Asymmetric Wave Propagation Through Saturable Nonlinear Oligomers

TL;DR

This paper investigates asymmetric wave propagation in nonlinear oligomers with saturable nonlinearity embedded in a linear lattice, analyzing stationary states, transmission, and stability, and demonstrating persistent asymmetry with Gaussian wavepackets.

Contribution

It provides analytical and numerical analysis of wave transmission and rectification in saturable nonlinear oligomers, highlighting asymmetry and stability properties.

Findings

Asymmetric transmission depends on wave direction.

Rectification factors quantify propagation asymmetry.

Asymmetry persists for Gaussian wavepackets.

Abstract

In the present paper we consider nonlinear dimers and trimers (more generally, oligomers) embedded within a linear Schr{\"o}dinger lattice where the nonlinear sites are of saturable type. 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 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. 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 also persists in the case of such wavepackets.