Left-handed optical torque on dipolar plasmonic nanoparticles induced by Fano-like resonance

Huajin Chen, Lv Feng, Jiangnan Ma, Chenghua Liang, Zhifang Lin, and Hongxia Zheng

Phys. Rev. B 106, 054301 – Published 1 August 2022

Abstract

We theoretically and numerically demonstrate that Fano-like resonance can induce a left-handed optical torque on a dipolar plasmonic core-shell nanoparticle in the interference optical field composed of two linearly polarized plane waves. It is shown that the optical torque on the dipolar plasmonic nanoparticle is significantly enhanced at the Fano-like resonance, and its direction is opposite to that of the angular momentum of the incident field, termed Fano-like resonance-induced left-handed optical torque. The extinction spectra exhibit that the Fano-like resonance stems from the coupling between a narrow electric quadrupole dark mode and a broad electric dipole bright mode. In addition, such Fano-like resonance-induced left-handed optical torque can flexibly be tailored by the particle morphology. To further trace the physical origin of the left-handed optical torque, we derive an analytical expression of optical torques up to electric quadrupole in generic monochromatic optical fields based on the multipole expansion theory. The results obtained from our analytical expression show that the left-handed optical torque comes completely from the electric quadrupole terms while other terms from the electric dipole make no contribution. Our results may open a new avenue for tailoring optical torques on plasmonic structures.

Received 20 April 2022
Revised 6 July 2022
Accepted 13 July 2022

DOI:https://doi.org/10.1103/PhysRevB.106.054301

Physics Subject Headings (PhySH)

Angular momentum of light Light-matter interaction Optomechanics

Atomic, Molecular & Optical

Authors & Affiliations

Huajin Chen^1,2,3, Lv Feng², Jiangnan Ma², Chenghua Liang¹, Zhifang Lin^3,4, and Hongxia Zheng ^1,*

¹School of Electronic Engineering, Guangxi University of Science and Technology, Liuzhou, Guangxi 545006, China
²School of Automation, Guangxi University of Science and Technology, Liuzhou, Guangxi 545006, China
³State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, China
⁴Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China

^*hxzheng18@fudan.edu.cn

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Issue

Vol. 106, Iss. 5 — 1 August 2022

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Images

Figure 1
Schematic illustration of an Ag-Au nanoparticle illuminated by the incident optical field composed of two interference plane waves symmetric with respect to $z$ axis with the same incident angle $α = 55^{\circ}$ on the $x o z$ plane. Two plane waves share the same polarized vector $(p, q) = (1, 0)$ , denoted by the double-headed arrows the orientations along which the electric fields are polarized. The particle has core radius $R_{1} = 35 nm$ and shell radius $R_{2} = 43 nm$ , which is supposed to be immersed in water and located at $x = 52 nm$ .
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Figure 2
(a) The $y$ component of the optical torque $T_{y}^{FWS}$ (solid blue line) and corresponding angular momentum density $J_{y}$ with details given in Appendix pp2 (solid red line with triangle symbol) as functions of the incident wavelength $λ$ . Left-handed optical torque with direction opposite to that of the angular momentum is induced when an appropriate incident optical wave with $λ = 441 nm$ to $λ = 463 nm$ is adopted. (b) The total extinction efficiency $Q_{ext}$ as well as partial extinction efficiencies $Q_{an}$ and $Q_{bn}$ , suggesting that the left-handed optical torque is strongly associated with the Fano-like resonance. The overlap of the broad electric dipole mode with the narrow electric quadrupole mode leads to the appearance of a narrow asymmetric Fano dip at $λ = 463 nm$ , around which the left-handed optical torque is induced. All other parameters are the same as those in Fig. 1.
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Figure 3
Phase diagrams of the optical torque $T_{y}^{FWS}$ in units of $ɛ_{0} {| E_{0} |}^{2} R_{2}^{3}$ with respect to the incident wavelength $λ$ as well as the core radius $R_{1}$ (a) and shell radius $R_{2}$ (b) of the Ag-Au core-shell particle with fixed $R_{2} = 43 nm$ (a) and $R_{1} = 35 nm$ (b), respectively. All other parameters are the same as those in Fig. 1. Gray regions indicate the parameter space for the right-handed optical torque phase, while colored regions denote the parameter space to achieve the left-handed optical torque phase. The white line denotes the positions of the Fano dip arising from the interference between the electric dipole and quadrupole modes, which may serve roughly as a guide to the eyes for the onset of the left-handed optical torque phase.
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Figure 4
The optical torque calculated by the multipole expansion theory is denoted by $T_{y}$ , while $T_{y}^{FWS}$ computed by the full-wave calculation given in Fig. 2 is also reproduced here. The perfect agreement between $T_{y}$ and $T_{y}^{FWS}$ verify the reliability of the multipolar expansion theory of optical torque. Also shown are constituent terms of $T_{y}$ originating from different coupling channels, specifically, $T_{e}^{y}$ and $T_{ee}^{y}$ from the lowest two coupling channels regarding electric dipole while $T_{Q^{e}}^{y}$ and $T_{Q^{e} Q^{e}}^{y}$ from interaction concerning electric quadrupole. Both $T_{m}^{y}$ and $T_{mm}^{y}$ give no contribution to the $T_{y}$ and thus are not demonstrated here for clarity. All the parameters are the same as those in Fig. 2.
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Figure 5
The optical torque $T_{y}$ for a naked Ag core with radius $R_{1} = 35 nm$ (a) and for a hollow Au shell particle with its empty core radius $R_{1} = 35 nm$ and shell radius $R_{2} = 43 nm$ (c). Corresponding total extinction efficiencies $Q_{ext}$ as well as partial extinction efficiencies $Q_{an}$ and $Q_{bn}$ are also shown in (b) and (d), respectively. All parameters are the same as those in Fig. 1.
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Figure 6
The decomposed contribution from low-order dipole coupling channels $T_{dip}^{y} = T_{e}^{y} + T_{ee}^{y}$ (a) (c) and high-order electric quadrupole coupling channels $T_{quad}^{y} = T_{Q^{e}}^{y} + T_{Q^{e} Q^{e}}^{y}$ (b) (d) for the total optical torque $T_{y}^{FWS}$ as shown in Fig. 3. All parameters are the same as those in Fig. 3.
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