Restoring the reciprocity invariance in nonlinear systems with broken mirror symmetry

TL;DR

This paper demonstrates how to restore reciprocal behavior in nonlinear asymmetric systems by tuning parameters, enabling symmetric wave transmission and phase control, which could advance elastic wave device design.

Contribution

It introduces a method to achieve stable, reciprocal nonlinear dynamics in asymmetric systems through parameter tuning, counteracting the typical nonreciprocal response.

Findings

Reciprocity can be restored in asymmetric nonlinear systems.

Response regimes show identical transmission characteristics in opposite directions.

Phase nonreciprocity enables direction-dependent phase shifts.

Abstract

Circumventing the reciprocity invariance has posed an interesting challenge in the design of modern devices for wave engineering. In passive devices, operating the device in the nonlinear response regime is a common means for realizing nonreciprocity. Because mirror-symmetric systems are trivially reciprocal, breaking the mirror symmetry is a necessary requirement for nonreciprocal dynamics to exist in nonlinear systems. However, the response of an asymmetric nonlinear system is not necessarily nonreciprocal. In this work, we report on the existence of stable, steady-state nonlinear reciprocal dynamics in coupled asymmetric systems subject to external harmonic excitation. We restore reciprocity in the asymmetric system by tuning two symmetry-breaking parameters simultaneously. We identify response regimes in the vicinity of the primary resonances of the system where the steady-state left-to-right transmission characteristics are identical to the right-to-left characteristics in terms of frequency, amplitude and phase. We interpret these regimes of reciprocal dynamics in the context of phase nonreciprocity, wherein incident waves undergo a nonreciprocal phase shift depending on their direction of travel. We hope these findings help design devices with new functionalities for controlling and steering of elastic waves.