Reciprocity in reflection and transmission: What is a ‘phonon 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.

Detecting thermal rectification

“…35 42 and R=140 in a metal-superconductor hybrid. 43 It must be emphasized that although proving non-reciprocity is a prerequisite for observing thermal rectification, 44 some experiments may not satisfy the prerequisite due to technical difficulties. Thus, some of the previous experimental findings might not be genuine thermal rectifiers.…”

Subwavelength ultrasonic circulator based on spatiotemporal modulation

“…The conditions under which Rayleigh reciprocity theorem holds can be broken in three different ways: (i) breaking linearity, (ii) biasing with a vector that is odd under time reversal, or (iii) breaking time invariance [6,7]. Large acoustic isolation has been obtained using option (i) in a non-linear medium paired with a frequency selective mirror [8,9], or with the help of nonlinear acoustic inclusions [10]; however, all these nonlinear solutions typically introduce severe signal distortions and only work for large acoustic intensities.…”

Non-reciprocal and highly nonlinear active acoustic metamaterials

“…There is an ongoing debate on what constitutes proper terminology. In this article, we take the more conservative approach of Maznev et al 16 and only consider non-reciprocal media capable of breaking the transmission symmetry property, that is, they transmit acoustic energy in only one direction regardless of the spatial spectrum of the incident acoustic excitation. In other words, we eliminate passive devices [9][10][11][12][13] that exhibit time-reversal symmetry.…”