We present results of our research on a multiple-pulse operation of passive mode-locked fiber lasers. The research has been performed on basis of numerical simulation. Multihysteresis dependence of both an intracavity energy and peak intensities of intracavity ultrashort pulses on pump power is found. It is shown that the change of a number of ultrashort pulses in a laser cavity can be realized by hard as well as soft regimes of an excitation and an annihilation of new solitons. Bound steady states of interacting solitons are studied for various mechanisms of nonlinear losses shaping ultrashort pulses. Possibility of coding of information on basis of soliton trains with various bonds between neighboring pulses is discussed. The role of dispersive wave emitted by solitons because of lumped intracavity elements in a formation of powerful soliton wings is analyzed. It is found that such powerful wings result in large bounding energies of interacting solitons in steady states. Various problems of a soliton interaction in passive mode-locked fiber lasers are discussed. 1. Introduction Lasers generating ultrashort optical pulses are widely employed in diversified areas of science, technology, and engineering [1–7]. Applications of such lasers range from testing of ultrahigh speed semiconductor devices to precision processing of materials, from triggering of tracing chemical reactions to sophisticated surgical applications in medicine. These lasers are used for study of ultrahigh speed processes in atomic and molecular physics, in solid-state physics, and in chemistry and biology. They are employed for investigation of light-matter interactions under ultrahigh intensity levels. Lasers of ultrashort optical pulse with a high repetition rate are a key element in high-speed optical communications. Ultrashort pulse lasers are extensively used for micromachining, biomedical diagnostic, in light detection, and ranging (lidar) systems, and so forth. The great diversity of applications of ultrashort pulse lasers calls for further development and perfection of this type of quantum generators. At the present time, one of main ways for creation of perfect ultrashort pulse sources is related to passive mode-locked fiber lasers [8–16]. Nonlinear losses forming ultrashort pulses in fiber lasers are usually realized by the nonlinear polarization rotation technique. These lasers have unique potentialities. They are reliable, compact, flexible, and of low cost. Such generators can be conveniently pumped with commercially available semiconductor lasers. The nonlinear losses
References
[1]
P. G. Kryukov, “Ultrashort-pulse lasers,” Quantum Electronics, vol. 31, no. 2, pp. 95–119, 2001.
[2]
A. A. Ivanov, M. V. Alfimov, and A. M. Zheltikov, “Femtosecond pulses in nanophotonics,” Physics-Uspekhi, vol. 47, no. 7, pp. 687–704, 2004.
[3]
M. E. Fermann and I. Hartl, “Ultrafast fiber laser technology,” IEEE Journal on Selected Topics in Quantum Electronics, vol. 15, no. 1, Article ID 4773318, pp. 191–206, 2009.
[4]
T. Brabec and F. Krausz, “Intense few-cycle laser fields: frontiers of nonlinear optics,” Reviews of Modern Physics, vol. 72, no. 2, pp. 545–591, 2000.
[5]
E. V. Baklanov and P. V. Pokasov, “Optical frequency standards and femtosecond lasers,” Quantum Electronics, vol. 33, no. 5, pp. 383–400, 2003.
[6]
G. P. Agrawal, Nonlinear Fiber Optics, Elsevier Science and Technology Books, Academ Press, Burlington, Mass, USA, 2006.
[7]
N. Akhmediev and A. Ankiewicz, Dissipative Solitons, Lecture Notes in Physics, Springer, Berlin, Germany, 2005.
[8]
F. W. Wise, A. Chong, and W. H. Renninger, “High-energy femtosecond fiber lasers based on pulse propagation at normal dispersion,” Laser & Photonics Reviews, vol. 2, no. 1-2, pp. 58–73, 2008.
[9]
S. Chouli and P. Grelu, “Rains of solitons in a fiber laser,” Optics Express, vol. 17, no. 14, pp. 11776–11781, 2009.
[10]
D. Y. Tang, L. M. Zhao, X. Wu, and H. Zhang, “Soliton modulation instability in fiber lasers,” Physical Review A, vol. 80, pp. 023806–023813, 2009.
[11]
F. Amrani, A. Haboucha, M. Salhi, H. Leblond, A. Komarov, and F. Sanchez, “Dissipative solitons compounds in a fiber laser. Analogy with the states of the matter,” Applied Physics B, vol. 99, no. 1-2, pp. 107–114, 2010.
[12]
S. Kobtsev, S. Kukarin, S. Smirnov, S. Turitsyn, and A. Latkin, “Generation of double-scale femto/pico-second optical lumps in mode-locked fiber lasers,” Optics Express, vol. 17, no. 23, pp. 20707–20713, 2009.
[13]
P. Grelu, F. Belhache, F. Gutty, and J. M. Soto-Crespo, “Relative phase locking of pulses in a passively mode-locked fiber laser,” Journal of the Optical Society of America B, vol. 20, no. 5, pp. 863–870, 2003.
[14]
H. A. Haus, “Mode-locking of lasers,” IEEE Journal on Selected Topics in Quantum Electronics, vol. 6, no. 6, pp. 1173–1185, 2000.
[15]
V. I. Denisov, B. N. Nyushkov, and V. S. Pivtsov, “Self-mode-locked all-fibre erbium laser with a low repetition rate and high pulse energy,” Quantum Electronics, vol. 40, no. 1, pp. 25–27, 2010.
[16]
A. Komarov, A. Haboucha, K. Komarov, H. Leblond, M. Salhi, and F. Sanchez, “Soliton interaction in fiber laser,” in Recent Research Developments in Optics, S. G. Pandalai, Ed., vol. 7, pp. 63–112, 2009.
[17]
D. Y. Tang, W. S. Man, and H. Y. Tam, “Stimulated soliton pulse formation and its mechanism in a passively mode-locked fibre soliton laser,” Optics Communications, vol. 165, no. 4, pp. 189–194, 1999.
[18]
A. Hideur, T. Chartier, M. Sahli, C. Ozkul, C. M. Brunel, and F. Sanchez, “Mode-lock, Q-switch and CW operation of an Yb-doped double-clad fiber ring laser,” Optics Communications, vol. 198, no. 1, pp. 141–146, 2001.
[19]
A. B. Grudinin, D. J. Richardson, and D. N. Payne, “Energy quantisation in figure eight fibre laser,” Electronics Letters, vol. 28, no. 1, pp. 67–68, 1992.
[20]
A. Komarov, H. Leblond, and F. Sanchez, “Multistability and hysteresis phenomena in passively mode-locked fiber lasers,” Physical Review A, vol. 71, no. 5, Article ID 053809, pp. 1–9, 2005.
[21]
D. Y. Tang, L. M. Zhao, B. Zhao, and A. Q. Liu, “Mechanism of multisoliton formation and soliton energy quantization in passively mode-locked fiber lasers,” Physical Review A, vol. 72, no. 4, pp. 1–9, 2005.
[22]
A. Komarov, H. Leblond, and F. Sanchez, “Theoretical analysis of the operating regime of a passively-mode-locked fiber laser through nonlinear polarization rotation,” Physical Review A, vol. 72, no. 6, pp. 063811–063818, 2005.
[23]
J.-C. Chiu, Y.-F. Lan, and J.-J. Kang, “Passivelly mode-locked lasers using saturable absorber incorporating dispersed single wall carbon nanotudes,” in Proceedings of the IEEE Electronic Component and Technology Conference, pp. 827–830, San Diego, Calif, USA, 2009.
[24]
H. Zhang, D. Tang, R. J. Knize, L. Zhao, Q. Bao, and K. P. Loh, “Graphene mode locked, wavelength-tunable, dissipative soliton fiber laser,” Applied Physics Letters, vol. 96, no. 11, Article ID 111112, 2010.
[25]
Z. Sun, T. Hasan, D. Popa et al., “Ultrafast fiber laser mode-locked by graphene based saturable absorber,” in Proceedings of the Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference: 2010 Laser Science to Photonic Applications (CLEO/QELS 2010), San Jose, Calif, USA, May 2010.
[26]
P. Grelu, F. Belhache, F. Gutty, and J. M. Soto-Crespo, “Phase-locked soliton pairs in a stretched-pulse fiber laser,” Optics Letters, vol. 27, no. 11, pp. 966–968, 2002.
[27]
M. Olivier, V. Roy, M. Piché, and F. Babin, “Pulse collisions in the stretched-pulse fiber laser,” Optics Letters, vol. 29, no. 13, pp. 1461–1463, 2004.
[28]
D. Y. Tang, W. S. Man, H. Y. Tam, and P. D. Drummond, “Observation of bound states of solitons in a passively mode-locked fiber laser,” Physical Review A, vol. 64, no. 3, Article ID 033814, 2001.
[29]
A. K. Komarov, K. P. Komarov, H. Leblond, and F. Sanchez, “Spectral control over the interaction of ultrashort pulses in fiber lasers,” Optics and Spectroscopy, vol. 103, no. 5, pp. 825–830, 2007.
[30]
N. Akhmediev, J. M. Soto-Crespo, M. Grapinet, and P. Grelu, “Dissipative soliton interactions inside a fiber laser cavity,” Optical Fiber Technology, vol. 11, no. 3, pp. 209–228, 2005.
[31]
B. A. Malomed, “Bound solitons in the nonlinear Schr?dinger-Ginzburg-Landau equation,” Physical Review A, vol. 44, no. 10, pp. 6954–6957, 1991.
[32]
N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo, “Multisoliton solutions of the complex ginzburg-landau equation,” Physical Review Letters, vol. 79, no. 21, pp. 4047–4051, 1997.
[33]
A. Komarov, K. Komarov, and F. Sanchez, “Quantization of binding energy of structural solitons in passive mode-locked fiber lasers,” Physical Review A, vol. 79, no. 3, Article ID 033807, 2009.
[34]
K. S. Abedin, J. T. Gopinath, L. A. Jiang, M. E. Grein, H. A. Haus, and E. P. Ippen, “Self-stabilized passive, harmonically mode-locked stretched-pulse erbium fiber ring laser,” Optics Letters, vol. 27, no. 20, pp. 1758–1760, 2002.
[35]
C. X. Yu, H. A. Haus, E. P. Ippen, W. S. Wong, and A. Sysoliatin, “Gigahertz-repetition-rate mode-locked fiber laser for continuum generation,” Optics Letters, vol. 25, no. 19, pp. 1418–1420, 2000.
[36]
B. Orta?, A. Hideur, G. Martel, and M. Brunel, “2-GHz passive harmonically mode-locked Yb-doped double-clad fiber laser,” Applied Physics B, vol. 81, no. 4, pp. 507–509, 2005.
[37]
A. Komarov, H. Leblond, and F. Sanchez, “Passive harmonic mode-locking in a fiber laser with nonlinear polarization rotation,” Optics Communications, vol. 267, no. 1, pp. 162–169, 2006.
[38]
A. Komarov, A. Haboucha, and F. Sanchez, “Ultrahigh-repetition-rate bound-soliton harmonic passive mode-locked fiber lasers,” Optics Letters, vol. 33, no. 19, pp. 2254–2256, 2008.
[39]
A. Haboucha, H. Leblond, M. Salhi, A. Komarov, and F. Sanchez, “Coherent soliton pattern formation in a fiber laser,” Optics Letters, vol. 33, no. 5, pp. 524–526, 2008.
[40]
Y. I. Khanin, Principles of Laser Dynamics, Elsevier, Amsterdam, The Netherlands, 1995.
[41]
A. Komarov, K. Komarov, D. Meshcheriakov, F. Amrani, and F. Sanchez, “Dissipative solitons in passive mode-locked fiber lasers with nonlinear polarization rotation technique,” in Proceedings of the Second International Conference:Nonlinear Waves—Theory and Applications, Technical Digest, p. 207, Beijing, China, June 2010.
[42]
K. P. Komarov, “Theory of stationary ultrashort pulses in solid-state lasers with passive mode-locking,” Optics and Spectroscopy, vol. 60, no. 2, pp. 231–234, 1986.
[43]
K. P. Komarov and V. D. Ugozhaev, “Steady-state pulses in solid-state lasers with passive mode locking,” Optics and Spectroscopy, vol. 55, no. 5, pp. 564–568, 1983.
[44]
A. K. Komarov, K. P. Komarov, and A. S. Kuch'yanov, “On phase-modulational bifurcation during passive mode locking in lasers,” JETP Letters, vol. 67, no. 4, pp. 280–283, 1998.
[45]
A. K. Komarov and K. P. Komarov, “Multistability and hysteresis phenomena in passive mode-locked lasers,” Physical Review E, vol. 62, no. 6 B, pp. R7607–R7610, 2000.
[46]
K. P. Komarov, A. S. Kuch'yanov, and V. D. Ugozhayev, “Generation of stationary ultra-short pulses by a passive mode-locking solid-state laser,” Optics Communications, vol. 57, no. 4, pp. 279–284, 1986.
[47]
L. M. Hocking, K. Stewartson, J. T. Stuart, and S. N. Brown, “A nonlinear instability burst in plane parallel flow,” Journal of Fluid Mechanics, vol. 51, no. 4, pp. 705–735, 1972.
[48]
L. M. Hocking and K. Stewartson, “On the nonlinear response of a marginally unstable plane parallel flow to a two-dimensional disturbance,” Proceedings of the Royal Society A, vol. 326, pp. 289–313, 1972.
[49]
A. C. Newell, “Envelope equations,” Lectures in Applied Mathematics, vol. 15, pp. 157–163, 1974.
[50]
A. C. Newell and J. A. Whitehead, “Finite bandwidth, finite amplitude convection,” Journal of Fluid Mechanics, vol. 38, no. 2, pp. 279–303, 1969.
[51]
N. R. Pereira and L. Stenflo, “Nonlinear Schr?dinger equation including growth and damping,” Physics of Fluids, vol. 20, no. 10, pp. 1733–1734, 1977.
[52]
V. V. Afanasjev, B. A. Malomed, and P. L. Chu, “Stability of Bound States of pulses in the Ginzburg-Landau equations,” Physical Review E, vol. 56, no. 5, pp. 6020–6023, 1997.
[53]
B. A. Malomed, A. Schwache, and F. Mitschke, “Soliton lattice and gas in passive fiber-ring resonators,” Fiber and Integrated Optics, vol. 17, no. 4, pp. 267–277, 1998.
[54]
S. Rutz and F. Mitschke, “Towards thermodynamics of solitons: cooling,” Journal of Optics B, vol. 2, no. 3, pp. 364–366, 2000.