Inelastic soliton interactions for nonlinear directional couplers in optical metamaterials with Kerr nonlinearity modulation stability

Abstract

A directional coupler is made up of two parallel monolayer wave guides filled with high nonlinear optical metamaterial. The model equations of the directional twin-core couplers, which are coupled nonlinear Schrödinger equations (CNLSEs), were proposed in the literature. These equations have received the attention of a variety of works. The results found, therein, show mainly dark, bright or singular soliton solutions. The objective of this work is to search for different soliton geometric structures, which show novel patterns. To this issue a novel transformation, with complex amplitude, is introduced. It allows to inspect the waves produced via soliton periodic wave collision. The collision is elastic whenever the waves generated are, everywhere, smooth. Otherwise it is inelastic. Here, the unified method is used to find the traveling wave solutions of the CNLSEs. The solutions obtained are evaluated numerically and they are used to display the amplitude and the real part of the optical field in figures. These figures exhibit super-lattices, zig-zag soliton with rhombus modulation and graded solitons with blow up. These behaviors occur due to inelastic collisions. The contour plots show lattice waves with gap (region of blow up) or without gap. Also, ripples that occur currently in optical cables are observed. Furthermore, it is found that modulation instability (MI) is triggered for positive nonlinear phase shift coefficients or in the case when the coupling coefficients exceed a critical value. As far as MI holds, this leads to traveling waves blow up and gaps.