Geometric spin Hall effect of light in tightly focused polarization-tailored light beams

Recently, it was shown that a nonzero transverse angular momentum manifests itself in a polarization-dependent intensity shift of the barycenter of a paraxial light beam [Aiello et al., Phys. Rev. Lett. 103, 100401 (2009)]. The underlying effect is phenomenologically similar to the spin Hall effect of light but does not depend on the specific light-matter interaction and can be interpreted as a purely geometric effect. Thus, it was named the geometric spin Hall effect of light. Here, we experimentally investigate the appearance of this effect in tightly focused vector beams. We use an experimental nanoprobing technique in combination with a reconstruction algorithm to verify the relative shifts of the components of the electric energy density and the shift of the intensity in the focal plane. By that, we experimentally demonstrate the geometric spin Hall effect of light in a highly nonparaxial beam.

Figure 1

Schematic illustration of the generation of light with purely transverse angular momentum. In front of the focusing system the paraxial beam propagating in the positive $z$ direction is spatially separated in a left- and right-handed circularly polarized part along the $x$ axis. The spin (red arrows) in the upper part of the beam is parallel to the optical axis while it is antiparallel in the lower part. Focusing of such a spin-segmented beam profile leads to the tilting of the spin vectors and, for symmetry reasons, to the generation of purely transverse angular momentum ${\mathbf{J}}_t$ in the focal plane.

Figure 2

(a) Normalized electric energy density distribution $|{\mathbf{E}}_0{|}^2$ of the incoming paraxial beam (${\mathrm{TEM}}_{10}$ mode, $w_0=1.9$ mm). The white ring corresponds to the geometric aperture of the microscope objective ($\mathrm{NA}=1.3$). The black arrows indicate spin segmentation. (b) Focal distribution of the intensity $S_z$, (c) focal distribution of the electric energy density $|{\mathbf{E}}_{\mathrm{tot}}{|}^2$. Both distributions are normalized to their respective maximum value. (d)–(f) Components of the electric energy density $|E_x{|}^2$, $|E_y{|}^2$, and $|E_z{|}^2$ [normalized to the maximum value of $|{\mathbf{E}}_{\mathrm{tot}}{|}^2$ in (c)], and their corresponding relative phases ${\Phi }_x$, ${\Phi }_y$, and ${\Phi }_z$ (see insets). Black and white crosses mark the position of the barycenter for each individual quantity and the dashed white line indicates the $y$ coordinate of the barycenter of $|{\mathbf{E}}_{\mathrm{tot}}{|}^2$ in (c) and is used as reference in (b)–(f).

Figure 3

(a) Schematics of the nanoprobe scanning technique. A subwavelength gold nanosphere (diameter 90 nm) is scanned through the focal plane of the tightly focused vector beam. At each position, the particle is excited by the local electric field. By measuring the scattered and transmitted light, the focal spot can be reconstructed. (b) Scheme of the experimental setup. The paraxial beam ($x$-polarized ${\mathrm{TEM}}_{10}$ mode) impinges on a segmented quarter-wave plate (SQWP) with perpendicular fast axes. As a result, a laterally separated left- and right-handed circularly polarized beam is generated (red arrows). This beam is coupled into a high-numerical-aperture immersion-type objective (MO) and focused onto the sample, consisting of a particle sitting on a glass substrate. The sample is embedded in immersion oil index matched to the substrate. A second MO, identical to the first one and with the same focal plane, is mounted below the sample. It collects the forward-scattered and transmitted light. The back focal plane of the second MO is imaged with a camera.

Figure 4

(a) Experimental scanning result, normalized to its maximum value, measured in transmission. The signal is dominated by the extinction of the transmitted beam. (b)–(f) The reconstructed distributions of $S_z$, $|{\mathbf{E}}_{\mathrm{tot}}{|}^2$, $|E_x{|}^2$, $|E_y{|}^2$, and $|E_z{|}^2$ are depicted. Both $|{\mathbf{E}}_{\mathrm{tot}}{|}^2$ and $S_z$ are normalized to their respective maxima, while $|E_x{|}^2$, $|E_y{|}^2$, and $|E_z{|}^2$ are normalized to the maximum value of $|{\mathbf{E}}_{\mathrm{tot}}{|}^2$.

Figure 5

(a)–(d), (m)–(p) Images of the back focal plane. Different integration areas are highlighted with a white frame. (e)–(h), (q)–(t) The associated experimental scanning images. Each pixel of a scanning image represents the measured power value within the integration area for the corresponding particle position. (i–l), (u–x) Fitted distributions.