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Effects of the third-order dispersion on continuous waves in complex potentials

  • Bin Liu
  • Lu LiEmail author
  • Boris A. Malomed
Regular Article

Abstract

A class of constant-amplitude (CA) solutions of the nonlinear Schrödinger equation with the third-order spatial dispersion (TOD) and complex potentials are considered. The system can be implemented in specially designed planar nonlinear optical waveguides carrying a distribution of local gain and loss elements, in a combination with a photonic-crystal structure. The complex potential is built as a solution of the inverse problem, which predicts the potential supporting a required phase-gradient structure of the CA state. It is shown that the diffraction of truncated CA states with a correct phase structure can be strongly suppressed. The main subject of the analysis is the modulational instability (MI) of the CA states. The results show that the TOD term tends to attenuate the MI. In particular, simulations demonstrate a phenomenon of weak stability, which occurs when the linear-stability analysis predicts small values of the MI growth rate. The stability of the zero state, which is a nontrivial issue in the framework of the present model, is studied too.

Graphical abstract

Keywords

Nonlinear Dynamics 

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Copyright information

© EDP Sciences, SIF, Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Institute of Theoretical Physics, Shanxi UniversityTaiyuanP.R. China
  2. 2.Department of Physical ElectronicsSchool of Electrical Engineering, Faculty of Engineering, Tel Aviv UniversityTel AvivIsrael
  3. 3.Laboratory of Nonlinear-Optical Informatics, ITMO UniversitySt. PetersburgRussia

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