Momentum, spin, and orbital angular momentum of electromagnetic, acoustic, and water waves

Abstract

Waves of various types carry momentum, which is associated with their propagation direction, i.e., the phase gradient. The circulation of the wave momentum density gives rise to orbital angular momentum (AM). Additionally, for waves described by vector fields, local rotation of the wavefield produces spin AM (or simply, spin). These dynamical wave properties become particularly significant in structured (i.e., inhomogeneous) wavefields. Here we provide an introduction and overview of the momentum and AM properties for a variety of classical waves: electromagnetic, sound, elastic, plasma waves, and water surface waves. A unified field-theory approach, based on Noether's theorem, offers a general framework to describe these diverse physical systems, encompassing longitudinal, transverse, and mixed waves with different dispersion characteristics. We also discuss observable manifestations of the wave momentum and AM providing clear physical interpretations of the derived quantities.