Measuring the transverse spin density of the magnetic field

Abstract

With regard to the angular momentum (AM) of light, we distinguish two different constituents: the spin AM referring to the polarization state and the orbital AM linked to the phase gradient of the electromagnetic wave [1-3]. Locally, these two dynamical quantities are described by the spin and orbital AM densities s and l. In the electric-magnetic-democracy or dual-symmetry representation [1-4], these constituents of the AM can be separated into two parts, which correspond to the electric (E) and magnetic (H) fields. In case of the spin AM density, we can write s Ξ Im (e 0 E∗ × E + μ 0 H∗ × H) /4ω ξ s e + s h . Considering simple paraxial scenarios, both distributions are equivalent, with se « sh. However, completely different distributions of se and sh occur in spatially highly confined and complex fields [1, 4]. In particular, the transverse components of s E and s H generally show entirely different distributions.