Coupled backward- and forward-propagating solitons in a composite right/left-handed transmission line

TL;DR

This paper investigates the coupling of backward- and forward-propagating solitons in a composite right/left-handed nonlinear transmission line, deriving coupled equations and analyzing the existence and stability of various vector solitons through simulations.

Contribution

It introduces a novel coupled nonlinear Schrödinger system for wave envelopes in a composite transmission line and explores the types and robustness of resulting vector solitons.

Findings

Bright-bright solitons propagate undistorted for long times.

Other soliton types have shorter lifetimes and are less robust.

Analytical predictions match numerical simulations well.

Abstract

We study the coupling between backward- and forward-propagating wave modes, with the same group velocity, in a composite right/left-handed nonlinear transmission line. Using an asymptotic multiscale expansion technique, we derive a system of two coupled nonlinear Schr{\"o}dinger equations governing the evolution of the envelopes of these modes. We show that this system supports a variety of backward- and forward propagating vector solitons, of the bright-bright, bright-dark and dark-bright type. Performing systematic numerical simulations in the framework of the original lattice that models the transmission line, we study the propagation properties of the derived vector soliton solutions. We show that all types of the predicted solitons exist, but differ on their robustness: only bright-bright solitons propagate undistorted for long times, while the other types are less robust, featuring shorter lifetimes. In all cases, our analytical predictions are in a very good agreement with the results of the simulations, at least up to times of the order of the solitons' lifetimes.