Photon Hall Pinwheel Radiation of Angular Momentum by a Diffusing Magneto-Optical Medium

We present a new optical effect that exchanges angular momentum between light and matter. The matter consists of an optically thick spherical, rigid agglomerate of magneto-optical scatterers placed in a homogeneous magnetic field. The light comes from an unpolarized, coherent central light source. The photon Hall effect induces a spiraling Poynting vector, both inside and outside the medium. Optical orbital angular momentum leaks out and induces a torque proportional to the injection power of the source and the photon Hall angle.

Figure 1

The photon Hall pinwheel: The photon Hall effect inside a diffuse sphere emerges as a Poynting vector spiraling around the origin, not affecting net energy transport but carrying a finite orbital angular momentum. The radiation leaves the sphere under the photon Hall angle ${\varphi }_H=D_H/D$ with the local normal (here drawn for $D_H<0$), decreasing as $1/r$ with distance.

Figure 2

Geometry of the PHE in the far field of the sphere. The diffuse light arriving from the source in the center initiates secondary random sources at ${\mathit{r}}_s$ within a skin layer of depth $\ell$ near the surface, that contribute to the Poynting vector $\mathbf{S}$ in the far field. The induced PHE at $\mathit{r}$ is largest when the magnetic field is perpendicular to the plane.

Figure 3

Proposed experimental setup for the observation of the photon pinwheel effect. (a) Side view: The sample consists of a sphere of radius $\mathit{a}$ of polydisperse particles with a large Faraday effect in a transparent rigid matrix, mounted on a optical fiber. The fiber also serves as a torsion wire, with the fiber cladding removed near the center of the sphere. The light injected into the two fiber ends is chopped at the torsion pendulum resonance frequency. (b) Mid-plane top view: Measurement of the torsion angle by deflection of a laser onto a position sensitive detector, readout with phase sensitive detection at the chopping frequency. By measuring only the deflection that changes sign with the sign of “B,” all artifacts related to the geometrical imprecision of the sample and setup are eliminated and only the photon Hall torque is measured.