Title :

Stochastic modulational instability in the nonlinear Schr\"odinger equation with colored random dispersion

Author(s) :

Armaroli, Andrea [Auteur]
Laboratoire de Physique des Lasers, Atomes et Molécules - UMR 8523 [PhLAM]
Dujardin, Guillaume [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Systèmes de particules et systèmes dynamiques [Paradyse]
Kudlinski, Alexandre [Auteur]
Laboratoire de Physique des Lasers, Atomes et Molécules - UMR 8523 [PhLAM]
Mussot, Arnaud [Auteur]
Laboratoire de Physique des Lasers, Atomes et Molécules - UMR 8523 [PhLAM]
Trillo, Stefano [Auteur]
Università degli Studi di Ferrara = University of Ferrara [UniFE]
De Bièvre, Stephan [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Systèmes de particules et systèmes dynamiques [Paradyse]
Conforti, Matteo [Auteur]
Laboratoire de Physique des Lasers, Atomes et Molécules - UMR 8523 [PhLAM]

Journal title :

PHYSICAL REVIEW A

Publisher :

American Physical Society

Publication date :

2022-01-07

ISSN :

2469-9926

HAL domain(s) :

Sciences de l'ingénieur [physics]/Optique / photonique
Science non linéaire [physics]/Formation de Structures et Solitons [nlin.PS]

English abstract : [en]

We study modulational instability (MI) in optical fibers with random group-velocity dispersion (GVD). We consider Gaussian and dichotomous colored stochastic processes. We resort to different analytical methods (namely, ...
Show more >We study modulational instability (MI) in optical fibers with random group-velocity dispersion (GVD). We consider Gaussian and dichotomous colored stochastic processes. We resort to different analytical methods (namely, the cumulant expansion and the functional approach) and assess their reliability in estimating the MI gain of stochastic origin. If the power spectral density (PSD) of the GVD fluctuations is centered at null wavenumber, we obtain low-frequency MI sidelobes which converge to those given by a white noise perturbation when the correlation length tends to 0. If instead the stochastic processes are modulated in space, one or more MI sidelobe pairs corresponding to the well-known parametric resonance (PR) condition can be found. A transition from small and broad sidelobes to peaks nearly indistinguishable from PR-MI is predicted, in the limit of large perturbation amplitudes and correlation lengths of the random process. We find that the cumulant expansion provides good analytical estimates for small PSD values and small correlation lengths, when the MI gain is very small. The functional approach is rigorous only for the dichotomous processes, but allows us to model a wider range of parameters and to predict the existence of MI sidelobes comparable to those observed in homogeneous fibers of anomalous GVDShow less >

Language :

Anglais

Popular science :

Non

ANR Project :

ULNE

Comment :

12 pages, 6 figures submitted

Collections :

• Laboratoire de Physique des Lasers, Atomes et Molécules (PhLAM) - UMR 8523

Source :

Harvested from HAL