Soliton Content of Fiber-Optic Light Pulses

This is a review of fiber-optic soliton propagation and of methods to determine the soliton content in a pulse, group of pulses or a similar structure. Of central importance is the nonlinear Schrodinger equation, an integrable equation that possesses soliton solutions, among others. Several extensions and generalizations of this equation are customary to better approximate real-world systems, but this comes at the expense of losing integrability. Depending on the experimental situation under discussion, a variety of pulse shapes or pulse groups can arise. In each case, the structure will contain one or several solitons plus small amplitude radiation. Direct scattering transform, also known as nonlinear Fourier transform, serves to quantify the soliton content in a given pulse structure, but it relies on integrability. Soliton radiation beat analysis does not suffer from this restriction, but has other limitations. The relative advantages and disadvantages of the methods are compared.

[1]  C. Desem,et al.  Reducing soliton interaction in single-mode optical fibres , 1987 .

[2]  A. Hasegawa,et al.  Nonlinear pulse propagation in a monomode dielectric guide , 1987 .

[3]  S. Turitsyn,et al.  Dispersion-managed solitons in optical amplifier transmission systems with zero average dispersion. , 1998, Optics letters.

[4]  J. Gordon.  Interaction forces among solitons in optical fibers. , 1983, Optics letters.

[5]  Govind P. Agrawal,et al.  Nonlinear Fiber Optics , 1989 .

[6]  A. Hasegawa,et al.  Amplification and reshaping of optical solitons in a glass fiber-I. , 1982, Optics letters.

[7]  F. M. Knox,et al.  Stable soliton-like propagation in dispersion managed systems with net anomalous, zero and normal dispersion , 1997 .

[8]  Soliton radiation beat analysis of optical pulses generated from two continuous-wave lasers. , 2015, Chaos.

[9]  B. Jalali,et al.  Optical rogue waves , 2007, Nature.

[10]  Jaroslaw E Prilepsky,et al.  Breakup of a multisoliton state of the linearly damped nonlinear Schrödinger equation. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  Ben M. Herbst,et al.  A numerical study of the large-period limit of a Zakharov–Shabat eigenvalue problem with periodic potentials , 2012 .

[12]  V. Zakharov,et al.  Exact Theory of Two-dimensional Self-focusing and One-dimensional Self-modulation of Waves in Nonlinear Media , 1970 .

[13]  A. Maruta,et al.  Soliton's eigenvalue based analysis on the generation mechanism of rogue wave phenomenon in optical fibers exhibiting weak third order dispersion. , 2015, Optics express.

[14]  Fedor Mitschke,et al.  Solitons Beyond Binary: Possibility of Fibre-Optic Transmission of Two Bits per Clock Period , 2012, Scientific Reports.

[15]  M. Kamalian,et al.  Periodic nonlinear Fourier transform for fiber-optic communications, Part II: eigenvalue communication. , 2016, Optics express.

[16]  Boris A. Malomed A. Schwache F. Mitschke.  Soliton Lattice and Gas in Passive Fiber-Ring Resonators , 1998 .

[17]  K. Khusnutdinova.  Nonlinear waves in integrable and nonintegrable systems (Mathematical Modeling and Computation 16) By Jianke Yang , 2015 .

[18]  Sergei K. Turitsyn,et al.  Dispersion-managed solitons in fibre systems and lasers , 2012 .

[19]  Hermann A. Haus,et al.  Raman response function of silica-core fibers , 1989, Annual Meeting Optical Society of America.

[20]  J. Kutz,et al.  Dispersion-managed breathers with average normal dispersion. , 1998, Optics letters.

[21]  P. Lax.  INTEGRALS OF NONLINEAR EQUATIONS OF EVOLUTION AND SOLITARY WAVES. , 1968 .

[22]  A. Hasegawa,et al.  Fission of optical solitons induced by stimulated Raman effect. , 1988, Optics letters.

[23]  F. Mitschke,et al.  Experimental observation of temporal soliton molecules. , 2005, Physical review letters.

[24]  A. Osborne,et al.  Computation of the direct scattering transform for the nonlinear Schroedinger equation , 1992 .

[25]  D. H. Peregrine,et al.  Water waves, nonlinear Schrödinger equations and their solutions , 1983, The Journal of the Australian Mathematical Society. Series B. Applied Mathematics.

[26]  W. Forysiak,et al.  The averaging method for finding exactly periodic dispersion-managed solitons , 2000, IEEE Journal of Selected Topics in Quantum Electronics.

[27]  F. Amrani,et al.  Dissipative solitons compounds in a fiber laser. Analogy with the states of the matter , 2010 .

[28]  C. S. Gardner,et al.  Method for solving the Korteweg-deVries equation , 1967 .

[29]  N. Zabusky,et al.  Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial States , 1965 .

[30]  L. Mollenauer,et al.  Experimental observation of interaction forces between solitons in optical fibers. , 1987, Optics letters.

[31]  F. Mitschke,et al.  Ultrashort light pulses generated from modulation instability: background removal and soliton content , 2014 .

[32]  P. Grelu,et al.  Dissipative solitons for mode-locked lasers , 2012, Nature Photonics.

[33]  Fedor Mitschke,et al.  Soliton content of arbitrarily shaped light pulses in fibers analysed using a soliton-radiation beat pattern , 2007 .

[34]  Fedor Mitschke,et al.  Possibility of an Akhmediev breather decaying into solitons , 2012 .

[35]  A. Husakou,et al.  Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers. , 2001, Physical review letters.

[36]  N. Akhmediev,et al.  Modulation instability and periodic solutions of the nonlinear Schrödinger equation , 1986 .

[37]  M. Ablowitz,et al.  Nonlinear-evolution equations of physical significance , 1973 .

[38]  Akira Hasegawa,et al.  Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion , 1973 .

[39]  Nail Akhmediev,et al.  Stability of the pulselike solutions of the quintic complex Ginzburg-Landau equation , 1996 .

[40]  J. Fatome,et al.  Observation of Kuznetsov-Ma soliton dynamics in optical fibre , 2012, Scientific Reports.

[41]  H. Vincent Poor,et al.  Introducing the fast nonlinear Fourier transform , 2013, 2013 IEEE International Conference on Acoustics, Speech and Signal Processing.

[42]  Sergei K. Turitsyn,et al.  Nonlinear Fourier Transform for Optical Data Processing and Transmission: Advances and Perspectives , 2017, 2018 European Conference on Optical Communication (ECOC).

[43]  A. Hasegawa,et al.  Generation of a train of soliton pulses by induced modulational instability in optical fibers. , 1984, Optics letters.

[44]  A. Hasegawa,et al.  Eigenvalue communication , 1993 .

[45]  F. Mitschke,et al.  Solitons in lossy fibers , 2007 .

[46]  M. Ablowitz,et al.  The Periodic Cubic Schrõdinger Equation , 1981 .

[47]  Sarah Rothstein,et al.  Optical Solitons From Fibers To Photonic Crystals , 2016 .

[48]  Chinlon Lin,et al.  Self-phase modulation in silica optical fibers (A) , 1978 .

[49]  Heuer,et al.  Dynamical pulse shaping in a nonlinear resonator. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[50]  Fedor Mitschke,et al.  Slow oscillations of dispersion-managed solitons , 2010 .

[51]  H. Vincent Poor,et al.  Fast Numerical Nonlinear Fourier Transforms , 2014, IEEE Transactions on Information Theory.

[52]  S V Chernikov,et al.  Ultrashort-pulse propagation in optical fibers. , 1990, Optics letters.

[53]  M. Zajnulina,et al.  Characteristics and stability of soliton crystals in optical fibres for the purpose of optical frequency comb generation , 2017, 1704.06083.

[54]  D. Schrader.  Explicit calculation of N-soliton solutions of the nonlinear Schroedinger equation , 1995 .

[55]  F. Mitschke,et al.  Binding mechanism of temporal soliton molecules , 2008 .

[56]  F. Dias,et al.  Modulation instability, Akhmediev Breathers and continuous wave supercontinuum generation. , 2009, Optics express.

[57]  S. Bhadra,et al.  Perturbation of higher-order solitons by fourth-order dispersion in optical fibers , 2009 .

[58]  H. Haus,et al.  Dispersion-managed solitons with net positive dispersion. , 1998, Optics letters.

[59]  F. Mitschke,et al.  Phase structure of soliton molecules , 2007 .

[60]  Ivan M. Uzunov,et al.  BREAK UP OF N-SOLITON BOUND STATES DUE TO INTRAPULSE RAMAN SCATTERING AND THIRD-ORDER DISPERSION : AN EIGENVALUE ANALYSIS , 1997 .

[61]  Frank R. Kschischang,et al.  Information Transmission Using the Nonlinear Fourier Transform, Part II: Numerical Methods , 2012, IEEE Transactions on Information Theory.

[62]  Fedor Mitschke,et al.  Fiber Optics: Physics and Technology , 2010 .

[63]  N. J. Smith,et al.  Enhanced power solitons in optical fibres with periodic dispersion management , 1996 .

[64]  Pierre Suret,et al.  Inverse scattering transform analysis of rogue waves using local periodization procedure , 2015, Scientific Reports.

[65]  Cristina Masoller,et al.  Roadmap on optical rogue waves and extreme events , 2016 .

[66]  Sergei K. Turitsyn,et al.  Physics and mathematics of dispersion-managed optical solitons , 2003 .

[67]  G. Agrawal,et al.  Raman response function for silica fibers. , 2006, Optics letters.

[68]  N Akhmediev,et al.  Breather turbulence versus soliton turbulence: Rogue waves, probability density functions, and spectral features. , 2016, Physical review. E.

[69]  Roger H. Stolen,et al.  Development of the stimulated Raman spectrum in single-mode silica fibers , 1984 .

[70]  J. Gordon,et al.  Theory of the soliton self-frequency shift. , 1986, Optics letters.

[71]  F. Mitschke,et al.  Two-soliton and three-soliton molecules in optical fibers , 2013 .

[72]  J. Dudley,et al.  Supercontinuum generation in photonic crystal fiber , 2006 .

[73]  Yan‐Chow Ma,et al.  The Perturbed Plane‐Wave Solutions of the Cubic Schrödinger Equation , 1979 .

[74]  S. V. Manakov,et al.  Nonlinear Fraunhofer diffraction , 1974 .

[75]  P. Grelu,et al.  Soliton rains in a fiber laser: An experimental study , 2010 .

[76]  Higher-order equilibria of temporal soliton molecules in dispersion-managed fibers , 2013 .

[77]  Fedor Mitschke,et al.  Soliton-radiation beat analysis. , 2006 .

[78]  James P. Gordon,et al.  Experimental observation of picosecond pulse narrowing and solitons in optical fibers (A) , 1980 .

[79]  C. Menyuk,et al.  Dispersion-managed solitons at normal average dispersion. , 1998, Optics letters.

[80]  Alfred R. Osborne,et al.  Nonlinear Ocean Waves and the Inverse Scattering Transform , 2010 .

[81]  D. Kaup.  A Perturbation Expansion for the Zakharov–Shabat Inverse Scattering Transform , 1976 .

[82]  Pavel M. Lushnikov,et al.  Oscillating tails of a dispersion-managed soliton , 2004 .

[83]  J. Satsuma,et al.  B Initial Value Problems of One-Dimensional self-Modulation of Nonlinear Waves in Dispersive Media (Part V. Initial Value Problems) , 1975 .

[84]  Frédéric Dias,et al.  The Peregrine soliton in nonlinear fibre optics , 2010 .

[85]  Adrian Ankiewicz,et al.  Dissipative solitons : from optics to biology and medicine , 2008 .

[86]  A. Maruta,et al.  Characterization of optical rogue wave based on solitons' eigenvalues of the integrable higher-order nonlinear Schrödinger equation , 2017 .

[87]  N Akhmediev,et al.  Spectral dynamics of modulation instability described using Akhmediev breather theory. , 2011, Optics letters.

[88]  on,et al.  Periodic nonlinear Fourier transform for fiber-optic communications , Part I : Theory and numerical methods , 2016 .

[89]  F. Mitschke,et al.  PROPERTIES OF AN OPTICAL SOLITON GAS , 1997 .

[90]  Chen,et al.  Nonlinear self-modulation: An exactly solvable model. , 1988, Physical review. A, General physics.

[91]  Hiroshi Inoue,et al.  Inverse Scattering Method for the Nonlinear Evolution Equations under Nonvanishing Conditions , 1978 .

[92]  V. Matveev,et al.  Schrödinger operators with finite-gap spectrum and N-soliton solutions of the Korteweg-de Vries equation , 1975 .

[93]  P. Grelu,et al.  Temporal soliton >molecules> in mode-locked lasers: Collisions, pulsations, and vibrations , 2008 .

[94]  Dan Anderson,et al.  Nonlinear asymmetric self-phase modulation and self-steepening of pulses in long optical waveguides , 1983 .