Revealing the behavior of soliton buildup in a mode-locked laser

Abstract. Real-time spectroscopy based on an emerging time-stretch technique can map the spectral information of optical waves into the time domain, opening several fascinating explorations of nonlinear dynamics in mode-locked lasers. However, the self-starting process of mode-locked lasers is quite sensitive to environmental perturbation, which causes the transient behaviors of lasers to deviate from the true buildup process of solitons. We optimize the laser system to improve its stability, which suppresses the Q-switched lasing induced by environmental perturbation. We, therefore, demonstrate the first observation of the entire buildup process of solitons in a mode-locked laser, revealing two possible pathways to generate the temporal solitons. One pathway includes the dynamics of raised relaxation oscillation, quasimode-locking stage, spectral beating behavior, and finally the stable single-soliton mode-locking. The other pathway contains, however, an extra transient bound-state stage before the final single-pulse mode-locking operation. Moreover, we propose a theoretical model to predict the buildup time of solitons, which agrees well with the experimental results. Our findings can bring real-time insights into ultrafast fiber laser design and optimization, as well as promote the application of fiber laser.

[1]  A fast method for nonlinear Schrodinger equation , 2003, IEEE Photonics Technology Letters.

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

[3]  J. Travers,et al.  Chirped pulse formation dynamics in ultra-long mode-locked fiber lasers. , 2014, Optics letters.

[4]  Jean-Marc Merolla,et al.  Real-time full-field characterization of transient dissipative soliton dynamics in a mode-locked laser , 2018, Nature Photonics.

[5]  F. Wise,et al.  Starting dynamics of dissipative-soliton fiber laser. , 2010, Optics letters.

[6]  H. Zeng,et al.  Build‐Up of Dissipative Optical Soliton Molecules via Diverse Soliton Interactions , 2018, Laser & Photonics Reviews.

[7]  Neil G. R. Broderick,et al.  Observation of soliton explosions in a passively mode-locked fiber laser , 2014, 1409.8373.

[8]  B. Jalali,et al.  Amplified wavelength–time transformation for real-time spectroscopy , 2008 .

[9]  Kerry J. Vahala,et al.  Microresonator soliton dual-comb spectroscopy , 2016, Science.

[10]  T. Herr,et al.  Temporal solitons in microresonators driven by optical pulses , 2016, Nature Photonics.

[11]  Zhipei Sun,et al.  Versatile multi-wavelength ultrafast fiber laser mode-locked by carbon nanotubes , 2013, Scientific Reports.

[12]  F. Krausz,et al.  Self-starting passive mode locking. , 1991, Optics letters.

[13]  Miro Erkintalo,et al.  Instabilities, breathers and rogue waves in optics , 2014, Nature Photonics.

[14]  R. Dändliker,et al.  Imperfectly mode-locked laser emission and its effects on nonlinear optics , 1969 .

[15]  Kenneth K. Y. Wong,et al.  Ultrafast measurements of optical spectral coherence by single-shot time-stretch interferometry , 2016, Scientific Reports.

[16]  Bahram Jalali,et al.  Fluctuations and correlations in modulation instability , 2012, Nature Photonics.

[17]  Yudong Cui,et al.  Real-Time Observation of the Buildup of Soliton Molecules. , 2018, Physical review letters.

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

[19]  Kenneth K Y Wong,et al.  Panoramic-reconstruction temporal imaging for seamless measurements of slowly-evolved femtosecond pulse dynamics , 2017, Nature Communications.

[20]  Bahram Jalali,et al.  Resolving the build-up of femtosecond mode-locking with single-shot spectroscopy at 90 MHz frame rate , 2016, Nature Photonics.

[21]  R. Dändliker,et al.  Influence of systematic phase deviations on the output of mode-locked lasers , 1969 .

[22]  Paul J. Ackerman,et al.  Diversity of knot solitons in liquid crystals manifested by linking of preimages in torons and hopfions , 2017, 1704.08196.

[23]  G. Agrawal,et al.  Amplification of ultrashort solitons in erbium-doped fiber amplifiers , 1990, IEEE Photonics Technology Letters.

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

[25]  P. Schweitzer,et al.  Theory of Intensity-Correlation Measurements on Imperfectly Mode-Locked Lasers , 1970 .

[26]  R. Dunsmuir.  Theory of Relaxation Oscillations in Optical Masers , 1961 .

[27]  B. Jalali,et al.  Serial time-encoded amplified imaging for real-time observation of fast dynamic phenomena , 2009, Nature.

[28]  U. Keller.  Recent developments in compact ultrafast lasers , 2003, Nature.

[29]  J. Herrmann.  Starting dynamic, self-starting condition and mode-locking threshold in passive, coupled-cavity or Kerr-lens mode-locked solid-state lasers , 1993 .

[30]  L Larger,et al.  Real time noise and wavelength correlations in octave-spanning supercontinuum generation. , 2013, Optics express.

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

[32]  K. Tsia,et al.  Spectral-temporal dynamics of multipulse mode-locking , 2017 .

[33]  Miles H. Anderson,et al.  Microresonator-based solitons for massively parallel coherent optical communications , 2016, Nature.

[34]  C. Pan,et al.  Completely self-starting picosecond and femtosecond Kerr-lens mode-locked Ti:sapphire laser , 1995 .

[35]  B. Jalali,et al.  Time stretch and its applications , 2017, Nature Photonics.

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

[37]  S. Coen,et al.  Universal mechanism for the binding of temporal cavity solitons , 2017, 1703.10604.

[38]  J. Shieh,et al.  Starting dynamics of a cw passively mode-locked picosecond Ti:sapphire/DDI laser. , 1995, Optics letters.

[39]  Electrometry Sb Ras,et al.  Stochasticity, periodicity and localized light structures in partially mode-locked fibre lasers , 2014, Nature Communications.

[40]  Rüdiger Paschotta,et al.  Q-switching stability limits of continuous-wave passive mode locking , 1999 .

[41]  Sergei K. Turitsyn,et al.  Carbon nanotubes for ultrafast fibre lasers , 2016 .

[42]  Erich P. Ippen,et al.  Principles of passive mode locking , 1994 .

[43]  K. Tsia,et al.  Unveiling multi-scale laser dynamics through time-stretch and time-lens spectroscopies , 2017 .

[44]  Steven A. Miller,et al.  Breather soliton dynamics in microresonators , 2016, Nature Communications.

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

[46]  Laurent Larger,et al.  Virtual chimera states for delayed-feedback systems. , 2013, Physical review letters.

[47]  Meucci,et al.  Two-dimensional representation of a delayed dynamical system. , 1992, Physical review. A, Atomic, molecular, and optical physics.

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

[49]  N. Radwell,et al.  Observation of mode-locked spatial laser solitons , 2016, 2017 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC).

[50]  Andy Chong,et al.  Ultrafast fiber lasers based on self-similar pulse evolution: a review of current progress , 2015, Reports on progress in physics. Physical Society.

[51]  Govind P. Agrawal,et al.  Applications of Nonlinear Fiber Optics , 2001 .

[52]  J. Javaloyes,et al.  Topological solitons as addressable phase bits in a driven laser , 2014, Nature Communications.

[53]  Y. Tong,et al.  Fibre dispersion or pulse spectrum measurement using a sampling oscilloscope , 1997 .

[54]  Claudio Conti,et al.  The mode-locking transition of random lasers , 2011, 1304.3652.

[55]  Logan G. Wright,et al.  Spatiotemporal mode-locking in multimode fiber lasers , 2017, Science.

[56]  G. Eisenstein,et al.  Transient dynamics in a self-starting passively mode-locked fiber-based soliton laser , 1993 .

[57]  M. Erkintalo,et al.  Dynamics of soliton explosions in passively mode-locked fiber lasers , 2015, 1511.02016.

[58]  Hermann A. Haus,et al.  Solitons in optical communications , 1996 .

[59]  P. Wasylczyk,et al.  Witnessing the pulse birth—transient dynamics in a passively mode-locked femtosecond laser , 2013 .

[60]  Jan Siegel,et al.  Experimental study of a self-starting Kerr-lens mode-locked titanium-doped sapphire laser , 1996 .

[61]  S. Coen,et al.  Ultraweak long-range interactions of solitons observed over astronomical distances , 2013, Nature Photonics.

[62]  Meng Liu,et al.  Successive soliton explosions in an ultrafast fiber laser. , 2016, Optics letters.

[63]  Michael L. Gorodetsky,et al.  Universal dynamics and deterministic switching of dissipative Kerr solitons in optical microresonators , 2017, 2017 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC).

[64]  Xueming Liu,et al.  Distributed ultrafast fibre laser , 2015, Scientific Reports.

[65]  K. Vahala,et al.  Counter-propagating solitons in microresonators , 2017, Nature Photonics.

[66]  S. Turitsyn,et al.  Real-time observation of dissipative soliton formation in nonlinear polarization rotation mode-locked fibre lasers , 2018, Communications Physics.

[67]  M. Gorodetsky,et al.  Temporal solitons in optical microresonators , 2012, Nature Photonics.

[68]  Meng Pang,et al.  All-optical bit storage in a fibre laser by optomechanically bound states of solitons , 2016 .

[69]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[70]  Anastasia Bednyakova,et al.  Adiabatic soliton laser. , 2015, Physical review letters.

[71]  Xinbai Li,et al.  Single-mode dispersive waves and soliton microcomb dynamics , 2016, Nature Communications.

[72]  J. Shieh,et al.  Pulse-forming dynamics of a cw passively mode-locked Ti:sapphire/DDI laser. , 1992, Optics letters.

[73]  L. Casperson,et al.  Principles of lasers , 1983, IEEE Journal of Quantum Electronics.

[74]  S. Coen,et al.  Coexistence of multiple nonlinear states in a tristable passive kerr resonator , 2017, 1702.00782.