Spin Orbit interactions of light in the dipolar approximation

Abstract

In addition to energy and linear momentum, a light wave carries angular momentum (AM), which has been traditionally splitted in spin (SAM) and orbital angular momentum (OAM). The AM re-distribution between these two components after scattering originates the spin-orbit interactions of light (SOI), which has attracted a great interest during the last decades. Among all the intriguing SOIs effects perhaps the most interesting is the appearance of optical mirages: a transversal displacement of a target localization after scattering. This apparent shift, induced by the AM exchange per photon, has been predicted and experimentally proved in a large variety of situations. These include SAM light impinging a dielectric surface, a single polarizability electric dipole and a high refractive index (HRI) Si sphere sustaining both electric and magnetic response. In the latter case, the optical mirage reaches its maximum value at backscattering when the scattering is dual, namely, when the helicity is preserved. Hence, it may be intuitive to suspect that the absorption, which is embedded in the electric and magnetic polarizabilities, together with other relevant optical properties, such as the particle size, kind of material or surrounding medium, may modify the optical mirage and therefore, the AM exchange per photon. However, as we demonstrate in this work, the key ingredient in the scattering pattern of the SOI per photon is nothing but the asymmetric factor, which contains all the significant optical properties. We present a general theory of spin-to-orbital conversion of angular momentum (AM) in the dipolar regime from the measurable (Stokes parameters representation) helicity density expression. Based on the conservation of the AM in the incident direction, as a consequence of the spherical symmetry, we prove that the asymmetry factor (g-factor) is the only relevant magnitude in the spin orbit interactions of light (SOI), independently of other detailed optical properties. This is verifiable via our universal spectra of both the helicity density and the spin angular momentum (SAM) in which any optical response, including absorptive effects, is intriguingly encoded.