Modulational Instability In A Pt-Symmetric Vector Nonlinear Schrödinger System

Keywords

Modulational instability; PT-symmetric potential; Vector NLS system

Abstract

A class of exact multi-component constant intensity solutions to a vector nonlinear Schrödinger (NLS) system in the presence of an external PT-symmetric complex potential is constructed. This type of uniform wave pattern displays a non-trivial phase whose spatial dependence is induced by the lattice structure. In this regard, light can propagate without scattering while retaining its original form despite the presence of inhomogeneous gain and loss. These constant-intensity continuous waves are then used to perform a modulational instability analysis in the presence of both non-hermitian media and cubic nonlinearity. A linear stability eigenvalue problem is formulated that governs the dynamical evolution of the periodic perturbation and its spectrum is numerically determined using Fourier–Floquet–Bloch theory. In the self-focusing case, we identify an intensity threshold above which the constant-intensity modes are modulationally unstable for any Floquet–Bloch momentum belonging to the first Brillouin zone. The picture in the self-defocusing case is different. Contrary to the bulk vector case, where instability develops only when the waves are strongly coupled, here an instability occurs in the strong and weak coupling regimes. The linear stability results are supplemented with direct (nonlinear) numerical simulations.

Publication Date

12-1-2016

Publication Title

Physica D: Nonlinear Phenomena

Volume

336

Number of Pages

53-61

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.physd.2016.07.001

Socpus ID

84992361808 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84992361808

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