Radiation forces and torques in optics and acoustics

TL;DR

This review presents a universal framework that unifies optical and acoustic radiation forces and torques by linking them to local energy, momentum, and spin densities in monochromatic, structured fields. It formulates the problem in a stress-tensor language and expresses forces/torques through dipole/monopole moments and their polarizabilities, covering isotropic, anisotropic, chiral, and bi-anisotropic particles, as well as near-interface and higher-multipole effects. The authors discuss resonant enhancements, Kerker-type recoil, Willis coupling in acoustics, and the role of wavefront shaping, with concrete examples in evanescent fields, vortex beams, trapping, chiral sorting, and acoustofluidics, highlighting experimental milestones and practical implications for tweezers, sorting, and optomechanics. By tying the mechanical actions of waves to canonical momentum and spin densities, the work provides a coherent, extensible framework that cross-patches across optics, acoustics, and beyond, enabling advances in manipulation technologies and fundamental wave-matter interactions.

Abstract

The mechanical action of various kinds of waves has been recognized for several centuries. The first tide of scientific interest in wave-induced forces and torques emerged at the turn of the 20th century, with the development of wave theories and the concepts of wave momentum and angular momentum. A second surge occurred in the past several decades, driven by technological breakthroughs: the invention of lasers and the controlled generation of structured wave fields. This resulted in major discoveries, including optical trapping and manipulation of small particles, from atomic to micro sizes, as well as acoustic manipulation of larger particles, including biological cells and samples. Nowadays, radiation forces and torques underpin numerous applications: optical and acoustic tweezers, acoustofluidic sorting of biological cells, optomechanical systems operating in both classical and quantum regimes, solar sails, quantum simulators, volumetric displays, etc. In this review, we present a unifying perspective on optical and acoustic forces and torques acting on various particles, addressing both their theoretical foundations and key applications. Our approach relies on the universal connection between the local energy, momentum, and spin densities of wave fields and the principal forces and torques exerted on small particles. Moreover, we describe important cases of nontrivial (e.g., lateral and pulling) forces and complex (e.g., chiral and anisotropic) particles. We also highlight significant experimental achievements involving optical and acoustic manipulation in structured wave fields. Our aim is to illuminate the common fundamental origins and close interconnections between the mechanical actions of optical and acoustic fields, thereby fostering a deeper understanding and advancing the development of optomechanical and acoustomechanical applications.

Figures (22)

• Figure 1: Examples of manifestations of optical and acoustic forces. (a) The story began with Kepler's 17th-century suggestion that a comet's tail points away from the Sun due to radiation pressure from sunlight [image by Fred Espenak, NASA GSFC]. (b) Modern manipulation of dielectric microparticles using holographic optical tweezers. From Curtis2002OC. (c) Acoustic holographic manipulation of millimeter-sized particles. From Marzo2015NC. (d) Acoustofluidic (ultrasound) sorting of human lipid and erythrocytes cells. From Petersson2005LC.
• Figure 2: 'Executive toys' inspired by early 19th-century experiments on the mechanical action of electromagnetic and acoustic waves. (a) The Crookes radiometer featuring vanes with absorbing (black) and reflecting (white) surfaces. (b) The acoustic Dvorak radiometer using Helmholtz resonators that emit sound from their open sides. Schematics of the radiation-induced rotations (excluding photophoretic and nonlinear acoustic effects) are shown on the right. The photo images are adapted from crookes_wikiRussell2011.
• Figure 3: Almost 150 years after the first experiments by Crookes and Dvorak: 3D images produced by volumetric displays based on optically (a) and acoustically (b) trapped small particles. From Smalley2018Nature and Hirayama2019N.
• Figure 4: (a) A complex scalar wave field $A(\vb{r})$ and its canonical momentum density $\vb{P} \propto \Im (A^* \grad A) = |A|^2 \grad {\rm Arg}(A)$. The phase ${\rm Arg}(A)$ and amplitude $|A|$ are presented by colors (online) and brightness, respectively Thaller_book. (b) A vector wave field $\vb{A} (\vb{r})$ visualized via its amplitude $|\vb{A}|$ (grayscale) and polarization ellipses traced by $\mathbfcal{A}(\vb{r}, t) = \Re\! \left[\vb{A}(\vb{r}) e^{-i \omega t }\right]$ in each point $\vb{r}$. The normalized spin density $\bar{\vb{S}} = \vb{S}/ |\vb{A}|^2 \propto \Im (\vb{A}^* \times \vb{A}) / |\vb{A}|^2$ is directed along the normal to the polarization ellipse and is proportional to its ellipticity. The electromagnetic and acoustic canonical momentum and spin densities, Eqs. (\ref{['eq:PEcan']})--(\ref{['eq:SEM']}) and (\ref{['eq:PAcan']})--(\ref{['eq:notation']}) are the natural counterparts of these quantities for the corresponding fields.
• Figure 5: (a) Schematic of the scattering problem, showing the incident wave field, the particle, and the resulting scattered field. The total field is a sum of the incident and scattered contributions, Eqs. (\ref{['eq:field-split']}). (b) Schematic of the energy, momentum, and angular momentum fluxes, Eqs. (\ref{['eq:Eflux']}) and (\ref{['eq:stress']}), which are quadratic in the wave fields. Separating the pure incident-field, pure scattered-field, and mixed contributions, Eq. (\ref{['eq:flux-split']}), the integral 'incident' fluxes through a closed surface $\Sigma$ vanish, while the integral 'scattered' and 'mixed' fluxes are generally nonzero. These latter fluxes determine the absorption rate, force, and torque on the particle, Eqs. (\ref{['eq:force_and_torque_average']}).