Transparent PT-symmetric nonlinear networks

TL;DR

This paper develops transparent boundary conditions for nonlocal nonlinear Schrödinger equations on metric graphs, enabling reflectionless wave propagation crucial for minimizing losses in various physical networks.

Contribution

It introduces a potential approach to derive transparent boundary conditions for NNLS equations on graphs, advancing control over wave reflection at vertices.

Findings

Elimination of backscattering at graph vertices

Enhanced signal transfer efficiency in networks

Framework applicable to optical and electronic systems

Abstract

We consider reflectionless wave propagation in networks modeled in terms of the nonlocal nonlinear Schr\"odinger (NNLS) equation on metric graphs, for which transparent boundary conditions are imposed at the vertices. By employing the ``potential approach" previously used for the nonlinear Schr\"odinger equation, we derive transparent boundary conditions for the NNLS equation on metric graphs. These conditions eliminate backscattering at graph vertices, which is crucial for minimizing losses in signal, heat, and charge transfer in various applications such as optical fibers, optoelectronic networks, and low-dimensional materials.