Reciprocity in reflection and transmission: what is a "phonon diode"?

TL;DR

This paper clarifies the concept of phonon diodes by analyzing reciprocity in wave reflection and transmission, showing that linear acoustic structures obey reciprocity and that true acoustic or thermal diodes remain unachieved.

Contribution

It reviews the reciprocity theorem in acoustics, clarifies misconceptions about linear acoustic diodes, and discusses the challenges in realizing effective nonlinear acoustic and thermal diodes.

Findings

Linear structures obey R-T reciprocity under power conservation and time reversibility.

Nonlinear designs can violate reciprocity, but effective acoustic isolators are not yet demonstrated.

Ballistic phonon transport in linear structures is unlikely to serve as a thermal diode.

Abstract

The newly popular topic of "phonon diodes" is discussed in the context of a broader issue of reciprocity in reflection/transmission (R-T) of waves. We first review a theorem well known in electromagnetism and optics but underappreciated in acoustics and phonon physics, stating that the matrix of R-T coefficients for properly normalized amplitudes is symmetric for linear systems that conform to power conservation and time reversibility for wave fields. It is shown that linear structures proposed for "acoustic diodes" in fact do obey R-T reciprocity, and thus should not strictly be called diodes or isolators. We also review examples of nonlinear designs violating reciprocity, and conclude that an efficient acoustic isolator has not yet been demonstrated. Finally, we consider the relationship between acoustic isolators and "thermal diodes", and show that ballistic phonon transport through a linear structure, whether an acoustic diode or not, is unlikely to form the basis for a thermal diode.