Mode-Locked Soliton Lasers

A comprehensive treatment is given for the formation of mode-locked soliton pulses in optical fiber and solid state lasers. The pulse dynamics is dominated by the interaction of the cubic Kerr nonlinearity and chromatic dispersion with an intensity-dependent perturbation provided by the mode-locking element in the laser cavity. The intensity-dependent perturbation preferentially attenuates low intensity electromagnetic radiation which makes the mode-locked pulses attractors of the laser cavity. A review of the broad spectrum of mode-locked laser models, both qualitative and quantitative, is considered with the basic pulse formation phenomena highlighted. The strengths and weaknesses of each model are considered with two key instabilities studied in detail: Q-switching and harmonic mode-locking. Although the numerous mode-locking models are considerably different, they are unified by the fact that stable solitons are exhibited in each case due to the intensity discrimination perturbation in the laser cavity.

[1]  J. Kutz,et al.  Pulse-train uniformity in optical fiber lasers passively mode-locked by nonlinear polarization rotation , 2000, IEEE Journal of Quantum Electronics.

[2]  J. S. Aitchison,et al.  Discrete Spatial Optical Solitons in Waveguide Arrays , 1998 .

[3]  D. Marcuse.  Theory of dielectric optical waveguides , 1974 .

[4]  Lederer,et al.  Discrete self-trapping, soliton interactions, and beam steering in nonlinear waveguide arrays. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[5]  Miller,et al.  Femtosecond ac Stark effect in semiconductor quantum wells: Extreme low- and high-intensity limits. , 1989, Physical review letters.

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

[7]  A. Tünnermann,et al.  Nonlinearity and disorder in fiber arrays. , 2004, Physical review letters.

[8]  R. Morandotti,et al.  Optical discrete solitons in waveguide arrays. 2. Dynamic properties , 2002 .

[9]  J. Nathan Kutz,et al.  Stability of Pulses in Nonlinear Optical Fibers Using Phase-Sensitive Amplifiers , 1996, SIAM J. Appl. Math..

[10]  S. V. Manakov.  On the theory of two-dimensional stationary self-focusing of electromagnetic waves , 1973 .

[11]  K R Wilson,et al.  Third harmonic generation microscopy. , 1998, Optics express.

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

[13]  T. Maiman.  Optical and Microwave-Optical Experiments in Ruby , 1960 .

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

[15]  J R Taylor,et al.  Femtosecond soliton generation in a praseodymium fluoride fiber laser. , 1994, Optics letters.

[16]  Hwa-Yaw Tam,et al.  Mechanism of intrinsic wavelength tuning and sideband asymmetry in a passively mode-locked soliton fiber ring laser , 2000 .

[17]  G. Eesley,et al.  Generation of nonequilibrium electron and lattice temperatures in copper by picosecond laser pulses. , 1986, Physical review. B, Condensed matter.

[18]  J. Judkins,et al.  Nonlinear Pulse Propagation In Long Period Fiber Gratings , 1997, QELS '97., Summaries of Papers Presented at the Quantum Electronics and Laser Science Conference.

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

[20]  Curtis R. Menyuk,et al.  Pulse propagation in an elliptically birefringent Kerr medium , 1989 .

[21]  Qirong Xing,et al.  Regular, period-doubling, quasi-periodic, and chaotic behavior in a self-mode-locked Ti:sapphire laser , 1999 .

[22]  Theory of Q switching in actively mode-locked lasers , 2006 .

[23]  A. V. Luchnikov,et al.  Electrostriction mechanism of soliton interaction in optical fibers. , 1990, Optics letters.

[24]  H. Haus.  Mode-locking of lasers , 2000, IEEE Journal of Selected Topics in Quantum Electronics.

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

[26]  D. Richardson,et al.  Energy quantisation in figure eight fibre laser , 1992 .

[27]  J. Cunningham,et al.  Low-loss intracavity AlAs/AlGaAs saturable Bragg reflector for femtosecond mode locking in solid-state lasers. , 1995, Optics letters.

[28]  Graham Town,et al.  Tunable erbium-ytterbium fiber sliding-frequency soliton laser , 1995 .

[29]  F. Kärtner,et al.  Stabilization of solitonlike pulses with a slow saturable absorber. , 1995, Optics letters.

[30]  F. Wise,et al.  High-energy femtosecond stretched-pulse fiber laser with a nonlinear optical loop mirror. , 2002, Optics letters.

[31]  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.

[32]  Michael I. Weinstein,et al.  Modulational Stability of Ground States of Nonlinear Schrödinger Equations , 1985 .

[33]  Stephan W Koch,et al.  Quantum theory of the optical and electronic properties of semiconductors, fifth edition , 2009 .

[34]  J. Fujimoto,et al.  Structures for additive pulse mode locking , 1991 .

[35]  James G. Fujimoto,et al.  Analytic theory of additive pulse and Kerr lens mode locking , 1992 .

[36]  Todd Kapitula,et al.  The Evans function for nonlocal equations , 2004 .

[37]  J. Judkins,et al.  All-optical switching in long-period fiber gratings. , 1997, Optics letters.

[38]  Kin Seng Chiang,et al.  Simultaneous existence of a multiplicity of stable and unstable solitons in dissipative systems , 2001 .

[39]  Björn Sandstede,et al.  Stability of pulses on optical fibers with phase-sensitive amplifiers , 1997 .

[40]  H. Winful,et al.  Passive mode locking through nonlinear coupling in a dual-core fiber laser. , 1992, Optics letters.

[41]  H. Tam,et al.  Modulational instability in a fiber soliton ring laser induced by periodic dispersion variation , 2000 .

[42]  S. Orszag,et al.  Advanced Mathematical Methods For Scientists And Engineers , 1979 .

[43]  M M Murnane,et al.  Sub-10-fs operation of Kerr-lens mode-locked lasers. , 1996, Optics letters.

[44]  F. Kärtner,et al.  Solitary-pulse stabilization and shortening in actively mode-locked lasers , 1995 .

[45]  Chennupati Jagadish,et al.  Multipulse operation of a Ti:sapphire laser mode locked by an ion-implanted semiconductor saturable-absorber mirror , 1999 .

[46]  D. Christodoulides,et al.  Discrete self-focusing in nonlinear arrays of coupled waveguides. , 1988, Optics letters.

[47]  S. Kinoshita,et al.  Stable multipulse generation from a self-mode-locked Ti:sapphire laser , 1998 .

[48]  Irl N. Duling,et al.  Compact Sources of Ultrashort Pulses , 1995 .

[49]  William L. Kath,et al.  Hamiltonian dynamics of solutions in optical fibers , 1991 .

[50]  I. Duling.  Subpicosecond all-fibre erbium laser , 1991 .

[51]  Todd Kapitula,et al.  Stability criterion for bright solitary waves of the perturbed cubic-quintic Schro¨dinger equation , 1997, patt-sol/9701011.

[52]  J. Kutz,et al.  Theory and simulation of the dynamics and stability of actively modelocked lasers , 2002 .

[53]  Masaki Asobe,et al.  Applications of highly nonlinear chalcogenide glass fibers in ultrafast all-optical switches , 1993 .

[54]  A. Schawlow.  Lasers , 2018, Acta Ophthalmologica.

[55]  Donald Umstadter,et al.  Extreme light. , 2002, Scientific American.

[56]  C. Menyuk.  Nonlinear pulse propagation in birefringent optical fibers , 1987 .

[57]  Wolfgang Rudolph,et al.  Multiple pulse operation of a femtosecond Ti:sapphire laser , 1997 .

[58]  B. Fischer,et al.  Phase transition theory of many-mode ordering and pulse formation in lasers. , 2002, Physical review letters.

[59]  M. Cross,et al.  Pattern formation outside of equilibrium , 1993 .

[60]  J. K. Shaw,et al.  Mathematical principles of optical fiber communications , 2004 .

[61]  Todd Kapitula,et al.  Stability of pulses in the master mode-locking equation , 2002 .

[62]  R. Fork,et al.  Robust operation of a dual-core fiber ring laser , 1995 .

[63]  Mode-locking of fiber lasers via nonlinear mode-coupling , 2005 .

[64]  H. Weitzner,et al.  Perturbation Methods in Applied Mathematics , 1969 .

[65]  H. Haus,et al.  Self-starting additive pulse mode-locked erbium fibre ring laser , 1992 .

[66]  J. Kutz,et al.  Theory and simulation of passive modelocking dynamics using a long-period fiber grating , 2003 .

[67]  J. Nathan Kutz,et al.  Nonlinear Dynamics of Mode-locking Optical Fiber Ring Lasers , 2002 .

[68]  K. M. Yoo,et al.  Pulse splitting in a self-mode-locked Ti:sapphire laser , 1997 .

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

[70]  L. Stenflo,et al.  Nonlinear Schrödinger equation including growth and damping , 1977 .

[71]  Allister I. Ferguson,et al.  Interacting solutions in erbium fibre laser , 1991 .

[72]  S. M. Jensen.  The Nonlinear Coherent Coupler , 1982 .

[73]  J. Minelly,et al.  Cladding-pumped passive harmonically mode-locked fiber laser. , 1996, Optics letters.

[74]  Martin Koch,et al.  Short cavity erbium/ytterbium fiber lasers mode-locked with a saturable Bragg reflector , 1997 .

[75]  Joshua Kiddy K. Asamoah,et al.  Fractal–fractional age-structure study of omicron SARS-CoV-2 variant transmission dynamics , 2022, Partial Differential Equations in Applied Mathematics.

[76]  J. Proctor,et al.  Passive mode-locking by use of waveguide arrays. , 2005, Optics letters.

[77]  B. Fischer,et al.  Statistical-mechanics theory of active mode locking with noise. , 2004, Optics letters.

[78]  K Bergman,et al.  Stable multigigahertz pulse-train formation in a short-cavity passively harmonic mode-locked erbium/ytterbium fiber laser. , 1998, Optics letters.

[79]  K. Bergman,et al.  Observation of Polarization-Locked Vector Solitons in an Optical Fiber , 1999 .

[80]  J. Judkins,et al.  Long-period fiber gratings as band-rejection filters , 1995 .

[81]  P. Holmes,et al.  Mode-locking pulse dynamics in a fiber laser with a saturable Bragg reflector , 1997 .

[82]  B. Fischer,et al.  Phase transition theory of pulse formation in passively mode-locked lasers with dispersion and Kerr nonlinearity , 2003 .

[83]  H. Haus,et al.  Random walk of coherently amplified solitons in optical fiber transmission. , 1986, Optics letters.

[84]  T. Kolokolnikov,et al.  The Q-switching instability in passively mode-locked lasers , 2005, EQEC '05. European Quantum Electronics Conference, 2005..

[85]  R. Morandotti,et al.  Optical discrete solitons in waveguide arrays. I. Soliton formation , 2002 .

[86]  W. Kath,et al.  Pulse propagation in nonlinear optical fiber lines that employ phase-sensitive parametric amplifiers , 1994 .

[87]  Akira Hasegawa,et al.  Optical solitons in fibers , 1993, International Commission for Optics.

[88]  M. W. Phillips,et al.  SELFSTARTING, PASSIVELY MODELOCKED ERBIUM FIBRE RING LASER BASED ON THE AMPLIFYING SAGNAC SWITCH , 1991 .

[89]  J. Nathan Kutz,et al.  Guiding-center pulse dynamics in nonreturn-to-zero (return-to-zero) communications systems with mean-zero dispersion , 1997 .

[90]  D. Mcbranch,et al.  Femtosecond high-sensitivity, chirp-free transient absorption spectroscopy using kilohertz lasers. , 1998, Optics letters.

[91]  N Akhmediev,et al.  Pulsating solitons, chaotic solitons, period doubling, and pulse coexistence in mode-locked lasers: complex Ginzburg-Landau equation approach. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[92]  C R Menyuk,et al.  Soliton fiber ring laser. , 1992, Optics letters.

[93]  C. C. Wang,et al.  Nonlinear optics. , 1966, Applied optics.

[94]  Keren Bergman,et al.  Polarization-locked temporal vector solitons in a fiber laser: experiment , 2000 .

[95]  J. Nathan Kutz,et al.  Dynamics of the Optical Parametric Oscillator Near Resonance Detuning , 2005, SIAM J. Appl. Dyn. Syst..

[96]  I. Christov,et al.  Fourth-order dispersion-limited solitary pulses. , 1994, Optics letters.

[97]  W. Kath,et al.  Long-distance pulse propagation in nonlinear optical fibers by using periodically spaced parametric amplifiers. , 1993, Optics letters.

[98]  D. Miller,et al.  Quantum Well Optical Switching Devices , 1995 .

[99]  H. Haus,et al.  A theory of forced mode locking , 1975, IEEE Journal of Quantum Electronics.

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

[101]  F. Krausz,et al.  Kerr lens mode locking. , 1992, Optics letters.

[102]  Shu Namiki,et al.  Energy rate equations for mode-locked lasers , 1997 .

[103]  Hermann A. Haus,et al.  Additive-pulse modelocking in fiber lasers , 1994 .

[104]  G. Stegeman,et al.  Polarized soliton instability and branching in birefringent fibers , 1989 .

[105]  H P Yuen,et al.  Reduction of quantum fluctuation and suppression of the Gordon-Haus effect with phase-sensitive linear amplifiers. , 1992, Optics letters.

[106]  W. S. Man,et al.  Stimulated soliton pulse formation and its mechanism in a passively mode-locked fibre soliton laser , 1999 .

[107]  Y Kodama,et al.  Guiding-center soliton in fibers with periodically varying dispersion. , 1991, Optics letters.

[108]  M. Dennis,et al.  High repetition rate figure eight laser with extracavity feedback , 1992 .

[109]  D. Chemla,et al.  The excitonic optical stark effect in semiconductor quantum wells probed with femtosecond optical pulses , 1989 .

[110]  Itaru Yokohama,et al.  Fabrication of Bragg grating in chalcogenide glass fibre using the transverse holographic method , 1996 .