https://doi.org/10.1140/epjd/e2017-70700-3
Regular Article
Effects of the third-order dispersion on continuous waves in complex potentials
1 Institute of Theoretical Physics, Shanxi University, Taiyuan 030006, P.R. China
2 Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, 69978 Tel Aviv, Israel
3 Laboratory of Nonlinear-Optical Informatics, ITMO University, 197101 St. Petersburg, Russia
a
e-mail: llz@sxu.edu.cn
Received: 7 November 2016
Published online: 9 June 2017
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.
Key words: Nonlinear Dynamics
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2017
