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The Physics of the one-dimensional nonlinear Schr?dinger equation in fiber optics: rogue waves, modulation instability and self-focusing phenomena

DOI:10.1016/j.revip.2019.100037 期刊:Reviews in Physics 出版年份:2019 更新时间:2025-09-12 10:27:22
摘要: We review the different dynamical mechanisms leading to the emergence of coherent structures in physical systems described by the integrable one-dimensional nonlinear Schr?dinger equation (1DNLSE) in the focusing regime. In this context, localized and coherent structures are very often associated to rogue wave events. We focus on one-dimensional optical experiments and in particular on (single mode) optical fibers experiments. In the focusing regime of 1DNLSE, the so-called modulation instability (MI), arising from nonlocal perturbation of the plane waves, is the most common phenomenon. Alongside the standard MI, other mechanisms are responsible for the emergence of rogue waves. We classify the different scenarios by considering those induced by small perturbations of unstable stationary state (the plane waves) and the ones arising from the self-focusing of large pulses without any perturbation. In the former case, the perturbations can be local, global, random or deterministic. In the latter case, the self-focusing dynamics can be observed both with isolated pulses or with large initial fluctuations of the optical power. We review the dynamics of emergence of localized structures in all these different scenarios.
作者: Fran?ois Copie,Stéphane Randoux,Pierre Suret
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To review the different dynamical mechanisms leading to the emergence of coherent structures in physical systems described by the integrable one-dimensional nonlinear Schr?dinger equation (1DNLSE) in the focusing regime, with a focus on one-dimensional optical experiments and particularly on optical fibers experiments.

The review highlights the rich dynamics of the 1DNLSE in optical fibers, including the emergence of rogue waves through modulation instability and self-focusing. It underscores the importance of initial conditions in determining the system's evolution and the role of integrable turbulence in understanding the statistical properties of nonlinear random waves. The paper also points out the challenges in fully understanding the statistical features of nonlinear random waves in integrable systems and suggests future research directions, including the influence of high-order effects and losses.

The review is limited to phenomena described by the integrable 1DNLSE, acknowledging that real experiments may involve additional effects like higher order dispersion, dissipation, and Raman scattering which break integrability. The focus is primarily on one-dimensional optical systems, particularly single-mode fibers.

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