Soliton Molecules and Multisoliton States in Ultrafast Fibre Lasers: Intrinsic Complexes in Dissipative Systems

Benefiting from ultrafast temporal resolution, broadband spectral bandwidth, as well as high peak power, passively mode-locked fibre lasers have attracted growing interest and exhibited great potential from fundamental sciences to industrial and military applications. As a nonlinear system containing complex interactions from gain, loss, nonlinearity, dispersion, etc., ultrafast fibre lasers deliver not only conventional single soliton but also soliton bunching with different types. In analogy to molecules consisting of several atoms in chemistry, soliton molecules (in other words, bound solitons) in fibre lasers are of vital importance for in-depth understanding of the nonlinear interaction mechanism and further exploration for high-capacity fibre-optic communications. In this Review, we summarize the state-of-the-art advances on soliton molecules in ultrafast fibre lasers. A variety of soliton molecules with different numbers of soliton, phase-differences and pulse separations were experimentally observed owing to the flexibility of parameters such as mode-locking techniques and dispersion control. Numerical simulations clearly unravel how different nonlinear interactions contribute to formation of soliton molecules. Analysis of the stability and the underlying physical mechanisms of bound solitons bring important insights to this field. For a complete view of nonlinear optical phenomena in fibre lasers, other dissipative states such as vibrating soliton pairs, soliton rains, rogue waves and coexisting dissipative solitons are also discussed. With development of advanced real-time detection techniques, the internal motion of different pulsing states is anticipated to be characterized, rendering fibre lasers a versatile platform for nonlinear complex dynamics and various practical applications.

[1]  A. Komarov,et al.  Quantization of binding energy of structural solitons in passive mode-locked fiber lasers , 2009 .

[2]  D. Churkin,et al.  Rogue waves generation via nonlinear soliton collision in multiple-soliton state of a mode-locked fiber laser. , 2016, Optics express.

[3]  O. Okhotnikov,et al.  Impact of Gain Medium Dispersion on Stability of Soliton Bound States in Fiber Laser , 2013, IEEE Photonics Technology Letters.

[4]  H. Tam,et al.  Bound states of dispersion-managed solitons in a fiber laser at near zero dispersion. , 2007, Applied optics.

[5]  Anthony Turner,et al.  Proceedings of the Society of Photo-Optical Instrumentation Engineers , 2004 .

[6]  Changxi Yang,et al.  Harmonic mode-locking in a Tm-doped fiber laser: Characterization of its timing jitter and ultralong starting dynamics , 2015 .

[7]  Gianluca Galzerano,et al.  Double-Wall Carbon Nanotube Hybrid Mode-Locker in Tm-doped Fibre Laser: A Novel Mechanism for Robust Bound-State Solitons Generation , 2017, Scientific Reports.

[8]  Olivier Pottiez,et al.  Adjustable noiselike pulses from a figure-eight fiber laser , 2011 .

[9]  F. Lederer,et al.  Multi-soliton complexes in mode-locked fiber lasers , 2011 .

[10]  D. Tang,et al.  Bound States of Vector Dissipative Solitons , 2015, IEEE Photonics Journal.

[11]  P. Grelu,et al.  Soliton pairs in a fiber laser: from anomalous to normal average dispersion regime. , 2003, Optics express.

[12]  J. Soto-Crespo,et al.  Experimental evidence for soliton explosions. , 2002, Physical review letters.

[13]  Frank W. Wise,et al.  Properties of normal-dispersion femtosecond fiber lasers , 2008 .

[14]  Adrian Ankiewicz,et al.  Stable soliton pairs in optical transmission lines and fiber lasers , 1998 .

[15]  B. Malomed,et al.  Bound solitons in the nonlinear Schrödinger-Ginzburg-Landau equation. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[16]  Nail Akhmediev,et al.  Dissipative rogue waves: extreme pulses generated by passively mode-locked lasers. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  B. Malomed,et al.  Stability of bound states of pulses in the Ginzburg-Landau equations , 2008 .

[18]  Changxi Yang,et al.  Dissipative Rogue Waves Among Noise-Like Pulses in a Tm Fiber Laser Mode Locked by a Monolayer MoS2 Saturable Absorber , 2018, IEEE Journal of Selected Topics in Quantum Electronics.

[19]  P. Grelu,et al.  Vibrating soliton pairs in a mode-locked laser cavity. , 2006, Optics letters.

[20]  Y. Lai,et al.  Bound Soliton Fiber Laser Mode-Locking Without Saturable Absorption Effect , 2016, IEEE Photonics Journal.

[21]  A. V. Luchnikov,et al.  Long-range interaction of picosecond solitons through excitation of acoustic waves in optical fibers , 1992 .

[22]  M. Bolshtyansky,et al.  Model of temperature dependence for gain shape of erbium-doped fiber amplifier , 2000, Journal of Lightwave Technology.

[23]  Temperature Dependence of the Gain in Doped Fibers , 1991 .

[24]  J. Soto-Crespo,et al.  Multisoliton regime of pulse generation by lasers passively mode locked with a slow saturable absorber , 1999 .

[25]  Jing Li,et al.  A Simplified Method of Making Flexible Blue LEDs on a Plastic Substrate , 2015, IEEE Photonics Journal.

[26]  N. Akhmediev,et al.  Soliton interaction and bound states in amplified-damped fiber systems. , 1995, Optics letters.

[27]  P. Grelu,et al.  Soliton complexes in dissipative systems: vibrating, shaking, and mixed soliton pairs. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[28]  Rabah Attia,et al.  Numerical demonstration of generation of bound solitons in figure of eight microstructured fiber laser in normal dispersion regime , 2013 .

[29]  D. Mao,et al.  Harmonic mode locking of bound-state solitons fiber laser based on MoS(2) saturable absorber. , 2015, Optics express.

[30]  Hung-yi Lee,et al.  Bound States of Dispersion-Managed Solitons From Single-Mode Yb-Doped Fiber Laser at Net-Normal Dispersion , 2015, IEEE Photonics Journal.

[31]  C R Menyuk,et al.  Acoustic effect in passively mode-locked fiber ring lasers. , 1995, Optics letters.

[32]  Pu Zhou,et al.  Pulse bundles and passive harmonic mode-locked pulses in Tm-doped fiber laser based on nonlinear polarization rotation. , 2014, Optics express.

[33]  Chengying Bao,et al.  Observation of Coexisting Dissipative Solitons in a Mode-Locked Fiber Laser. , 2015, Physical review letters.

[34]  D. Y. Tang,et al.  Mechanism of Spectrum Moving, Narrowing, Broadening, and Wavelength Switching of Dissipative Solitons in All-Normal-Dispersion Yb-Fiber Lasers , 2014, IEEE Photonics Journal.

[35]  B. Jalali,et al.  Real-time spectral interferometry probes the internal dynamics of femtosecond soliton molecules , 2017, Science.

[36]  J. Soto-Crespo,et al.  Composite solitons and two-pulse generation in passively mode-locked lasers modeled by the complex quintic Swift-Hohenberg equation. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[37]  U. Khawaja Stability and dynamics of two-soliton molecules , 2010, 1004.3000.

[38]  S. Ruan,et al.  Soliton dynamic patterns of a passively mode-locked fiber laser operating in a 2 μm region , 2015 .

[39]  Malomed Bound solitons in coupled nonlinear Schrödinger equations. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[40]  François Sanchez,et al.  Ultrahigh-repetition-rate bound-soliton harmonic passive mode-locked fiber lasers. , 2008, Optics letters.

[41]  J. Bai,et al.  Observation of bound state solitons in tunable all-polarization-maintaining Yb-doped fiber laser , 2017 .

[42]  P. Grelu,et al.  Phase-locked soliton pairs in a stretched-pulse fiber laser. , 2002, Optics letters.

[43]  François Gutty,et al.  Relative phase locking of pulses in a passively mode-locked fiber laser , 2003 .

[44]  A Cylindrical Tuber Encapsulant Geometry for Enhancing Optical Performance of Chip-on-Board Packaging Light-Emitting Diodes , 2016, IEEE Photonics Journal.

[45]  F. Amrani,et al.  Dispersive-wave mechanism of interaction between ultrashort pulses in passive mode-locked fiber lasers , 2012 .

[46]  Miro Erkintalo,et al.  Raman rogue waves in a partially mode-locked fiber laser. , 2014, Optics letters.

[47]  A Ankiewicz,et al.  Pulsating, creeping, and erupting solitons in dissipative systems. , 2000, Physical review letters.

[48]  P. Grelu,et al.  Rains of solitons in a fiber laser. , 2009, Optics express.

[49]  Changxi Yang,et al.  Suppression of continuous lasing in a carbon nanotube polyimide film mode-locked erbium-doped fiber laser. , 2011, Applied optics.

[50]  G. Millot,et al.  Selection of Extreme Events Generated in Raman Fiber Amplifiers Through Spectral Offset Filtering , 2010, IEEE Journal of Quantum Electronics.

[51]  P. Grelu,et al.  Real-Time Observation of Internal Motion within Ultrafast Dissipative Optical Soliton Molecules. , 2017, Physical review letters.

[52]  S. Kelly,et al.  Characteristic sideband instability of periodically amplified average soliton , 1992 .

[53]  M. Piché,et al.  Origin of the bound states of pulses in the stretched-pulse fiber laser. , 2009, Optics express.

[54]  Kevin P. Chen,et al.  All-fiber ultrafast thulium-doped fiber ring laser with dissipative soliton and noise-like output in normal dispersion by single-wall carbon nanotubes , 2013 .

[55]  Deming Liu,et al.  Group-velocity-locked vector soliton molecules in fiber lasers , 2017, Scientific Reports.

[56]  F. W. Wise,et al.  Erratum: Recent advances in fibre lasers for nonlinear microscopy , 2013 .

[57]  F. W. Wise,et al.  Area theorem and energy quantization for dissipative optical solitons , 2009, 2009 Conference on Lasers and Electro-Optics and 2009 Conference on Quantum electronics and Laser Science Conference.

[58]  P. Grelu,et al.  Dissipative rogue waves generated by chaotic pulse bunching in a mode-locked laser. , 2012, Physical review letters.

[59]  G. Millot,et al.  Emergence of extreme events in fibre-based parametric processes driven by a partially incoherent pump wave , 2009, CLEO/Europe - EQEC 2009 - European Conference on Lasers and Electro-Optics and the European Quantum Electronics Conference.

[60]  Changxi Yang,et al.  Observation of various bound solitons in a carbon-nanotube-based erbium fiber laser , 2013 .

[61]  J. Tredicce,et al.  Extreme events in the Ti:sapphire laser. , 2011, Optics letters.

[62]  Caroline Lecaplain,et al.  Rogue waves among noiselike-pulse laser emission: An experimental investigation , 2014 .

[63]  Spectral sidebands and multipulse formation in passively mode-locked lasers , 2011, 1101.4829.

[64]  F. Lederer,et al.  Impact of slow gain dynamics on soliton molecules in mode-locked fiber lasers. , 2012, Optics letters.

[65]  Meng Liu,et al.  Dissipative rogue waves induced by long-range chaotic multi-pulse interactions in a fiber laser with a topological insulator-deposited microfiber photonic device. , 2015, Optics letters.

[66]  Li Zhan,et al.  Generation of Soliton Molecules in a Normal-Dispersion Fiber Laser , 2013, IEEE Photonics Technology Letters.

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

[68]  Bo Gao,et al.  Soliton molecules in a fiber laser mode-locked by a graphene-based saturable absorber , 2015 .

[69]  Changxi Yang,et al.  Widely Spaced Bound States in a Soliton Fiber Laser With Graphene Saturable Absorber , 2013, IEEE Photonics Technology Letters.

[70]  M. Brunel,et al.  Generation of bound states of three ultrashort pulses with a passively mode-locked high-power Yb-doped double-clad fiber laser , 2004, IEEE Photonics Technology Letters.

[71]  S. Wen,et al.  Bound states of gain-guided solitons in a passively mode-locked fiber laser. , 2007, Optics letters.

[72]  F. Lederer,et al.  Dissipative soliton molecules with independently evolving or flipping phases in mode-locked fiber lasers , 2009 .

[73]  J. N. Kutz,et al.  Stabilized pulse spacing in soliton lasers due to gain depletion and recovery , 1998 .

[74]  A. Komarov,et al.  Structural dissipative solitons in passive mode-locked fiber lasers. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[75]  Anatoly B. Grudinin,et al.  Passive harmonic mode locking of soliton fiber lasers , 1995 .

[76]  Xueming Liu,et al.  Generation and Propagation of Bound-State Pulses in a Passively Mode-Locked Figure-Eight Laser , 2012, IEEE Photonics Journal.

[77]  L. Gui,et al.  Observation of various bound solitons of a fiber laser with carbon nanotubes and graphene as saturable absorbers , 2011, 2011 International Quantum Electronics Conference (IQEC) and Conference on Lasers and Electro-Optics (CLEO) Pacific Rim incorporating the Australasian Conference on Optics, Lasers and Spectroscopy and the Australian Conference on Optical Fibre Technology.

[78]  Dug Young Kim,et al.  Experimental observation of stable bound solitons in a figure-eight fiber laser. , 2002, Optics letters.

[79]  D. Tang,et al.  Gain-guided soliton in a positive group-dispersion fiber laser. , 2006, Optics letters.

[80]  Li Zhan,et al.  Harmonic mode locking of bound solitons. , 2015, Optics letters.

[81]  I. Prigogine,et al.  Formative Processes. (Book Reviews: Self-Organization in Nonequilibrium Systems. From Dissipative Structures to Order through Fluctuations) , 1977 .

[82]  J. Limpert,et al.  Generation of parabolic bound pulses from a Yb-fiber laser. , 2006, Optics express.

[83]  J. Gordon Dispersive perturbations of solitons of the nonlinear Schrödinger equation , 1992 .

[84]  Sergei K. Turitsyn,et al.  Polarisation Dynamics of Vector Soliton Molecules in Mode Locked Fibre Laser , 2013, Scientific Reports.

[85]  Zhi-Chao Luo,et al.  Dissipative rogue waves induced by soliton explosions in an ultrafast fiber laser. , 2016, Optics letters.

[86]  Changxi Yang,et al.  Quantized pulse separations of phase-locked soliton molecules in a dispersion-managed mode-locked Tm fiber laser at 2  μm. , 2017, Optics letters.

[87]  F. Wise,et al.  Self-similar evolution of parabolic pulses in a laser. , 2004, Physical review letters.

[88]  Akhmediev,et al.  Soliton interaction in nonequilibrium dynamical systems. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[89]  Nail Akhmediev,et al.  Dissipative rogue wave generation in multiple-pulsing mode-locked fiber laser , 2013 .

[90]  C Lu,et al.  Gain-guided solitons in dispersion-managed fiber lasers with large net cavity dispersion. , 2006, Optics letters.

[91]  Ingmar Hartl,et al.  Ultrafast fibre lasers , 2013, Nature Photonics.

[92]  W. Knox,et al.  Polarization locking in an isotropic, modelocked soliton Er/Yb fiber laser. , 1997, Optics express.

[93]  P. Grelu,et al.  Quantized separations of phase-locked soliton pairs in fiber lasers. , 2003, Optics letters.

[94]  X. Wu,et al.  Bound states of solitons in a fiber laser mode locked with carbon nanotube saturable absorber , 2011 .

[95]  Xueming Liu Dynamic evolution of temporal dissipative-soliton molecules in large normal path-averaged dispersion fiber lasers , 2010 .

[96]  K. Chow,et al.  High Fundamental-Repetition-Rate Bound Solitons in Carbon Nanotube-Based Fiber Lasers , 2015, IEEE Photonics Technology Letters.

[97]  H. Tam,et al.  Bound twin-pulse solitons in a fiber ring laser. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[98]  Zhengqian Luo,et al.  Bidirectional operation of 100 fs bound solitons in an ultra-compact mode-locked fiber laser. , 2016, Optics express.

[99]  Adrian Ankiewicz,et al.  Multisoliton Solutions of the Complex Ginzburg-Landau Equation , 1997 .

[100]  Foued Amrani,et al.  Rains of solitons in a figure-of-eight passively mode-locked fiber laser , 2014 .

[101]  C. Finot,et al.  Extreme optical fluctuations in lumped Raman fibre amplifiers , 2013 .

[102]  Changwen Xu,et al.  Black Phosphorus Quantum Dots as an Efficient Saturable Absorber for Bound Soliton Operation in an Erbium Doped Fiber Laser , 2016, IEEE Photonics Journal.

[103]  Chengying Bao,et al.  Generation of wavelength-tunable soliton molecules in a 2-μm ultrafast all-fiber laser based on nonlinear polarization evolution. , 2016, Optics letters.

[104]  H. Tam,et al.  Observation of bound states of solitons in a passively mode-locked fiber laser , 2001 .

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

[106]  J. Limpert,et al.  Generation of soliton molecules with independently evolving phase in a mode-locked fiber laser , 2010 .

[107]  H. Tam,et al.  Compound pulse solitons in a fiber ring laser , 2003 .

[108]  Yichang Meng,et al.  Observation of soliton bound states in a graphene mode locked erbium-doped fiber laser , 2012 .

[109]  M. Piché,et al.  Influence of the Raman effect on bound states of dissipative solitons. , 2006, Optics express.

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

[111]  F. Wise,et al.  Rogue waves in a normal-dispersion fiber laser , 2015, 2015 Conference on Lasers and Electro-Optics (CLEO).

[112]  D Y Tang,et al.  Coexistence and interaction of vector and bound vector solitons in a dispersion-managed fiber laser mode locked by graphene. , 2016, Optics express.