Reciprocity in reflection and transmission: What is a ‘phonon diode’?

• Reciprocity in reflection and transmission in linear lossless and time-reversible systems holds for waves of any nature.
• Linear structures hitherto proposed for ‘acoustic diodes’ are reciprocal.
• No proper acoustic isolator with single-mode to single-mode operation has been demonstrated.
• Ballistic phonon transport through a linear structure does not yield a ‘thermal diode’.

The newly popular topic of ‘phonon diodes’ is discussed in the context of a broader issue of reciprocity in reflection/transmission (R–TR–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–TR–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 hitherto proposed for ‘acoustic diodes’ in fact do obey R–TR–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.