Linear Nonreciprocal Dynamics of Coupled Modulated Systems

TL;DR

This paper investigates the nonreciprocal vibration transmission in short, strongly modulated coupled waveguide systems, emphasizing the role of phase differences and resonance overlaps in breaking reciprocity.

Contribution

It develops a methodology to analyze nonreciprocal dynamics in strongly modulated coupled systems, highlighting phase effects often overlooked in prior studies.

Findings

Phase difference is the main contributor to nonreciprocity.

Resonance overlaps influence the breaking of reciprocity.

Modulation amplitude and wavenumber affect system resonances.

Abstract

Waveguides subject to spatiotemporal modulations are known to exhibit nonreciprocal vibration transmission, whereby interchanging the locations of the source and receiver change the end-to-end transmission characteristics. The scenario of typical interest is unidirectional transmission in long, weakly modulated systems: when transmission is possible in one direction only. Here, with a view toward expanding their potential application as devices, we explore the vibration characteristics of spatiotemporally modulated systems that are short and strongly modulated. Focusing on two coupled systems, we develop a methodology to investigate the nonreciprocal vibration characteristics of both weakly and strongly modulated systems. In particular, we highlight the contribution of phase to nonreciprocity, a feature that is often overlooked. We show that the difference between the transmitted phases is the main contributor to breaking reciprocity in short systems. We clarify the roles of primary and side-band resonances, and their overlaps, in breaking reciprocity. We discuss the influence of modulation amplitude and wavenumber on the resonances of the modulated system.