On the wave transmission in a discrete nonlinear left-handed electrical lattice

Abstract

ABSTRACT In this work, we study some nonlinear left-handed metamaterial lattices subjected to a harmonic driving source. Using the semi-discrete rotating-wave approximation, a nonlinear Schrödinger equation is obtained from the physical model. Using this Schrödinger system, we obtain an analytical approximation to the nonlinear supratransmission threshold of the left-handed lattice. As a consequence of the analytical approximation, if supratransmission is to occur in the pass-band left-handed line then it will only take place within the upper forbidden band-gap. On the other hand, supratransmission will never occur in the homogeneous left-handed transmission line. The numerical simulations of the discrete equation describing the voltage across the line and the total energy of the lattice show that there is no nonlinear band-gap transmission in the forbidden band predicted by the threshold. Contrary to the supratransmision phenomenon in conventional lattices, there is no threshold in the bang-gap where the phenomenon appears. The present manuscript advances the fundamental understanding of the nonlinear supratransmission phenomenon and, at the same time, opens the way for its application to left-handed metamaterial lattices. In that sense, the results of this manuscript may serve to provide a deeper understanding to this nonlinear process.