Modulational instability in the nonlocal \(\chi ^{(2)}\)-model
type: Item
instance of: scholarly article
title: Modulational instability in the nonlocal \(\chi ^{(2)}\)-model
zbMATH Open document ID: 1117.78006
author: Wiesław Z. Królikowski
author: Ole Bang
author: Dan Erik Petersen
author: J. Juul Rasmussen
author: J. Wyller
published in: Physica D
publication date: 2007-04-13T00:00:00Z
full work available at URL: http://hdl.handle.net/1885/38045
review text: The paper deals with a model approximating the nonlinear propagation of waves in \(\chi^{(2)}\) media. The proposed model is a nonlocal version of the Nonlinear Schrödinger Equation and resembles the generic Kerr type nonlocal model but with different nonlocal term that retains some phase information. The main goal of the paper is to link the dynamical properties of the proposed model with those of the full \(\chi^{(2)}\)-model, with the emphasis on the modulational instability (MI) properties. It is shown that the MI is of the oscillatory type and of finite bandwidth. Moreover, it is possible to identify regions in the parameter space for which a fundamental gain band exists, and regions for which higher order gain bands and modulational stability exist. It is shown that the MI analysis for the nonlocal model is applicable in the finite walk-off rank and that the plane waves of the nonlocal \(\chi^{(2)}\)-model are recovered as the asymptotic limit of one of the branches of the plane waves of the full \(\chi^{(2)}\)-model by means of a singular perturbation approach.
Mathematics Subject Classification ID: 78A60
Mathematics Subject Classification ID: 35Q60
Mathematics Subject Classification ID: 35B35
Mathematics Subject Classification ID: 35B25
zbMATH DE Number: 5142354
zbMATH Keywords: nonlinear optics
zbMATH Keywords: nonlocal systems
zbMATH Keywords: modulational instability
zbMATH Keywords: perturbation theory
reviewed by: Dmitry Shepelsky
MaRDI profile type: Publication
OpenAlex ID: W1993062467
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DOI: 10.1016/J.PHYSD.2007.01.002
description: scientific article; zbMATH DE number 5142354