Measuring the Transverse Spin Density of Light

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Measuring the Transverse Spin Density of Light

Martin Neugebauer, Thomas Bauer, Andrea Aiello, and Peter Banzer

Phys. Rev. Lett. 114, 063901 – Published 9 February 2015

Abstract

We generate tightly focused optical vector beams whose electric fields spin around an axis transverse to the beams’ propagation direction. We experimentally investigate these fields by exploiting the directional near-field interference of a dipolelike plasmonic field probe placed adjacent to a dielectric interface. This directionality depends on the transverse electric spin density of the excitation field. Near- to far-field conversion mediated by the dielectric interface enables us to detect the directionality of the emitted light in the far field and, therefore, to measure the transverse electric spin density with nanoscopic resolution. Finally, we determine the longitudinal electric component of Belinfante’s elusive spin momentum density, a solenoidal field quantity often referred to as “virtual.”

Received 19 November 2014

DOI:https://doi.org/10.1103/PhysRevLett.114.063901

Authors & Affiliations

Martin Neugebauer^1,2, Thomas Bauer^1,2, Andrea Aiello^1,2, and Peter Banzer^1,2,3,*

¹Max Planck Institute for the Science of Light, Guenther-Scharowsky-Straße 1, D-91058 Erlangen, Germany
²Institute of Optics, Information and Photonics, University Erlangen-Nuremberg, Staudtstraße 7/B2, D-91058 Erlangen, Germany
³Department of Physics, University of Ottawa, 25 Templeton Street, Ottawa, Ontario K1N 6N5, Canada

^*http://www.mpl.mpg.de; peter.banzer@mpl.mpg.de

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Vol. 114, Iss. 6 — 13 February 2015

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Images

Figure 1
Experimental concept, setup, and far-field detection scheme. (a) A transversely spinning dipole (here: counterclockwise spinning denoted by the black arrow in the inset) in close proximity to a dielectric interface has a directional emission pattern (green line) into the region above the critical angle (red arc). The actual critical angle is indicated by the dashed black line at the numerical aperture (NA) equal to 1. (b) An incoming (here: radially or linearly polarized) paraxial beam is tightly focused onto a gold nanoparticle ( $radius = 40 nm$ ) sitting on a glass substrate. The light emitted by the dipole into the region above the critical angle ( $NA > 1$ ) can be collected up to a NA of 1.3 by the immersion-type objective. An exemplarily measured far-field pattern of a transversely spinning dipole is depicted in (c). Only the light scattered by the particle is detected above the critical angle. Averaging the intensity in four small regions in $k$ -space (white circles) yields four intensity values ( $I_{1}$ , $I_{2}$ , $I_{3}$ , and $I_{4}$ ).
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Figure 2
(a) The beam profile of the incoming paraxial radially polarized beam, and (b) the respective theoretically calculated focal energy density distribution of the electric field ${| E_{tot} |}^{2}$ . The measured distributions of the two components of the transverse spin density $s_{E}^{x}$ and $s_{E}^{y}$ (normalized to their common maximum value) are depicted in (c) and (d), and the experimentally reconstructed component of Belinfante’s spin momentum $p_{s, E}^{z}$ (normalized to its maximum value) is shown in (e). The corresponding theoretically calculated distributions are plotted as insets. A side view of the tightly focused beam propagating in the $z$ direction (green arrow) is sketched in (f). Counterclockwise and clockwise transverse spinning of the local electric field vector to the left and right of the optical axis (gray arrows) yields an antiparallel $p_{s, E}^{z}$ (red arrow) on the optical axis.
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Figure 3
(a) The beam profile of the incoming paraxial linearly polarized beam, and (b) the respective theoretically calculated focal distribution of ${| E_{tot} |}^{2}$ . The measured distributions of $s_{E}^{x}$ and $s_{E}^{y}$ (normalized to their common maximum value) are depicted in (c) and (d), and the experimentally reconstructed distribution of $p_{s, E}^{z}$ (normalized to its maximum value) is shown in (e). The corresponding theoretically calculated distributions are plotted as insets. A side view of the tightly focused beam propagating in the $z$ direction (green arrow) is sketched in (f). Clockwise and counterclockwise transverse spinning of the local electric field vector to the left and right of the optical axis (gray arrows) yields a parallel $p_{s, E}^{z}$ (red arrow) on the optical axis.
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