Mimicking chiral light-matter interaction

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Mimicking chiral light-matter interaction

Sergey Nechayev and Peter Banzer

Phys. Rev. B 99, 241101(R) – Published 4 June 2019

Abstract

We demonstrate that achiral electric-dipole scatterers can mimic an interaction of light with chiral matter by generating far-field circular polarization upon scattering, even though the optical chirality of the incident field as well as that of the scattered light is zero. On the one hand, the presented effect originates from the fact that electric-dipole scatterers respond selectively only to the incident electric field, which eventually results in depolarization of the transmitted beam and in generation of far-field circular polarization. On the other hand, although the incident beam does not possess any optical chirality, it lacks reflection symmetry and therefore it is geometrically chiral. To experimentally demonstrate this effect, we utilize a cylindrical vector beam with spiral polarization and a spherical gold nanoparticle positioned on the optical axis—the axis of rotational symmetry of the system. Our experiment and a simple theoretical model address the fundamentals of duality symmetry in optics and chiral light-matter interactions, accentuating their richness and ubiquity yet in highly symmetric configurations.

Received 3 April 2019
Revised 23 May 2019

DOI:https://doi.org/10.1103/PhysRevB.99.241101

Physics Subject Headings (PhySH)

Beam polarization Chirality Mie scattering Nanoantennas Nanophotonics Polarization in interactions & scattering

Atomic, Molecular & Optical

Authors & Affiliations

Sergey Nechayev^* and Peter Banzer

Max Planck Institute for the Science of Light, Staudtstr. 2, D-91058 Erlangen, Germany and Institute of Optics, Information and Photonics, University Erlangen-Nuremberg, Staudtstr. 7/B2, D-91058 Erlangen, Germany

^*sergey.nechayev@mpl.mpg.de

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Vol. 99, Iss. 24 — 15 June 2019

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Images

Figure 1
(a) An aplanatic high numerical aperture (NA) microscope objective (MO) focuses the incident field distribution in its back focal plane (BFP) $E_{inc}^{ψ}$ . The focal plane ( $z = 0$ ) constitutes a boundary between two dielectric media with refractive indices $n_{1}$ and $n_{2}$ . The focal field $E_{foc}^{ψ}$ excites a spherical electric-dipole-like nanoparticle positioned along the optical axis $z$ at the position $z = z_{0}$ . The second confocally aligned index-matched aplanatic MO collimates the incident beam and collects the scattered light $E_{sc}^{ψ}$ . The interference pattern of $E_{inc}^{ψ}$ and $E_{sc}^{ψ}$ is observed in the BFP of the second MO. The theoretical description is given for the case of $n_{1} = n_{2} = 1$ , ${NA}_{1} = {NA}_{2} = 1$ , and $z_{0} = 0$ . In the experimental section, we use $n_{1} = 1$ , $n_{2} = 1.52$ , ${NA}_{1} = n_{1} max {sin (θ_{1})} = 0.9$ , ${NA}_{2} = n_{2} max {sin (θ_{2})} = 1.3$ , and $z_{0} = - d / 2 = 70 nm$ , where $d = 140 nm$ is the diameter of the nanoparticle. (b) Distribution of the incident spirally polarized cylindrical vector beam (SPCVB) in the BFP of the first MO. The intensity pattern is shown as the color map, while the white arrows depict the polarization pattern. (c) Mirror reflection properties of a SPCVB with $ψ = + 45^{\circ}$ , which can be represented as an in-phase superposition of a radially (TM) and azimuthally (TE) polarized beams with equal amplitudes. The TE component acquires a $π$ phase upon mirror reflection, which switches the sense of rotation of the SPCVB and the angle to $ψ = - 45^{\circ}$ . Importantly, this SPCVB is a three-dimensional chiral object, similar to a seashell or a human hand, while the third dimension corresponds to the propagation direction or the optical axis $z$ .
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Figure 2
(a) Sketch of the experimental setup. The incident beam is focused onto a gold nanoparticle by a microscope objective (MO). The light propagating in the forward direction is collected and collimated by an immersion-type MO and transmitted through an achromatic quarter-wave plate (QWP) and a rotatable linear polarizer (LP). A subsequent lens images the back focal plane of the second MO onto a camera. (b) The calculated (solid line) and measured (markers) averaged normalized value of the third Stokes parameter ${\tilde{S}}_{3}$ as a function of the spiral polarization angle $ψ$ at the wavelength of $λ = 600 nm$ . (c) Longitudinal (along the substrate normal) electric-dipole polarizability $α_{e}$ , normalized to its own maximal value, of a spherical gold particle of diameter $d = 140 nm$ positioned on a glass substrate with the refractive index $n = 1.52$ . (d) The calculated (solid lines) and measured (markers) ${\tilde{S}}_{3}$ in the forward scattering hemisphere (fwd.) as a function of wavelength for the spiral polarization angles $ψ = + 45^{\circ}$ (red) and $ψ = - 45^{\circ}$ (blue). The red dashed and blue dotted lines display the corresponding calculated ${\tilde{S}}_{3}$ over the full $4 π$ solid angle (tot.), showing the overall degree of polarization handedness. The black circles show the measured ${\tilde{S}}_{3}$ for radial excitation $ψ = 0^{\circ}$ . (e) Calculated (left column) and measured (right column) angularly resolved $S_{3}$ parameters for $ψ = + 45^{\circ}$ (top row) and $ψ = - 45^{\circ}$ (bottom row) at $λ = 630 nm$ , normalized to the maximal value of $S_{0}$ . These images show that $S_{3}$ is only significant in the angular region containing both the incident and the scattered light (NA $\leq 0.9$ ), while the scattered light itself ( $0.9 < NA$ $\leq 1.3$ ) does not contain significant circular polarization.
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