Circular Dichroism in Rotating Particles

Deng Pan, Hongxing Xu, and F. Javier García de Abajo

Phys. Rev. Lett. 123, 066803 – Published 9 August 2019

Abstract

Light interaction with rotating nanostructures gives rise to phenemona as varied as optical torques and quantum friction. Surprisingly, the most basic optical response function of nanostructures undergoing rotation has not been clearly addressed so far. Here we reveal that mechanical rotation results in circular dichroism in optically isotropic particles, which show an unexpectedly strong dependence on the particle internal geometry. More precisely, particles with one-dimensionally confined electron motion in the plane perpendicular to the rotation axis, such as nanorings and nanocrosses, exhibit a splitting of $2 Ω$ in the particle optical resonances, while compact particles, such as nanodisks and nanospheres, display weak circular dichroism. We base our findings on a quantum-mechanical description of the polarizability of rotating particles, incorporating the mechanical rotation by populating the particle electronic states according to the principle that they are thermally equilibrated in the rotating frame. We further provide insight into the rotational superradience effect and the ensuing optical gain, originating in population inversion as regarded from the lab frame, in which the particle is out of equilibrium. Surprisingly, we find the optical frequency cutoff for superradiance to deviate from the rotation frequency $Ω$ . Our results unveil a rich, unexplored phenomenology of light interaction with rotating objects, which might find applications in various fields, such as optical trapping and sensing.

Received 3 March 2019

DOI:https://doi.org/10.1103/PhysRevLett.123.066803

Physics Subject Headings (PhySH)

Casimir effect & related phenomena

Atomic, Molecular & Optical

Authors & Affiliations

Deng Pan^1,*, Hongxing Xu², and F. Javier García de Abajo^1,3,†

¹ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
²School of Physics and Technology, Wuhan University, Wuhan 430072, China
³ICREA-Institució Catalana de Recerca i Estudis Avançats, Passeig Lluís Companys 23, 08010 Barcelona, Spain

^*Corresponding author. deng.pan@icfo.eu
^†Corresponding author. javier.garciadeabajo@nanophotonics.es

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Issue

Vol. 123, Iss. 6 — 9 August 2019

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Images

Figure 1
We consider optically isotropic particles characterized by a resonance frequency $ω_{0}$ when they are at rest. (a) When the particles rotate with angular velocity $Ω$ , the optical resonance frequency becomes $ω_{\pm} = ω_{0} \pm η Ω + β Ω^{2}$ for RCP ( $+$ ) and LCP ( $-$ ) illumination in the lab frame (both equal to $ω_{0}$ at $Ω = 0$ ), where the shape-dependent $η$ and $β$ terms are corrections due to Coriolis and centrifugal forces, respectively. (b) In the frame rotating with the particles, internal electrons experience Coriolis ( $F_{co}$ ) and centrifugal ( $F_{ce}$ ) forces, while the apparent frequency of circularly polarized incident light shifts to $ω \mp Ω$ . The effect of $F_{co}$ and $F_{ce}$ depends on particle morphology.
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Figure 2
(a) Energy spectra (black curves) and thermal population (red shaded curve) of the electron states $| m ⟩$ in a quasi-one-dimensional nanoring. Solid and dashed black curves correspond to electron states in the ring observed in the lab frame (energies $E_{m}$ ) and in a frame rotating at a frequency $Ω$ (energies ${\tilde{E}}_{m}$ ), respectively. If the ring rotates at frequency $Ω$ , its internal states are in thermal equilibrium in the rotating frame, so the population $f_{m}$ of states $| m ⟩$ is determined by ${\tilde{E}}_{m}$ . (b) Quantum-mechanical results for the LCP and RCP polarizability tensor components of a rotating nanoring (radius $a = 8 nm$ , 80 electrons, damping $ℏ γ = 20 meV$ ) for $ℏ Ω = 50 meV$ . Results for the motionless particle (dashed curve) are displayed for comparison. The particle temperature is taken to be 300 K. (c) Position of the resonance frequencies for LCP and RCP light as a function of rotation frequency.
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Figure 3
(a) Energy spectrum of a nanodisk (radius $a = 12 nm$ ) observed in the lab frame, where $m$ and $l$ denote azimuthal and radial quantum numbers. The black curve shows the Fermi level when the disk contains 80 electrons. (b) Energy spectrum in a rotating frame for the disk in (a) with $ℏ Ω = 5 meV$ . The ground state shifts from $| l, m ⟩ = | 1, 0 ⟩$ in the lab frame to $| 1, 4 ⟩$ in the rotating frame. Energies are referred to the respective ground state energies $E_{g}$ and ${\tilde{E}}_{g}$ .
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Figure 4
(a) Polarizability of a disk (radius $a = 12 nm$ , 80 electrons, damping $ℏ γ = 10 meV$ ) rotating at different frequencies $Ω$ (see labels) for LCP (blue) and RCP (red) light. (b) Rotation-frequency dependence of the cutoff for superradiance. (c),(d) $Ω$ dependence of the resonance frequency $ω_{\pm}$ (c) and maximum polarizability (d) extracted from (a).
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