossRefGoogle Scholar
  62. W. Forysiak, Dispersion Managed Solitons and Real-World Link Installations, paper ThI2, Lasers and Electro-Optics Society LEOS 2003. The 16th Annual Meeting of the IEEE (2003)Google Scholar
  63. P.A. Franken, A.E. Hill, C.W. Peters, G. Weinreich, Generation of optical harmonics. Phys. Rev. Lett. 7, 118 (1961)CrossRefGoogle Scholar
  64. L. Froehly, J. Meteau, Supercontinuum sources in optical coherence tomography: a state of the art and the application to scan-free time domain correlation techniques and depth dependant dispersion compensation. Opt. Fiber Technol. 18, 411 (2012)CrossRefGoogle Scholar
  65. I. Gabitov, S.K. Turitsyn, Averaged pulse dynamics in a cascaded transmission system with passive dispersion compensation. Opt. Lett. 21, 327 (1996)CrossRefGoogle Scholar
  66. I. Gabitov, R. Indik, L. Mollenauer, M. Shkarayev, M. Stepanov, P.M. Lushnikov, Twin families of bisolitons in dispersion-managed systems. Opt. Lett. 32, 605 (2007)CrossRefGoogle Scholar
  67. C.S. Gardner, J.M. Greene, M.D. Kruskal, R.M. Miura, Method for solving the Korteweg-de Vries equation. Phys. Rev. Lett. 19, 1095 (1967)CrossRefGoogle Scholar
  68. G. Genty, M. Surakka, J. Tutunen, A.T. Friberg, Complete characterization of supercontinuum coherence. J. Opt. Soc. Am. B 28, 2301 (2011)CrossRefGoogle Scholar
  69. E.A. Golovchenko, E.M. Dianov, A.M. Prokhorov, V.N. Serkin, Decay of optical solitons, JETP Lett. 42, 87 (1985)Google Scholar
  70. M. Göppert-Mayer, Über Elementarakte mit zwei Quantensprüngen. Annalen der Physik 401, 273 (1931)CrossRefGoogle Scholar
  71. A. Gorbach, D. Skryabin, Gravity-Like Potential Traps Light and Stretches Optical Supercontinuum, paper NThB5, Nonlinear Photonics 2007, Quebec (The Optical Society of America, Washington, DC, 2007)Google Scholar
  72. J.P. Gordon, Interaction forces among solitons in optical fibers. Opt. Lett. 8, 596 (1983)CrossRefGoogle Scholar
  73. J.P. Gordon, Theory of the soliton self frequency shift. Opt. Lett. 11, 662 (1986)CrossRefGoogle Scholar
  74. J.P. Gordon, H.A. Haus, Random walk of coherently amplified solitons in optical fiber transmission. Opt. Lett. 11, 665 (1986)CrossRefGoogle Scholar
  75. P. Grelu, N. Akhmediev, Dissipative solitons for mode-locked lasers. Nat. Photon. 6, 84 (2012)CrossRefGoogle Scholar
  76. P. Grelu, J.M. Soto-Crespo, Temporal soliton “molecules” in mode-locked lasers: collisions, pulsations, and vibrations, in Akhmediev and Ankiewicz (2008), p. 137Google Scholar
  77. V.S. Grigoryan, C.R. Menyuk, Dispersion-managed solitons at normal average dispersion. Opt. Lett. 23, 609 (1998)CrossRefGoogle Scholar
  78. K. Hammani, B. Wetzel, B. Kibler, J. Fatome, C. Finot, G. Millot, N. Akhmediev, J.M. Dudley, Spectral dynamics of modulation instability described using Akhmediev breather theory. Opt. Lett. 36, 2140 (2011)CrossRefGoogle Scholar
  79. S. Hari, F. Kschischang, M. Yousefi, Multi-eigenvalue Communication Via the Nonlinear Fourier Transform, in 27th Biennial Symposium on Communications (QBSC) (2014)Google Scholar
  80. H. Hartwig, M. Böhm, A. Hause, F. Mitschke, Slow oscillations of dispersion managed solitons. Phys. Rev. A 81, 033810 (2010)CrossRefGoogle Scholar
  81. G.T. Harvey, L.F. Mollenauer, Harmonically mode-locked fiber ring laser with an internal Fabry-Perot stabilizer for soliton transmission. Opt. Lett. 18, 107 (1993)CrossRefGoogle Scholar
  82. A. Hasegawa, Generation of a train of soliton pulses by induced modulational instability in optical fibers. Opt. Lett. 9, 288 (1984a)CrossRefGoogle Scholar
  83. A. Hasegawa, Numerical study of optical soliton transmission amplified periodically by the stimulated Raman effect. Appl. Opt. 23, 3302 (1984b)CrossRefGoogle Scholar
  84. A. Hasegawa, Effect of polarization mode dispersion in optical soliton transmission in fibers. Phys. D 188, 241 (2004)CrossRefGoogle Scholar
  85. A. Hasegawa, Y. Kodama, Signal transmission by optical solitons in monomode fiber. Proc. IEEE 69, 1145 (1981)CrossRefGoogle Scholar
  86. A. Hasegawa, T. Nyu, Eigenvalue communication. J. Lightwave Technol. 11, 395 (1993)CrossRefGoogle Scholar
  87. A. Hasegawa, F. Tappert, Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. II. Normal dispersion. Appl. Phys. Lett. 23, 171 (1973a)CrossRefGoogle Scholar
  88. A. Hasegawa, F. Tappert, Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion. Appl. Phys. Lett. 23, 142 (1973b)CrossRefGoogle Scholar
  89. A. Hause, F. Mitschke, Higher-order equilibria of temporal soliton molecules in dispersion-managed fibers. Phys. Rev. A 88, 063843 (2013)CrossRefGoogle Scholar
  90. A. Hause, H. Hartwig, B. Seifert, H. Stolz, M. Böhm, F. Mitschke, Phase structure of soliton molecules. Phys. Rev. A 75, 063836 (2007)CrossRefGoogle Scholar
  91. A. Hause, H. Hartwig, M. Böhm, F. Mitschke, Binding mechanism of temporal soliton molecules. Phys. Rev. A 78, 063817 (2008)CrossRefGoogle Scholar
  92. W. He, M. Pang, C.R. Menyuk, P.S.J. Russell, Sub-100-fs 1.87 GHz mode-locked fiber laser using stretched-soliton effects. Optica 3, 1366 (2016)CrossRefGoogle Scholar
  93. J. Hecht, City of Light. The Story of Fiber Optics (Oxford University Press, Oxford, 1999)Google Scholar
  94. H. Heffner, The fundamental noise limit of linear amplifiers. Proc. IRE 50, 1604 (1962)CrossRefGoogle Scholar
  95. G. Herink, F. Kurtz, B. Jalali, D.R. Solli, C. Ropers, Real-time spectral interferometry probes the internal dynamics of femtosecond soliton molecules. Science 356, 50 (2017)CrossRefGoogle Scholar
  96. R. Holzwarth, T. Udem, T.W. Hänsch, J.C. Knight, W.J. Wadsworth, P.S.J. Russell, Optical frequency synthesizer for precision spectroscopy. Phys. Rev. Lett. 85, 2264 (2000)CrossRefGoogle Scholar
  97. A.V. Husakou, J. Herrmann, Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers. Phys. Rev. Lett. 87, 203901 (2001)CrossRefGoogle Scholar
  98. E. Iannone, F. Matera, A. Galtarossa, G. Gianello, M. Schiano, Effect of polarization dispersion on the performance of IM-DD communication systems. IEEE Photon. Technol. Lett. 5, 1247 (1993)CrossRefGoogle Scholar
  99. F.Ö. Ilday, J.R. Buckley, W.G. Clark, F.W. Wise, Self-similar evolution of parabolic pulses in a laser. Phys. Rev. Lett. 92, 213902 (2004)CrossRefGoogle Scholar
  100. E.P. Ippen, H.A. Haus, L.Y. Liu, Additive pulse mode locking. J. Opt. Soc. Am. B 6, 1736 (1989)CrossRefGoogle Scholar
  101. ITU recommendation ITU-T G.694.1 (2012). http://www.itu.int/rec/T-REC-G.694.1-201202-I/en
  102. S. Johnson, S. Pau, F. Küppers, Experimental demonstration of optical retiming using temporal soliton molecules. J. Lightwave Technol. 29, 3493 (2011)CrossRefGoogle Scholar
  103. D.J. Jones, S.A. Diddams, J.K. Ranka, A. Stentz, R.S. Windeler, J. Hall, S.T. Cundiff, Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis. Science 288, 635 (2000)CrossRefGoogle Scholar
  104. J.M. Kahn, K.-P. Ho, A bottleneck for optical fibres. Nature 411, 1007 (2001)CrossRefGoogle Scholar
  105. M. Kamalian, J.E. Prilepski, S.T. Le, S.K. Turitsyn, Periodic nonlinear Fourier transform for fiber-optic communications, Part I: theory and numerical methods. Opt. Express 24, 18353 (2016a)Google Scholar
  106. M. Kamalian, J.E. Prilepski, S.T. Le, S.K. Turitsyn, Periodic nonlinear Fourier transform for fiber-optic communications, Part II: eigenvalue communication. Opt. Express 24, 18370 (2016b)Google Scholar
  107. K.C. Kao, G.A. Hockham, Dielectric-fibre surface waveguides for optical frequencies. Proc. IEE 113, 1151 (1966)Google Scholar
  108. V.I. Karpman, E.M. Maslov, Perturbation theory for solitons. Sov. Phys. JETP 46(2), 281 (1977)Google Scholar
  109. V.I. Karpman, V.V. Solov’ev, A perturbational approach to the two soliton systems. Physica 3D, 487 (1981)Google Scholar
  110. A. Kastler, Optical methods of atomic orientation and of magnetic resonance. J. Opt. Soc. 47, 460 (1957)CrossRefGoogle Scholar
  111. D.J. Kaup, A perturbation expansion for the Zakharov-Shabat inverse scattering transform. SIAM J. Appl. Math. 31, 121 (1976)CrossRefGoogle Scholar
  112. S.M. Kelly, Characteristic sideband instability of periodically amplified average soliton. Electron. Lett. 28, 806 (1992)CrossRefGoogle Scholar
  113. B. Kibler, J. Fatome, C. Finot, F. Dias, G. Genty, N. Akhmediev, J.M. Dudley, The Peregrine soliton in nonlinear fiber optics. Nat. Phys. 6, 790 (2010)CrossRefGoogle Scholar
  114. B. Kibler, J. Fatome, C. Finot, G. Millot, G. Genty, B. Wetzel, N. Akhmediev, F. Dias, J.M. Dudley, Observation of the Kuznetsov-Ma soliton dynamics in optical fibre. Sci. Rep. 2, 463 (2012)CrossRefGoogle Scholar
  115. Y.S. Kivshar, B.A. Malomed, Dynamics of solitons in nearly integrable systems. Rev. Mod. Phys. 61, 763 (1989)CrossRefGoogle Scholar
  116. Y.S. Kivshar, M. Haelterman, P. Emplit, J.-P. Hamaide, Gordon-Haus effect on dark solitons. Opt. Lett. 19, 19 (1994)CrossRefGoogle Scholar
  117. Y. Kodama, A. Hasegawa, Generation of asymptotically stable optical solitons and suppression of the Gordon-Haus effect. Opt. Lett. 17, 31 (1992)CrossRefGoogle Scholar
  118. Y. Kodama, K. Nozaki, Soliton interaction in optical fibers. Opt. Lett. 12, 1038 (1987)CrossRefGoogle Scholar
  119. S.K. Korotky, Semi-empirical description and pojections of internet traffic trends using a hyperbolic compound annual growth rate. Bell Labs Tech. J. 18, 5 (2013)CrossRefGoogle Scholar
  120. F. Krausz, T. Brabec, C. Spielmann, Self-starting passive mode locking. Opt. Lett. 16, 235 (1991)CrossRefGoogle Scholar
  121. D. Krökel, N.J. Halas, G. Giuliani, D. Grischkowsky, Dark-pulse propagation in optical fibers. Phys. Rev. Lett. 60, 29 (1988)CrossRefGoogle Scholar
  122. M.D. Kruskal, N.J. Zabusky, Interaction of “solitons” in a collisionless plasma and the recurrence of initial states. Phys. Rev. Lett. 15, 240 (1965)Google Scholar
  123. H. Kubota, M. Nakazawa, Long-distance optical soliton transmission with lumped amplifiers. IEEE J. Quantum Electron. 26, 692 (1990)CrossRefGoogle Scholar
  124. A. Kudlinski, A. Mussot, Visible CW-pumped supercontinuum. Opt. Lett. 33, 2407 (2008)CrossRefGoogle Scholar
  125. J.N. Kutz, S.G. Evangelides, Dispersion-managed breathers with average normal dispersion. Opt. Lett. 23, 685 (1998)CrossRefGoogle Scholar
  126. G.N. Lewis, D. Lipkin, T.T. Magel, Reversible photochemical processes in rigid media. A study of the phosphorescent state. J. Am. Chem. Soc. 63, 3005 (1941)CrossRefGoogle Scholar
  127. G. Li, Recent advances in coherent optical communication. Adv. Opt. Photon. 1, 279 (2009)CrossRefGoogle Scholar
  128. Q. Lin, G.P. Agrawal, Raman response function for silica fibers. Opt. Lett. 31, 3086 (2006)CrossRefGoogle Scholar
  129. A.G. Litvak, V.I. Talanov, A parabolic equation for calculating the fields in dispersive nonlinear media. Izvestiya VUZ. Radiofizika 10, 539 (1967); Radiophysics quant. Electron. 10, 296 (1967)CrossRefGoogle Scholar
  130. L.Y. Liu, J.M. Huxley, E.P. Ippen, H.A. Haus, Self-starting additive-pulse mode locking of a Nd:YAG laser. Opt. Lett. 15, 553 (1990)CrossRefGoogle Scholar
  131. P.M. Lushnikov, Oscillating tails of a dispersion-managed soliton. J. Opt. Soc. Am. B 21, 1913 (2004)CrossRefGoogle Scholar
  132. R. Mack, The global fiber optics market: running faster than 40,000 km per hour, in Proceedings of 64th International Wire & Cable Symposium (IWCS) 2015 paper 1.1; for current figure R. Mack cited after H. Hogan, For optical fiber, more bandwidth looms, Photonics Spectra Mar 2017, p. 36Google Scholar
  133. M. Maeda, W.B. Sessa, W.I. Way, A. Yi-Yan, L. Curtis, R. Spicer, R.I. Laming, The effect of four-wave mixing in fibers on optical frequency-division multiplexed systems. J. Lightwave Technol. 8, 1402 (1990)CrossRefGoogle Scholar
  134. C. Mahnke, F. Mitschke, Possibility of an Akhmediev breather decaying into solitons. Phys. Rev. A 82, 033808 (2012)CrossRefGoogle Scholar
  135. C. Mahnke, F. Mitschke, Ultrashort light pulses generated from modulation instability: background removal and soliton content. Appl. Phys. B 116, 15 (2013)CrossRefGoogle Scholar
  136. P.V. Mamyshev, S.V. Chernikov, Ultrashort-pulse propagation in optical fibers. Opt. Lett. 15, 1076 (1990)CrossRefGoogle Scholar
  137. P.V. Mamyshev, L.F. Mollenauer, Wavelength-division-multiplexing channel energy self-equalization in a soliton transmission line by guiding filters. Opt. Lett. 21, 1658 (1996)CrossRefGoogle Scholar
  138. P.V. Mamyshev, L.F. Mollenauer, Soliton collisions in wavelength-division–multiplexed dispersion-managed systems. Opt. Lett. 24, 448 (1999)CrossRefGoogle Scholar
  139. S.V. Manakov, On the theory of two-dimensional stationary self-focusing of electromagnetic waves. Sov. Phys. JETP 38, 248 (1974)Google Scholar
  140. Marconi Introduces Soliton-Based Ultra Long Haul System at SuperComm 2001: 1.6 Terabit/s Solution Eliminates Need for High-Cost Regenerators, Marconi Corporation, press Release 5 June (2001). Archived at: https://www.thefreelibrary.com/Marconi+Introduces+Soliton-Based+Ultra+Long+Haul+System+At+Supercomm...-a075272418
  141. A. Maruta, Y. Yoshika, Family of multi-hump solitons propagating in dispersion-managed optical fiber transmission system and their existent parameter ranges. Eur. Phys. J. Spec. Top. 173, 139 (2009)CrossRefGoogle Scholar
  142. A. Maruta, T. Inoue, Y. Nonaka, Y. Yoshika, Bisoliton propagating in dispersion-managed system and its application to high-speed and long-haul optical transmission. IEEE J. Sel. Top. Quantum Electron. 8, 640 (2002)CrossRefGoogle Scholar
  143. F. Matera, S. Wabnitz, Nonlinear polarization evolution and instability in a twisted birefringent fiber. Opt. Lett. 11, 467 (1986)CrossRefGoogle Scholar
  144. V.J. Matsas, T.P. Newson, D.J. Richardson, D.J. Payne, Selfstarting passively mode-locked fiber ring soliton laser exploiting nonlinear polarization rotation. Electron. Lett. 28, 1391 (1992)CrossRefGoogle Scholar
  145. J. McEntee, Solitons go the distance in ultralong-haul DWDM, FibreSystems Europe, Jan 2003, p. 19Google Scholar
  146. C.J. McKinstrie, Frequency shifts caused by collisions between pulses in dispersion-managed systems. Opt. Commun. 205, 123 (2002)CrossRefGoogle Scholar
  147. R.J. Mears, L. Reekie, I.M. Jauncey, D.N. Payne, Low noise Erbium-doped fibre amplifier operating at 1.54 μm. Electron. Lett. 23, 1026 (1987)CrossRefGoogle Scholar
  148. A. Mecozzi, Soliton transmission control by Butterworth filters. Opt. Lett. 20, 1859 (1995)CrossRefGoogle Scholar
  149. A. Mecozzi, J.D. Moores, H.A. Haus, Y. Lai, Soliton transmission control. Opt. Lett. 16, 1841 (1991)CrossRefGoogle Scholar
  150. C.R. Menyuk, Stability of solitons in birefringent optical fibers I: equal propagation amplitudes. Opt. Lett. 12, 614 (1987)CrossRefGoogle Scholar
  151. C.R. Menyuk, Pulse propagation in an elliptically birefringent Kerr medium. IEEE J. Quantum Electron. 25, 2674 (1989)CrossRefGoogle Scholar
  152. P.P. Mitra, J.B. Stark, Nonlinear limits to the information capacity of optical fibre communications. Nature 411, 1027 (2001)CrossRefGoogle Scholar
  153. F. Mitschke, Optische Signalübertragung – Kommt das Ende des Wachstums? Plenary talk (in German). Symposium on Photonics, Spring Meeting of DPG. Verhandlg. DPG (VI) 37, SYIP II (2002)Google Scholar
  154. F. Mitschke, Fiber Optics. Physics and Technology, 2nd edn. (Springer, Berlin, 2016)Google Scholar
  155. F. Mitschke, L.F. Mollenauer, Stabilizing the soliton laser. IEEE J. Quantum Electron. 22, 2242 (1986a)CrossRefGoogle Scholar
  156. F.M. Mitschke, L.F. Mollenauer, Discovery of the soliton self frequency shift. Opt. Lett. 11, 659 (1986b)CrossRefGoogle Scholar
  157. F. Mitschke, L.F. Mollenauer, Ultrashort pulses from the soliton laser. Opt. Lett. 12, 407 (1987a)CrossRefGoogle Scholar
  158. F. Mitschke, L.F. Mollenauer, Experimental observation of interaction forces between solitons in optical fibers. Opt. Lett. 12, 355 (1987b)CrossRefGoogle Scholar
  159. F.M. Mitschke, G. Steinmeyer, M. Ostermeyer, U. Morgner, H. Welling, Additive pulse mode-locked Nd-YAG laser: an experimental account. Appl. Phys. B 56, 335 (1993)CrossRefGoogle Scholar
  160. L.F. Mollenauer, The future of fiber communications: solitons in an all-optical system. Opt. News 12, 42 (1986)CrossRefGoogle Scholar
  161. L.F. Mollenauer, K. Smith, Demonstration of soliton transmission over more than 4000 km in fiber with loss periodically compensated by Raman gain. Opt. Lett. 13, 675 (1988)CrossRefGoogle Scholar
  162. L.F. Mollenauer, R.H. Stolen, The soliton laser. Opt. Lett. 9, 13 (1984)CrossRefGoogle Scholar
  163. L.F. Mollenauer, R.H. Stolen, J.P. Gordon, Experimental observation of picosecond pulse narrowing and solitons in optical fibers. Phys. Rev. Lett. 45, 1095 (1980)CrossRefGoogle Scholar
  164. L.F. Mollenauer, R.H. Stolen, M.N. Islam, Experimental demonstration of soliton propagation in long fibers: loss compensated by Raman gain. Opt. Lett. 10, 229 (1985)CrossRefGoogle Scholar
  165. L.F. Mollenauer, M.J. Neubelt, S.G. Evangelides, J.P. Gordon, J.R. Simpson, L.G. Cohen, Experimental study of soliton transmission over more than 10,000 km in dispersion-shifted fiber. Opt. Lett. 15, 1203 (1990)CrossRefGoogle Scholar
  166. L.F. Mollenauer, S.G. Evangelides, J.P. Gordon, Wavelength division multiplexing with solitons in ultra-long distance transmission using lumped amplifiers. J. Lightwave Technol. 9, 362 (1991)CrossRefGoogle Scholar
  167. L.F. Mollenauer, E. Lichtman, G.T. Harvey, M.J. Neubelt, B.M. Nyman, Demonstration of error-free soliton transmission over more than 15,000 km at 5 Gbits/s, single-channel, and over more than 11,000 km at 10 Gbits/s in a two-channel WDM. Electron. Lett. 28, 792 (1992a)CrossRefGoogle Scholar
  168. L.F. Mollenauer, J.P. Gordon, S.G. Evangelides, The sliding-frequency guiding filter: an improved form of soliton jitter control. Opt. Lett. 17, 1575 (1992b)CrossRefGoogle Scholar
  169. L.F. Mollenauer, A. Grant, X. Liu, X. Wei, Ch. Xie, I. Kang, Experimental test of dense wavelength-division multiplexing using novel, periodic-group-delay-complemented dispersion compensation and dispersion-managed solitons. Opt. Lett. 28, 2043 (2003)CrossRefGoogle Scholar
  170. K. Mori, K. Sato, H. Takara, T. Ohara, Supercontinuum light source generating 50 GHz spaced optical ITU grid seamlessly over S-, C- and L-bands. Electron. Lett. 39, 544 (2003)CrossRefGoogle Scholar
  171. M. Morin, M. Piché, Interferential mode locking: Gaussian pulse analysis. Opt. Lett. 14, 1119 (1989)CrossRefGoogle Scholar
  172. R.-M. Mu, T. Yu, V.S. Grigoryan, C.R. Menyuk, Dynamics of the chirped return-to-zero modulation format. J. Lightwave Technol. 20, 47 (2002)CrossRefGoogle Scholar
  173. S. Mushid, B. Grossman, P. Narakorn, Spatial domain multiplexing: a new dimension in fiber optic multiplexing. Opt. Laser Technol. 40, 1030 (2008)CrossRefGoogle Scholar
  174. A. Mussot, A. Kudlinski, M. Droques, P. Szriftgiser, N. Akhmediev, Appearances and disappearances of Fermi Pasta Ulam recurrence in nonlinear fiber optics, in Conference on Lasers and Electro-Optics Europe and International Quantum Electronics Conference (CLEO EUROPE/IQEC) (2013)Google Scholar
  175. M. Nakazawa, E. Yamada, H. Kubota, K. Suzuki, 10 Gbit/s soliton data transmission over one million kilometers. Electron. Lett. 27, 1270 (1991)CrossRefGoogle Scholar
  176. M. Nakazawa, K. Suzuki, E. Yamada, H. Kubota, Y. Kimura, M. Takaya, Experimental demonstration of soliton data transmission over unlimited distances with soliton control in time and frequency domains. Electron. Lett. 29, 729 (1993)CrossRefGoogle Scholar
  177. 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. 33, 1726 (1997)CrossRefGoogle Scholar
  178. O.G. Okhotnikov (ed.), Fiber Lasers (Wiley-VCH, Weinheim, 2012)Google Scholar
  179. F. Ouellette, M. Piché, Ultrashort pulse reshaping with a nonlinear FabryPerot cavity matched to a train of short pulses. J. Opt. Soc. Am. B 5, 1228 (1988)CrossRefGoogle Scholar
  180. C. Parè, P.-A. Bèlanger, Antisymmetric soliton in a dispersion-managed system. Opt. Commun. 168, 103 (1999)CrossRefGoogle Scholar
  181. D.H. Peregrine, Water waves, nonlinear Schrödinger equations and their solutions. J. Aust. Math. Soc. B 25, 16 (1983)CrossRefGoogle Scholar
  182. A.R. Pratt, P. Harper, S.B. Alleston, P. Bontemps, B. Charbonnier, W. Forysiak, L. Gleeson, D.S. Govan, G.L. Jones, D. Nesset, J.H.B. Nijhof, I.D. Phillips, M.F.C. Stephens, A.P. Walsh, T. Widdowson, N.J. Doran, 5745 km DWDM transcontinental field trial using 10 Gbit/s dispersion managed solitons and dynamic gain equalization, paper PD26-1, in Optical Fiber Communications Conference OFC (2003)Google Scholar
  183. J.E. Prilepsky, S.A. Derevyanko, K.J. Blow, I. Gabitov, S.K. Turitsyn, Nonlinear inverse synthesis and eigenvalue division multiplexing in optical fiber channels. Phys. Rev. Lett. 113, 013901 (2014)CrossRefGoogle Scholar
  184. D. Qian, E. Ip, M.-F. Huang, M.-J. Li, A. Dogariu, S. Zhang, Y. Shao, Y.-K. Huang, Y. Zhang, X. Cheng, Y. Tian, P. Ji, A. Collier, Y. Geng, J. Linares, C. Montero, V. Moreno, X. Prieto, T. Wang, 1.05 Pb/s transmission with 109 b/s/Hz spectral efficiency using hybrid single- and few-mode cores, FW6C.3, in Frontiers in Optics/Laser Science Conference (FiO/LS) XXVIII (2012)Google Scholar
  185. J.K. Ranka, R.S. Windeler, A.J. Stentz, Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm. Opt. Lett. 25, 25 (2000)CrossRefGoogle Scholar
  186. D.J. Richardson, Filling the light pipe. Science 30, 329 (2010)Google Scholar
  187. W.H. Renninger, A. Chong, F.W. Wise, Self-similar pulse evolution in an all-normal-dispersion laser. Phys. Rev. A 82, 021805 (2010)CrossRefGoogle Scholar
  188. P. Rohrmann, A. Hause, F. Mitschke, Solitons beyond binary: possibility of fibre-optic transmission of two bits per clock period. Sci. Rep. 2, 866 (2012)CrossRefGoogle Scholar
  189. P. Rohrmann, A. Hause, F. Mitschke, Two-soliton and three-soliton molecules in optical fibers. Phys. Rev. A 87, 043834 (2013)CrossRefGoogle Scholar
  190. S. Roy, S.K. Bhadra, G.P. Agrawal, Perturbation of higher-order solitons by fourth-order dispersion in optical fibers. Opt. Commun. 282, 3798 (2009)CrossRefGoogle Scholar
  191. E. Rubino, J. McLenaghan, S.C. Kehr, F. Belgiorno, D. Townsend, S. Rohr, C.E. Kuklewicz, U. Leonhardt, F. König, D. Faccio, Negative-frequency resonant radiation. Phys. Rev. Lett. 108, 253901 (2012)CrossRefGoogle Scholar
  192. P. Russell, Photonic crystal fibers. Science 299, 358 (2003)CrossRefGoogle Scholar
  193. K. Saitoh, S. Matsuo, Multicore fiber technology. J. Lightwave Technol. 34, 55 (2016)CrossRefGoogle Scholar
  194. J. Satsuma, N. Yajima, Initial value problem of one-dimensional self-modulation of nonlinear waves in dispersive media. Suppl. Progr. Theor. Phys. 55, 284 (1974)CrossRefGoogle Scholar
  195. C.E. Shannon, A mathematical theory of communication. Bell Syst. Tech. J. 27, 379, 623 (1948)CrossRefGoogle Scholar
  196. M. Shkarayev, M.G. Stepanov, New bisoliton solutions in dispersion managed systems. Phys. D 238, 840 (2009)CrossRefGoogle Scholar
  197. V.I. Shrira, V.V. Geogjaev, What makes the Peregrine soliton so special as a prototype of freak waves? J. Eng. Math. 67, 11 (2010)CrossRefGoogle Scholar
  198. D.V. Skryabin, F. Luan, J.C. Knight, P.S.J. Russell, Soliton self-frequency shift cancellation in photonic crystal fibers. Science 301, 1705 (2003)CrossRefGoogle Scholar
  199. K. Smith, L.F. Mollenauer, Experimental onservation of adiabatic compression and expansion of soliton pulses over long fiber paths. Opt. Lett. 14, 751 (1989)CrossRefGoogle Scholar
  200. N.J. Smith, F.M. Knox, N.J. Doran, K.J. Blow, I. Bennion, Enhanced power solitons in optical fibres with periodic dispersion management. Electron. Lett. 32, 54 (1996)CrossRefGoogle Scholar
  201. Soliton wave receives crowd of admirers. Nature 376, 373 (1995)Google Scholar
  202. D.R. Solli, C. Ropers, P. Koonath, B. Jalali, Optical rogue waves. Nature 450, 1054 (2007)CrossRefGoogle Scholar
  203. J.M. Soto-Crespo, N.N. Akhmediev, V.V. Afanasjev, Stability of the pulselike solutions of the quintic complex Ginzburg-Landau equation. J. Opt. Soc. Am. B 13, 1439 (1996)CrossRefGoogle Scholar
  204. J.M. Soto-Crespo, M. Grapinet, P. Grelu, N. Akhmediev, Bifurcations and multiple-period soliton pulsations in a passively mode-locked fiber laser. Phys. Rev. E 70, 066612 (2004)CrossRefGoogle Scholar
  205. R.H. Stolen, C. Lin, Self-phase-modulation in silica optical fibers. Phys. Rev. A 17, 1448 (1978)CrossRefGoogle Scholar
  206. R.H. Stolen, C. Lee, R.K. Jain, Development of the stimulated Raman spectrum in single-mode silica fibers. J. Opt. Soc. Am. B 1, 652 (1984)CrossRefGoogle Scholar
  207. R.H. Stolen, J.P. Gordon, W.J. Tomlinson, H.A. Haus, Raman response function of silica-core fibers. J. Opt. Soc. Am. B 6, 1159 (1989)CrossRefGoogle Scholar
  208. M. Stratmann, M. Böhm, F. Mitschke, Stable propagation of dark solitons in dispersion maps of either sign of path-average dispersion. Electron. Lett. 37, 1182 (2001)CrossRefGoogle Scholar
  209. M. Stratmann, T. Pagel, F. Mitschke, Experimental observation of temporal soliton molecules. Phys. Rev. Lett. 95, 143902 (2005)CrossRefGoogle Scholar
  210. M. Suzuki, N. Edagawa, H. Taga, H. Tanaka, S. Yamamoto, S. Akiba, Feasibility demonstration of 20 Gbit/s single channel soliton transmission over 11,500 km using alternating amplitude solitons. Electron. Lett. 30, 1083 (1994)CrossRefGoogle Scholar
  211. M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, H. Taga, A. Akiba, Reduction of Gordon-Haus timing jitter by periodic dispersion compensation in soliton transmission. Electron. Lett. 31, 2027 (1995)CrossRefGoogle Scholar
  212. J. Swiderski, M. Maciejewska, Watt-level, all-fiber supercontinuum source based on telecom-grade fiber components. Appl. Phys. B 109, 177 (2012)CrossRefGoogle Scholar
  213. K. Tai, A. Hasegawa, A. Tomita, Observation of modulational instability in optical fiber. Phys. Rev. Lett. 56, 135 (1986)CrossRefGoogle Scholar
  214. H. Takara, A. Sano, T. Kobayashi, H. Kubota, H. Kawakami, A. Matsuura, Y. Miyamoto, Y. Abe, H. Ono, K. Shikama, Y. Goto, K. Tsujikawa, Y. Sasaki, I Ishida, K. Takenaga, S. Matsuo, K. Saitoh, M. Koshiba, T. Morioka, 1.01-Pb/s (12 SDM/222 WDM/456 Gb/s) Crosstalk-Managed Transmission with 91.4-b/s/Hz Aggregate Spectral Efficiency, in European Conference on Optical Communication (ECOC), Th 3 C. 1 (2012)Google Scholar
  215. K. Tamura, E.P. Ippen, H.A. Haus, L.E. Nelson, 77-fs pulse generation from a stretched-pulse mode-locked all-fiber ring laser. Opt. Lett. 18, 1080 (1993)CrossRefGoogle Scholar
  216. T. Taniuti, N. Yajima, Perturbation method for a nonlinear wave modulation. I. J. Math. Phys. 10, 1369 (1969)CrossRefGoogle Scholar
  217. P. Taylor, The Shape of the Draupner Wave of 1st January, Department of Engineering Science, University of Oxford. http://www.icms.org.uk/archive/meetings/2005/roguewaves/presentations/Taylor.pdf
  218. B.D.H. Tellegen, Interaction between Radio-Waves? Nature 131, 840 (1933)CrossRefGoogle Scholar
  219. The Atlantic Cable website, History of the Atlantic Cable & Undersea Communications: Cyrus Field (2011). http://atlantic-cable.com//Field/
  220. The world’s first terabit transcontinental optical communications system exploiting dispersion managed solitons, Impact case study REF3b, Research Excellence Framework (2014). www.impact.ref.ac.uk/casestudies2/refservice.svc/GetCaseStudyPDF/37025
  221. R.W. Tkach, Scaling optical communications for the next decade and beyond. Bell Labs Techn. J. 14, 3 (2010)CrossRefGoogle Scholar
  222. W.J. Tomlinson, R.H. Stolen, A.M. Johnson, Optical wave breaking of pulses in nonlinear optical fiber. Opt. Lett. 10, 457 (1985)CrossRefGoogle Scholar
  223. J.C. Travers, A.B. Rulkov, B.A. Cumberland, S.V. Popov, J.R. Taylor, Visible supercontinuum generation in photonic crystal fibers with a 400 W continuous wave fiber laser. Opt. Express 16, 14435 (2008)CrossRefGoogle Scholar
  224. M.L.V. Tse, P. Horak, N.G.R. Broderick, J.H.V. Price, J.R. Hayes, D.J. Richardson, Supercontinuum generation at 1.06 μm in holey fibers with dispersion flattened profiles. Opt. Express 14, 4445 (2006)CrossRefGoogle Scholar
  225. S.K. Turitsyn, Nonlinear communication channels with capacity above the linear Shannon limit. Opt. Lett. 37, 3600 (2012)CrossRefGoogle Scholar
  226. S.K. Turytsin, E.G. Shapiro, Dispersion-managed solitons in optical amplifier transmission systems with zero average dispersion. Opt. Lett. 23, 682 (1998)CrossRefGoogle Scholar
  227. S. Turitsyn, E. Shapiro, S. Medvedev, M.P. Fedoruk, V. Mezentsev, Physics and mathematics of dispersion managed optical solitons. C. R. Phys. 4, 145 (2003)CrossRefGoogle Scholar
  228. S.K. Turitsyn, B.G. Bale, M.P. Fedoruk, Dispersion-managed solitons in fibre systems and lasers. Phys. Rep. 521, 135 (2012)CrossRefGoogle Scholar
  229. I.M. Uzunov, V.D. Stoev, T.I. Tzoleva, Influence of the initial phase difference between pulses on the N-soliton interaction in trains of unequal solitons in optical fibers. Opt. Commun. 97, 307 (1993)CrossRefGoogle Scholar
  230. P.K.A. Wai, C.R. Menyuk, Y.C. Lee, H.H. Chen, Nonlinear pulse propagation in the neighborhood of the zero-dispersion wavelength of monomode optical fibers. Opt. Lett. 11, 464 (1986)CrossRefGoogle Scholar
  231. P.K. Wai, C.R. Menyuk, H.H. Chen, Stability of solitons in randomly varying birefringent fibers. Opt. Lett. 16, 1231 (1991)CrossRefGoogle Scholar
  232. J. Wang, Analysis of passive additive-pulse mode locking with eigenmode theory. IEEE J. Quantum Electron. 28, 562 (1992)CrossRefGoogle Scholar
  233. H.G. Winful, Polarization instabilities in birefringent nonlinear media: application to fiber-optic devices. Opt. Lett. 11, 33 (1985)CrossRefGoogle Scholar
  234. C. Xie, L. Möller, H. Haunstein, S. Hunsche, Comparison of system tolerance to polarization-mode dispersion between different modulation formats. IEEE Photon. Technol. Lett. 15, 1168 (2003)CrossRefGoogle Scholar
  235. M.I. Yousefi, F.R. Kschischang, Information transmission using the nonlinear Fourier transform, Part I: mathematical tools. IEEE Trans. Inf. Theory 60, 4312 (2014a)Google Scholar
  236. M.I. Yousefi, F.R. Kschischang, Information transmission using the nonlinear Fourier transform, Part II: numerical methods. IEEE Trans. Inf. Theory 60, 4329 (2014b)Google Scholar
  237. V.E. Zakharov, L.A. Ostrovsky, Modulation instability: the beginning. Phys. D 238, 540 (2009)CrossRefGoogle Scholar
  238. V.E. Zakharov, A.B. Shabat, Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media. Sov. Phys. JETP 34, 62 (1972)Google Scholar
  239. V.E. Zakharov, A.B. Shabat, Interaction between solitons in a stable medium. Zh. Eksp. Teor. Fiz 64, 1627 (1973); Sov. Phys.-JETP 37, 823 (1973)Google Scholar
  240. X. Zhao, X. Liu, S. Wang, W. Wang, Y. Han, Z. Liu, S. Li, L. Hou, Numerical calculation of phase-matching properties in photonic crystal fibers with three and four zero-dispersion wavelengths. Opt. Express 23, 27899 (2015)CrossRefGoogle Scholar
  241. X. Zhu, P.N. Kean, W. Sibbett, Coupled-cavity mode locking of a KCl:Tl laser using an Erbium-doped optical fiber. Opt. Lett. 14, 1192 (1989)CrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Institut für PhysikUniversität RostockRostockGermany

Personalised recommendations