Modulational instability in a PT-symmetric vector nonlinear Schrodinger system

PHYSICA D-NONLINEAR PHENOMENA

卷:336

Article

Cole, J. T.¹  Makris, K. G.²  Musslimani, Z. H.¹  Christodoulides, D. N.³  Rotter, S.⁴ 

[1] Florida State Univ, Dept Math, Tallahassee, FL 32306 USA

[2] Univ Crete, Dept Phys, Crete Ctr Quantum Complex & Nanotechnol, POB 2208, Iraklion 71003, Greece

[3] Univ Cent Florida, CREOL, Coll Opt, Orlando, FL 32816 USA

[4] Vienna Univ Technol, TU Wien, Inst Theoret Phys, A-1040 Vienna, Austria

关键词: Vector NLS system;    PT-symmetric potential;    Modulational instability;   

DOI  :  10.1016/j.physd.2016.07.001

来源: Elsevier

【 摘 要 】

A class of exact multi-component constant intensity solutions to a vector nonlinear Schrodinger (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. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

Free