Magnetic and Electric Transverse Spin Density of Spatially Confined Light

Abstract

When a beam of light is laterally confined, its field distribution can exhibit points where the local magnetic and electric field vectors spin in a plane containing the propagation direction of the electromagnetic wave. The phenomenon indicates the presence of a nonzero transverse spin density. Here, we experimentally investigate this transverse spin density of both magnetic and electric fields, occurring in highly confined structured fields of light. Our scheme relies on the utilization of a high-refractive-index nanoparticle as a local field probe, exhibiting magnetic and electric dipole resonances in the visible spectral range. Because of the directional emission of dipole moments that spin around an axis parallel to a nearby dielectric interface, such a probe particle is capable of locally sensing the magnetic and electric transverse spin density of a tightly focused beam impinging under normal incidence with respect to said interface. We exploit the achieved experimental results to emphasize the difference between magnetic and electric transverse spin densities.

Alternate abstract:

Plain Language Summary

Electromagnetic waves carry both linear and angular momenta. Typically, the “spin angular momentum” points either forward or backward along the direction that the wave travels. But when the wave is strongly confined, the spin can point perpendicularly to the propagation direction. This “transverse spin” can be used to build photonic devices where the flow of information is controlled by the orientation of the spin. However, most studies are concerned with the transverse spin of only the electric field, while from a theoretical point of view, the magnetic field contributes to the transverse spin as well and even behaves differently than its electric counterpart. Here, we experimentally and theoretically investigate how both magnetic and electric fields contribute to the transverse spin in a tightly focused beam of light.

Our experimental setup consists of a silicon-based nanosphere that responds differently to electric and magnetic fields. We aim a laser beam with tailored polarization at the probe. By measuring the light scattered by the probe, we can determine how electric and magnetic dipoles are excited in the probe, which, in turn, allows us to reconstruct the transverse spin density of the laser. In a linearly polarized beam, we find that the electric and magnetic spins are rotated 90 degrees relative to one another. In a radially polarized beam, the transverse spin density is purely electric, while in an azimuthally polarized beam, the spin density is entirely magnetic.

Our results should allow researchers to unravel the electric and magnetic contributions to spin-dependent effects and demonstrate that the magnetic transverse spin can provide an extra handle for controlled spin-dependent directional coupling.