Stable soliton pairs in optical transmission lines and fiber lasers

Optical-fiber transmission of pulses can be modeled with the complex Ginzburg–Landau equation. We find novel stable soliton pairs and trains, which are relevant in this case, and analyze them. We suggest that the distance between the pulses and the phase difference between them is defined by energy and momentum balance equations, rather than by equations of standard perturbation theory. We present a two-dimensional phase plane (interaction plane) for analyzing the stability properties and general dynamics of two-soliton solutions of the Complex Ginzburg–Landau equation.

[1]  J. Alexander,et al.  Existence and stability of asymptotically oscillatory double pulses. , 1994 .

[2]  H. Haus,et al.  Soliton transmission control. , 1991, Optics letters.

[3]  J. Alexander,et al.  Existence and stability of asymptotically oscillatory triple pulses , 1993 .

[4]  Hermann A. Haus,et al.  Stretched-Pulse Additive Pulse Mode-Locking in Fiber , 1994 .

[5]  Kramer,et al.  Small-amplitude periodic and chaotic solutions of the complex Ginzburg-Landau equation for a subcritical bifurcation. , 1991, Physical review letters.

[6]  Nail Akhmediev,et al.  Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion , 1997 .

[7]  C R Menyuk,et al.  Stability of passively mode-locked fiber lasers with fast saturable absorption. , 1994, Optics letters.

[8]  J. Soto-Crespo,et al.  Three forms of localized solutions of the quintic complex Ginzburg-Landau equation. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[9]  A. Hasegawa,et al.  Generation of asymptotically stable optical solitons and suppression of the Gordon-Haus effect. , 1992, Optics letters.

[10]  Kazuhiro Nozaki,et al.  Exact Solutions of the Generalized Ginzburg-Landau Equation , 1984 .

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

[12]  J. Moores.  On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term , 1993 .

[13]  D N Payne,et al.  Characterization of a self-starting, passively mode-locked fiber ring laser that exploits nonlinear polarization evolution. , 1993, Optics letters.

[14]  K. Nozaki,et al.  Formations of spatial patterns and holes in the generalized Ginzburg-Landau equation , 1985 .

[15]  C. Paré,et al.  Solitary pulses in an amplified nonlinear dispersive medium. , 1989, Optics letters.

[16]  van Saarloos W,et al.  Pulses and fronts in the complex Ginzburg-Landau equation near a subcritical bifurcation. , 1990, Physical review letters.

[17]  M. H. Ober,et al.  Mode locking with cross-phase and self-phase modulation. , 1991, Optics letters.

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

[19]  Graham Town,et al.  Soliton coding based on shape invariant interacting soliton packets: the three-soliton case , 1994 .

[20]  Akhmediev,et al.  Singularities and special soliton solutions of the cubic-quintic complex Ginzburg-Landau equation. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

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

[22]  Buryak,et al.  Stability criterion for stationary bound states of solitons with radiationless oscillating tails. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

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

[24]  Brand,et al.  Interaction of localized solutions for subcritical bifurcations. , 1989, Physical review letters.

[25]  Lev A. Ostrovsky,et al.  Interactions of solitons in nonintegrable systems: Direct perturbation method and applications , 1981 .

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

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

[28]  V. V. Afanasjev,et al.  Interpretation of the effect of reduction of soliton interaction by bandwidth-limited amplification. , 1993, Optics letters.

[29]  Akira Hasegawa,et al.  Stable soliton transmission in the system with nonlinear gain , 1995 .

[30]  J. Gordon,et al.  The sliding-frequency guiding filter: an improved form of soliton jitter control. , 1992, Optics letters.

[31]  P. C. Hohenberg,et al.  Fronts, pulses, sources and sinks in generalized complex Ginzberg-Landau equations , 1992 .

[32]  Yuji Kodama,et al.  Soliton stability and interactions in fibre lasers , 1992 .

[33]  P. Bélanger.  Coupled-cavity mode locking: a nonlinear model , 1991 .

[34]  Y. Pomeau,et al.  Fronts vs. solitary waves in nonequilibrium systems , 1990 .

[35]  V. Karpman,et al.  A perturbational approach to the two-soliton systems , 1981 .

[36]  Adrian Ankiewicz,et al.  Solitons : nonlinear pulses and beams , 1997 .

[37]  M. Lisak,et al.  Bandwidth limits due to mutual pulse interaction in optical soliton communication systems. , 1986, Optics letters.

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

[39]  C. Paré,et al.  Spatial solitary wave in a weakly saturated amplifying/absorbing medium , 1989 .