Universal Geometric Relations of Acoustic Spin, Energy Flux, and Reactive Power

Abstract

An understanding of acoustic spin, energy flux, and reactive power is crucial for manipulating and directing near-field sound. However, despite their importance, the relationship between these physical quantities has not been fully explored. In this paper, we aim to address this gap in knowledge by presenting a proof of some universal geometric relations between the acoustic spin, the cross product of the time-averaged energy flux and reactive power, and the local vorticity of the energy flux. These relations are independent of the specific wave structure and are verified for various acoustic systems. Moreover, our study demonstrates the mechanical torques and forces on small lossy particles generated by three different types of acoustic near-field sources, namely Janus, Huygens, and spin sources. These findings reveal hidden locking relations beyond the simple spin-momentum locking of near-field waves and provide valuable insights into the fundamental principles underlying the relationship between acoustic spin, radiation torque, energy flux, and reactive power in the field of acoustics.