Magnetic and Electric Transverse Spin Density of Spatially Confined Light

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Magnetic and Electric Transverse Spin Density of Spatially Confined Light

Martin Neugebauer, Jörg S. Eismann, Thomas Bauer, and Peter Banzer

Phys. Rev. X 8, 021042 – Published 14 May 2018

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.

Received 6 December 2017
Revised 7 February 2018

DOI:https://doi.org/10.1103/PhysRevX.8.021042

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Angular momentum of light Nanophotonics Polarization of light

Light scattering Optical techniques

Atomic, Molecular & Optical

Authors & Affiliations

Martin Neugebauer^1,2, Jörg S. Eismann^1,2, Thomas Bauer³, and Peter Banzer^1,2,*

¹Max Planck Institute for the Science of Light, Staudtstraße 2, D-91058 Erlangen, Germany
²Institute of Optics, Information and Photonics, University Erlangen-Nuremberg, Staudtstraße 7/B2, D-91058 Erlangen, Germany
³Department of Quantum Nanoscience, Kavli Institute of Nanoscience, Delft University of Technology, Lorentzweg 1, 2628 CJ Delft, Netherlands

^*peter.banzer@mpl.mpg.de

Popular 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.

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Issue

Vol. 8, Iss. 2 — April - June 2018

Subject Areas

Optics

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Images

Figure 1
TSD of a linearly polarized Gaussian beam. Panel (a) depicts the energy density $w$ and the spin density $s$ (yellow arrowheads). Panel (b) illustrates the transverse $x$ and $y$ components of $s_{E}$ and $s_{H}$ .
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Figure 2
Experimental concept and setup. (a) Sketch of an incoming tightly focused beam being probed by a silicon nanoparticle sitting on a glass substrate. The light scattered and transmitted into the glass half-space is collected in the far field. Only the light emitted into the solid angle above the critical angle ( $NA = 1$ , indicated by the dashed black lines) is required. Blocking the light collected below $NA = 1$ results in a ringlike far-field pattern visualized by red color coding. A scanning electron micrograph depicted in the inset shows the particle (the black scale bar indicates 100 nm). (b) Scattering cross section $σ_{scat}$ of a core-shell nanosphere (silicon core with a diameter of 158 nm and silicon dioxide shell with 8-nm thickness) calculated using Mie theory. (c) Directional emission (red line) of a transversely spinning magnetic dipole [dipole moment spinning clockwise, $m \propto (0, 1, 𝚤)$ , indicated by the black arrow] sitting on a glass substrate with refractive index $n = 1.5$ . (d) Experimental setup. An incoming monochromatic beam of light ( $λ = 630 nm$ ) is focused onto the nanosphere sitting on a glass substrate by a microscope objective with a NA of 0.9. The transmitted light is collected by a microscope objective with a NA of 1.3. A Wollaston prism (WP) is utilized to determine the polarization state ( $x$ and $y$ polarization) of the far-field pattern, which is measured by imaging the back focal plane of the lower microscope objective onto a CCD camera.
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Figure 3
Polarization-resolved BFP images. Panels (a) and (b) show exemplarily measured $x$ - and $y$ -polarized BFP images in the angular range defined by $1 \leq k_{⊥} / k_{0} \leq 1.3$ . Both images are normalized to their common maximum value. The inner dashed black circle corresponds to the critical angle $k_{⊥} / k_{0} = 1$ . The inner and outer semitransparent blue circles indicate $k_{⊥ 1} / k_{0} \equiv 1.1$ and $k_{⊥ 2} / k_{0} \equiv 1.25$ . The outer dashed black circle indicates $k_{⊥} / k_{0} = 1.3$ , representing the NA of the collection objective. An additional eight small black circles mark regions in the BFP, for which an averaged intensity value is determined, $I_{s i}^{j}$ and $I_{p i}^{j}$ , with $i = 1$ , 2, 3, 4 indicating the azimuthal position and $j = 1$ , 2 referring to $k_{⊥ 1}$ and $k_{⊥ 2}$ .
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Figure 4
Experimentally measured and theoretically calculated focal distributions of the magnetic and electric TSDs of tightly focused linearly, azimuthally, and radially polarized beams. The left column shows the TSD distributions of a tightly focused linearly polarized beam. Panels (a) and (b) depict the $x$ and $y$ components of $s_{H}$ , while panels (c) and (d) depict the $x$ and $y$ components of $s_{E}$ . Panels (e)–(h) display the corresponding distributions of a tightly focused azimuthally polarized beam (central column), and panels (i)–(l) present the corresponding distributions of a tightly focused radially polarized beam (right column). All distributions of the magnetic and the electric TSD are normalized to their common maximum value, respectively, in order to enable a direct comparison between all three beams.
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