$\mathcal{PT}$-symmetric ladders with a scattering core

TL;DR

This paper investigates a $$-symmetric ladder system governed by the discrete nonlinear Schrdinger equation, revealing asymmetric wave transmission and stability properties through analytical and numerical methods.

Contribution

It introduces a novel $$-symmetric ladder model with nonlinear central rungs and systematically analyzes its scattering solutions and non-reciprocal transmission.

Findings

Found two branches of scattering solutions with asymmetric transmission.

Confirmed stability of certain solutions through analysis.

Demonstrated asymmetric wavepacket transmission via simulations.

Abstract

We consider a $\mathcal{PT}$-symmetric chain (ladder-shaped) system governed by the discrete nonlinear Schr\"odinger equation where the cubic nonlinearity is carried solely by two central "rungs" of the ladder. Two branches of scattering solutions for incident plane waves are found. We systematically construct these solutions, analyze their stability, and discuss non-reciprocity of the transmission associated with them. To relate these results to finite-size wavepacket dynamics, we also perform direct simulations of the evolution of the wavepackets, which confirm that the transmission is indeed asymmetric in this nonlinear system with the mutually balanced gain and loss.