Asymmetric Wave Propagation in Nonlinear Systems

TL;DR

This paper introduces a mechanism for asymmetric wave transmission in nonlinear layered systems, demonstrating how wave direction affects transmission due to nonlinear resonance shifts, with potential applications in wave control.

Contribution

It presents exact solutions for asymmetric wave transmission in a nonlinear layered model, highlighting the role of nonlinear resonances and demonstrating the effect through numerical simulations.

Findings

Asymmetric transmission occurs with simple two-layer systems.

Nonlinear resonance shifts cause nonreciprocal wave propagation.

Numerical simulations confirm the rectifying effect.

Abstract

A mechanism for asymmetric (nonreciprocal) wave transmission is presented. As a reference system, we consider a layered nonlinear, non mirror-symmetric model described by the one-dimensional Discrete Nonlinear Schreodinger equation with spatially varying coefficients embedded in an otherwise linear lattice. We construct a class of exact extended solutions such that waves with the same frequency and incident amplitude impinging from left and right directions have very different transmission coefficients. This effect arises already for the simplest case of two nonlinear layers and is associated with the shift of nonlinear resonances. Increasing the number of layers considerably increases the complexity of the family of solutions. Finally, numerical simulations of asymmetric wavepacket transmission are presented which beautifully display the rectifying effect.