The angular momentum of vectorial non-paraxial fields and the role of radial charges in orbit-spin coupling

¹ VSL Dutch Metrology Institute, Thijsseweg 11 2629 JA Delft, Netherlands
² Optics Research Group, Delft University of Technology, Lorentzweg 1 2628 CJ Delft, Netherlands

^* e-mail: o.elgawhary@tudelft.nl

Published online: 20 August 2020

Abstract

Electromagnetic fields carry a linear and an angular momentum, the first being responsible for the existence of the radiation pressure and the second for the transfer of torque from electromagnetic radiation to matter. The angular momentum is considered to have two components, one due to the polarization state of the field, usually called Spin Angular Momentum (SAM), and one due to existence of topological azimuthal charges in the field phase profile, which leads to the Orbital Angular Momentum (OAM). For non-paraxial fields these two contributions are not independent of each other, something which is described as spin-orbit coupling. It has been recently proved that electromagnetic fields necessarily carry also invariant radial charges that, as discussed in this work, play a key role in the angular momentum. Here we show that the total angular momentum consists in fact of three components: one component only dependent on the spin of the field, another dependent on the azimuthal charges carried by the field and a third component dependent on the spin and the radial charges contained in the field. By properly controlling the number and coupling among these radial charges it is possible to design electromagnetic fields with a desired total angular momentum. In this way it is also possible to discover fields with no orbital angular momentum and a spin angular momentum typical of spin-3/2 objects, irrespective of the fact that photons are spin-1 particles.