Asymmetric Wave Propagation Through Nonlinear PT-symmetric Oligomers

TL;DR

This paper investigates nonlinear PT-symmetric oligomers embedded in a linear lattice, analyzing their wave transmission properties, stability, and asymmetry in propagation for plane waves and Gaussian wavepackets.

Contribution

It provides analytical and numerical analysis of wave transmission and rectification in nonlinear PT-symmetric oligomers, highlighting their asymmetric propagation and stability characteristics.

Findings

Asymmetric transmission coefficients for left and right propagation.

Plane wave states are generally unstable.

Asymmetry persists for Gaussian wavepackets.

Abstract

In the present paper, we consider nonlinear PT-symmetric dimers and trimers (more generally, oligomers) embedded within a linear Schr{\"o}dinger lattice. We examine the stationary states of such chains in the form of plane waves, and analytically compute their reflection and transmission coefficients through the nonlinear PT symmetric oligomer, as well as the corresponding rectification factors which clearly illustrate the asymmetry between left and right propagation in such systems. We examine not only the existence but also the dynamical stability of the plane wave states and interestingly find them to be generically unstable. Lastly, we generalize our numerical considerations to the more physically relevant case of Gaussian initial wavepackets and confirm that the asymmetry in the transmission properties persists in the case of such wavepackets, as well.