Elastic Spin and Orbital Angular Momenta

TL;DR

This paper revisits the fundamental concepts of spin and orbital angular momentum in elastic waves, providing simple universal expressions that clarify their quantization and the importance of different wave contributions.

Contribution

It introduces a unified formalism for elastic wave angular momenta that corrects previous misconceptions and emphasizes the significance of all wave components.

Findings

Total angular momentum in cylindrical modes is quantized and matches azimuthal quantum number.

Longitudinal, transverse, and hybrid contributions are equally important.

Calculated transverse spin angular momentum of surface Rayleigh waves.

Abstract

Motivated by recent theoretical and experimental interest in the spin and orbital angular momenta of elastic waves, we revisit canonical wave momentum, spin, and orbital angular momentum in isotropic elastic media. We show that these quantities are described by simple universal expressions, which differ from the results of [G. J. Chaplain et al., Phys. Rev. Lett. 128, 064301 (2022)] and do not require separation of the longitudinal and transverse parts of the wavefield. For cylindrical elastic modes, the normalized z-component of the total (spin+orbital) angular momentum is quantized and equals the azimuthal quantum number of the mode, while the orbital and spin parts are not quantized due to the spin-orbit geometric-phase effects. In contrast to the claims of the above article, longitudinal, transverse, and `hybrid' contributions to the angular momenta are equally important and cannot be neglected. As another application of the general formalism, we calculate the transverse spin angular momentum of a surface Rayleigh wave.