“Phonon diodes” and reciprocity in reflection and transmission

Recent years have seen increased interest in acoustic “diodes” or “rectifiers”. Surprisingly, many of the proposed designs of these devices are based on passive linear structures without magnetic fields that ought to be perfectly reciprocal. Furthermore, it has been suggested that ballistic phonon transport through such structures can yield “thermal diodes”. In this didactical presentation, acoustic “diodes” will be discussed in the broader context of reciprocity in reflection/transmission (R-T) of waves. We will review a theorem known in optoelectronics but under-appreciated 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. The power of this theorem is in that it is valid for waves of any nature and not limited to systems described by a particular set of equations, be it acoustics or electromagnetism. We will show how this theorem applies to various wave phenomena, including inter-conversion of electromagnetic and acoustic waves in piezoelectric structures, and discuss a conjecture that R-T reciprocity is preserved in the presence of linear dissipation. We will see that linear structures hitherto proposed for acoustic “diodes” in fact do obey R-T reciprocity, and thus do not yield true isolators. In order to create a linear isolator one needs to break the time-reversal symmetry either by using a magnetic field or by actively modulating the parameters of the device. In acoustics, both paths can be pursued but neither has been explored so far. We will also review studies of nonlinear acoustic “diodes” and conclude that those, likewise, failed so far to demonstrate an acoustic isolator. Finally, we will consider the relationship between acoustic isolators and “thermal diodes”, and show that - allistic phonon transport through a linear structure, whether an acoustic isolator or not, is unlikely to form the basis for a thermal diode. This contribution was supported as part of the S³TEC Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Award No. DE-SC0001299.