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Modulational instability
About: Modulational instability is a research topic. Over the lifetime, 3241 publications have been published within this topic receiving 67899 citations.
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01 Jan 1995
TL;DR: Inverse scattering transform and N-Soliton solutions have been used in this paper for the control of optical solitons in dielectric fiber and other applications, such as stability and chaos.
Abstract: Preface Introduction 1. Electric properties of the dielectric fiber 2. Derivation of wave packet equation and introduction to soliton transmission systems 3. Inverse scattering transform and N-Soliton solutions 4. Perturbation methods 5. Effects on higher order terms 6. Reshaping of solitons and concept of guiding center (Average) solitons 7. Soliton transmission control 8. Interaction among solitons in same channel 9. Interaction among solitons in different channels 10. Femto second solitons 11. Soliton transmission experiments 12. Other applications of optical solitons 13. Spatial solitons, stability and chaos 14. Modulational instability 15. Dark solitons General references
1,118 citations
TL;DR: A review of physical mechanisms of the rogue wave phenomenon is given in this article, where the authors demonstrate that freak waves may appear in deep and shallow waters and demonstrate that these mechanisms remain valid but should be modified.
Abstract: A review of physical mechanisms of the rogue wave phenomenon is given. The data of marine observations as well as laboratory experiments are briefly discussed. They demonstrate that freak waves may appear in deep and shallow waters. Simple statistical analysis of the rogue wave probability based on the assumption of a Gaussian wave field is reproduced. In the context of water wave theories the probabilistic approach shows that numerical simulations of freak waves should be made for very long times on large spatial domains and large number of realizations. As linear models of freak waves the following mechanisms are considered: dispersion enhancement of transient wave groups, geometrical focusing in basins of variable depth, and wave-current interaction. Taking into account nonlinearity of the water waves, these mechanisms remain valid but should be modified. Also, the influence of the nonlinear modulational instability (Benjamin–Feir instability) on the rogue wave occurence is discussed. Specific numerical simulations were performed in the framework of classical nonlinear evolution equations: the nonlinear Schrodinger equation, the Davey–Stewartson system, the Korteweg–de Vries equation, the Kadomtsev–Petviashvili equation, the Zakharov equation, and the fully nonlinear potential equations. Their results show the main features of the physical mechanisms of rogue wave phenomenon.
962 citations
Book•
AT&T1
TL;DR: In this article, the authors presented the first experiment of all-optical solitons in a real optical fiber and showed that they can be used for information transfer in optical fibers.
Abstract: 1. Introduction.- 2. Wave Motion.- 2.1 What is Wave Motion?.- 2.2 Dispersive and Nonlinear Effects of a Wave.- 2.3 Solitary Waves and the Korteweg de Vries Equation.- 2.4 Solution of the Korteweg de Vries Equation.- 3. Lightwave in Fibers.- 3.1 Polarization Effects.- 3.2 Plane Electromagnetic Waves in Dielectric Materials.- 3.3 Kerr Effect and Kerr Coefficient.- 3.4 Dielectric Waveguides.- 4. Information Transfer in Optical Fibers and Evolution of the Lightwave Packet.- 4.1 How Information is Coded in a Lightwave.- 4.2 How Information is Transferred in Optical Fibers.- 4.3 Master Equation for Information Transfer in Optical Fibers: The Nonlinear Schrodinger Equation.- 4.4 Evolution of the Wave Packet Due to the Group Velocity Dispersion.- 4.5 Evolution of the Wave Packet Due to the Nonlinearity.- 4.6 Technical Data of Dispersion and Nonlinearity in a Real Optical Fiber.- 4.7 Nonlinear Schrodinger Equation and a Solitary Wave Solution.- 4.8 Modulational Instability.- 4.9 Induced Modulational Instability.- 4.10 Modulational Instability Described by the Wave Kinetic Equation.- 5. Optical Solitons in Fibers.- 5.1 Soliton Solutions and the Results of Inverse Scattering.- 5.2 Soliton Periods.- 5.3 Conservation Quantities of the Nonlinear Schrodinger Equation.- 5.4 Dark Solitons.- 5.5 Soliton Perturbation Theory.- 5.6 Effect of Fiber Loss.- 5.7 Effect of the Waveguide Property of a Fiber.- 5.8 Condition of Generation of a Soliton in Optical Fibers.- 5.9 First Experiments on Generation of Optical Solitons.- 6. All-Optical Soliton Transmission Systems.- 6.1 Raman Amplification and Reshaping of Optical Solitons-First Concept of All-Optical Transmission Systems.- 6.2 First Experiments of Soliton Reshaping and of Long Distance Transmission by Raman Amplifications.- 6.3 First Experiment of Soliton Transmission by Means of an Erbium Doped Fiber Amplifier.- 6.4 Concept of the Guiding Center Soliton.- 6.5 The Gordon-Haus Effect and Soliton Timing Jitter.- 6.6 Interaction Between Two Adjacent Solitons.- 6.7 Interaction Between Two Solitons in Different Wavelength Channels.- 7. Control of Optical Solitons.- 7.1 Frequency-Domain Control.- 7.2 Time-Domain Control.- 7.3 Control by Means of Nonlinear Gain.- 7.4 Numerical Examples of Soliton Transmission Control.- 8. Influence of Higher-Order Terms.- 8.1 Self-Frequency Shift of a Soliton Produced by Induced Raman Scattering.- 8.2 Fission of Solitons Produced by Self-Induced Raman Scattering.- 8.3 Effects of Other Higher-Order Dispersion.- 9. Polarization Effects.- 9.1 Fiber Birefringence and Coupled Nonlinear Schrodinger Equations.- 9.2 Solitons in Fibers with Constant Birefringence.- 9.3 Polarization-Mode Dispersion.- 9.4 Solitons in Fibers with Randomly Varying Birefringence.- 10. Dispersion-Managed Solitons (DMS).- 10.1 Problems in Conventional Soliton Transmission.- 10.2 Dispersion Management with Dispersion-Decreasing Fibers.- 10.3 Dispersion Management with Dispersion Compensation.- 10.4 Quasi Solitons.- 11. Application of Dispersion Managed Solitons for Single-Channel Ultra-High Speed Transmissions.- 11.1 Enhancement of Pulse Energy.- 11.2 Reduction of Gordon-Haus Timing Jitter.- 11.3 Interaction Between Adjacent Pulses.- 11.4 Dense Dispersion Management.- 11.5 Nonstationary RZ Pulse Propagation.- 11.6 Some Recent Experiments.- 12. Application of Dispersion Managed Solitons for WDM Transmission.- 12.1 Frequency Shift Induced by Collisions Between DM Solitons in Different Channels.- 12.2 Temporal Shift Induced by Collisions Between DM Solitons in Different Channels.- 12.3 Doubly Periodic Dispersion Management.- 12.4 Some Recent WDM Experiments Using DM Solitons.- 13. Other Applications of Optical Solitons.- 13.1 Soliton Laser.- 13.2 Pulse Compression.- 13.3 All-Optical Switching.- 13.4 Solitons in Fibers with Gratings.- 13.5 Solitons in Microstructure Optical Fibers.- References.
855 citations
TL;DR: The first observation of the modulational instability of light waves in dielectric material using a neodymium-doped yttrium aluminum garnet laser operated at 1.319 \ensuremath{\mu}m and single-mode optical fibers with anomalous group-velocity dispersion is reported.
Abstract: We report the first observation of the modulational instability of light waves in dielectric material using a neodymium-doped yttrium aluminum garnet laser operated at 1.319 \ensuremath{\mu}m and single-mode optical fibers with anomalous group-velocity dispersion. The observed results are in good agreement with the theoretical predictions. The relationship between the modulation instability and parametric four-wave mixing and the interplay with stimulated Raman and Brillouin scatterings are also presented.
712 citations
TL;DR: In this paper, the periodic amplification of solitons is shown to develop an instability, which is represented by the appearance of a series of discrete sidebands in the soliton power spectrum, which follow an inverse square root dependence on the amplification period.
Abstract: The periodic amplification of solitons is shown to develop an instability. This becomes evident through the appearance of a series of discrete sidebands in the soliton power spectrum. These sidebands do not exhibit the power tuning characteristic of the modulational instability, but instead follow an inverse square root dependence on the amplification period.<
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674 citations