Physics – Optics
Scientific paper
2011-10-20
Physics
Optics
88 pages, submitted to Physics Reports
Scientific paper
We present a review of the latest developments in one-dimensional (1D) optical wave turbulence. We describe theory, numerics and experimental observations for a 1D optical system. This system is described by two coupled nonlinear equations, which we explore within two wave limits allowing for the expression of the evolution of the complex amplitude in a single dynamical equation. We consider a long-wave limit corresponding to waves with wave numbers smaller than the electrical coherence length of the liquid crystal, and the opposite limit,with wave numbers are larger. We show that both of these systems are of a dual cascade type, analogous to two-dimensional turbulence, which can be described by wave turbulence (WT) theory. We show that the cascades are induced by a six-wave resonant interaction process. WT predicts several stationary solutions (non-equilibrium and thermodynamic) to both the long- and short-wave systems, and we investigate the necessary conditions required for their realization. Interestingly, the long-wave system is close to the integrable 1D nonlinear Schr\"{o}dinger equation (which contains exact nonlinear soliton solutions), and as a result during the inverse cascade, nonlinearity of the system at low wave numbers becomes strong. Subsequently, due to the focusing nature of the nonlinearity, this leads to modulational instability of the condensate and the formation of solitons. With the aid of the the PDF description of WT theory, we explain the coexistence and mutual interactions between solitons and the weakly nonlinear random wave background in the form of a wave turbulence life cycle.
Bortolozzo Umberto
Laurie Jason
Nazarenko Sergey
Residori Stefania
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