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The optical torque: Electromagnetic spin and orbital angular momenta conservation laws and their significance

The physics involved in the fundamental conservation equations of the spin and orbital angular momenta leads to new laws and phenomena that I disclose. To this end, I analyse the scattering of an electromagnetic wavefield by the canonical system constituted by a small particle, which I assume dipolar in the wide sense. Specifically, under quite general conditions these laws lead to understanding how is 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, I 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, I establish a decomposition of the electromagnetic torque into conservative and non-conservative components in which the helicity and its flow play a role analogous to the energy and its flux for electromagnetic forces. I illustrate these phenomena with examples of beams, also showing the difficulties of some paraxial formulations whose fields do not hold the transversality condition.