Optical Solitons - Abdullaev, Fatkhulla

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Résumé :
The investigation of nonlinear wave phenomena has been one of the main direc? tions of research in optics for the last few decades. Soliton concepts applied to the description of intense electromagnetic beams and ultrashort pulse propagation in various media have contributed much to this field. The notion of solitons has proved to be very useful in describing wave processes in hydrodynamics, plasma physics and condensed matter physics. Moreover, it is also of great importance in optics for ultrafast information transmission and storage, radiation propagation in resonant media, etc. In 1973, Hasegawa and Tappert made a significant contribution to optical soliton physics when they predicted the existence of an envelope soliton in the regime of short pulses in optical fibres. In 1980, Mollenauer et al. conducted ex? periments to elucidate this phenomenon. Since then the theory of optical solitons as well as their experimental investigation has progressed rapidly. The effects of inhomogeneities of the medium and energy pumping on optical solitons, the interaction between optical solitons and their generation in fibres, etc. have all been investigated and reported. Logical devices using optical solitons have been developed; new types of optical solitons in media with Kerr-type nonlinearity and in resonant media have been described.

Sommaire:
1. Introduction.- 2. Short Pulses in Optical Fibres.- 2.1 Solitons in Single-Mode Fibres.- 2.2 Self-Phase Modulation of Pulses.- 2.3 Soliton Regime of Ultrashort Pulse Propagation. Bright and Dark Solitons.- 2.4 Observations of Solitons.- 2.5 Electromagnetic Shock Waves.- 2.6 Influence of Higher Order Dispersion and Dissipation on Soliton Dynamics.- 2.7 Amplification of Optical Solitons in Fibres.- 2.8 Modulation Instability of Electromagnetic Waves.- 2.9 Generation of Periodic Pulse Sequences.- 2.10 Multi-Mode Effects on Soliton Regimes of Propagation.- 2.11 The Soliton Laser.- 2.12 The Soliton Self-Frequency Shift.- 2.13 Multi-Component (Vector) Optical Solitons.- 3. Soliton Interaction.- 3.1 General Representations in Integrable and Nonintegrable Systems: Direct and IST-Based Methods.- 3.2 Interaction Between Optical Solitons.- 3.3 Inelastic Soliton Interactions.- 3.4 Interaction Between a Soliton and a Nonlinear Periodic Wave in an Optical Fibre.- 3.5 Solitons in Two Tunnel-Coupled Optical Waveguides.- 4. Statistical Dynamics of Optical Solitons.- 4.1 Random Pulses in an Optical Fibre. Numerical Simulation in the Presoliton Region.- 4.2 Noise Signals in the Near Field.- 4.3 Noise Signals in the Far Field.- 4.4 Random Pulses in Fibres (Soliton Region).- 4.5 Solitons in Random Nonuniform Fibres.- 4.6 Random Amplification of Solitons.- 4.7 Dynamic Chaos of Optical Solitons.- 4.8 Optical Turbulence in Passive Optical Resonators.- 5. Optical Solitons in Resonant and Active Media.- 5.1 The Maxwell-Bloch System. Soliton Solutions.- 5.2 Optical Solitons in an Active Fibre.- 5.3 Scattering of a Weak Wave on an Optical Soliton.- 5.4 Theory of Superfluorescence.- 5.5 Solitons in Stimulated Raman Scattering.- 5.6 The Evolution of SRS Solitons Under the Action of Molecular Relaxation.- 6. Quantum Optical Solitons.- 6.1 Hamiltonian Formulation of the IST-Method and Classical r-Matrix.- 6.2 Quantum Nonlinear Schr?dinger Equation (QNLSE).- 6.3 Quantum Sine-Gordon System.- 6.4 The Dicke Model.- 7. Conclusion.- References.