Optical torque: Electromagnetic spin and orbital-angular-momentum conservation laws and their significance

Abstract

The physics involved in the fundamental conservation equations of the spin and orbital angular momenta leads to new laws and phenomena that are disclosed here. To this end, we analyse the scattering of an electromagnetic wavefield by the canonical system constituted by a small particle, which is assumed dipolar in the wide sense. Specifically, under quite general conditions these laws lead to understanding the contribution and weight of each of those angular momenta to the electromagnetic torque exerted by the field on the object, which is shown to consist of an extinction and a scattering, or recoil, part. This leads to an interpretation of its effect different to that taken up till now by many theoretical and experimental works, and implies that a part of the recoil torque cancels the usually called intrinsic torque which was often considered responsible of the particle spinning. In addition, we obtain the contribution of the spatial structure of the wave to this torque, unknown to this date, showing its effect in the orbiting of the object, and demonstrating that it often leads to a negative torque on a single particle, i.e. opposite to the incident helicity, producing an orbital motion contrary to its spinning. Furthermore, we establish a decomposition of the electromagnetic torque into conservative and non-conservative components in which the helicity and the spin angular momentum play a role analogous to the energy and its flux for electromagnetic forces. These phenomena are illustrated with examples of beams, also showing the difficulties of some paraxial formulations whose fields do not hold the transversality condition.

Acoustic versus electromagnetic field theory: scalar, vector, spinor representations and the emergence of acoustic spin

“…which is the appropriate analogue to the Lorenz-FitzGerald gauge in electromagnetism, reduces Eqs. (16) to the wave equation for the bivector potential:…”

“…In electromagnetic theory, the spin and orbital angular momenta are described by the quantities from the canonical energy-momentum and angular-momentum tensors, which are derived in the Lagrangian field theory via the Noether's theorem [3,11,12,13,14,15,16]. The key independent quantities there are the canonical momentum and spin densities, which correspond to the directly observable properties of monochromatic optical fields, namely, the radiation force and torque on small absorbing particles [17,18,19,20,21,22,23,16,24].…”

“…In electromagnetic theory, the spin and orbital angular momenta are described by the quantities from the canonical energy-momentum and angular-momentum tensors, which are derived in the Lagrangian field theory via the Noether's theorem [3,11,12,13,14,15,16]. The key independent quantities there are the canonical momentum and spin densities, which correspond to the directly observable properties of monochromatic optical fields, namely, the radiation force and torque on small absorbing particles [17,18,19,20,21,22,23,16,24]. Using complex amplitudesĒ(r) andH(r) of monochromatic electric and magnetic fields in free space (the real time-dependent fields E(r, t) and H(r, t) are obtained by applying the Re (... e −iωt ) operator), the cycleaveraged canonical spin and momentum densities can be written as [17,11,20,21,22,14] P = 1 4ω Im 0Ē * · (∇)Ē + µ 0H * · (∇)H ,…”

Negative optical spin torque wrench of a non-diffracting non-paraxial fractional Bessel vortex beam

“…In this case, the magnetic field would contribute to the generation of a magnetic spin torque [29,30] so that the total (i.e. electric + magnetic) left-handed (negative) spin torque rotating the magneto-dielectric sphere around its center of mass may be enhanced or reduced.…”

Acoustic Radiation Force and Torque on Small Particles as Measures of the Canonical Momentum and Spin Densities

“…Since Kepler's observation of the comet tail and early theoretical works by Euler and Poynting [13,14], the studies of optical and acoustic momentum and forces were developed in parallel ways. Remarkably, despite numerous works calculating radiation forces and torques acting on various small particles in optics [24][25][26][27][28][29][30] and acoustics [31][32][33][34][35][36][37][38][39][40][41], the explicit proportionality of the force and torque to the local wave momentum and spin angular momentum densities was properly established in optics only recently [42][43][44][45][46][47][48][49][50][51]. The reason for this is that, in generic inhomogeneous wave fields, the force and torque on an isotropic small absorbing particle are proprtional to the canonical momentum and spin densities rather than the Poynting (kinetic) momentum and angular momentum commonly used for many decades [45-48, 50, 52-54].…”