Eur. Phys. J. Plus (2014) 129: 279
https://doi.org/10.1140/epjp/i2014-14279-7

Regular Article

Effects of fourth-order dispersion on modulational instability in metamaterials with exponential saturable nonlinearity and self-steepening coefficients

¹ Higher Institute of the Sahel, University of Maroua, P.O Box. 46, Maroua, Cameroon
² Higher Teacher’s Training College of Maroua, University of Maroua, P.O. Box, 55, Maroua, Cameroon
³ Department of Physics, Faculty of Science, University of Maroua, P.O. Box, 814, Maroua, Cameroon
⁴ Max Planck Institute for the Physics of Complex Systems, Nothnitzer Strasse 38, 01187, Dreseden, Germany
⁵ The Abdus Salam International Centre for Theoretical Physics, Strada costiera 11, P.O. Box 538, I-34014, Trieste, Italy

^* e-mail: aboukaraboukar@yahoo.fr

Received: 5 September 2014
Revised: 24 October 2014
Accepted: 15 November 2014
Published online: 30 December 2014

Abstract

We studied the modulational instability in negative index materials with higher-order effects. An expression for the instability gain is derived through the linear stability analysis. We identify and discuss the salient features of the effect, like fourth-order dispersion, self-steepening and saturable nonlinearity on the modulational instability. The results show that the instability gain depends on the sign of the higher-order dispersion and, for anomalous dispersion, the instability regime is constituted of two parts: the conventional gain spectrum and the secondary gain spectrum induced by the fourth-order dispersion. For large values of the fourth-order dispersion, the secondary instability region spectrum vanishes and merges with the ordinary gain. In the normal dispersion regime, an efficient control of the modulation instability is successfully demonstrated by adjusting the fourth-order dispersion, depending on the presence of the self-steepening parameter or the normalized input power.