Extraordinary Multipole Modes and Ultra-Enhanced Optical Lateral Force by Chirality

Tongtong Zhu, Yuzhi Shi, Weiqiang Ding, Din Ping Tsai, Tun Cao, Ai Qun Liu, Manuel Nieto-Vesperinas, Juan José Sáenz, Pin Chieh Wu, and Cheng-Wei Qiu

Phys. Rev. Lett. 125, 043901 – Published 20 July 2020

Abstract

Strong mode coupling and Fano resonances arisen from exceptional interaction between resonant modes in single nanostructures have raised much attention for their advantages in nonlinear optics, sensing, etc. Individual electromagnetic multipole modes such as quadrupoles, octupoles, and their counterparts from mode coupling (toroidal dipole and nonradiating anapole mode) have been well investigated in isolated or coupled nanostructures with access to high $Q$ factors in bound states in the continuum. Albeit the extensive study on ordinary dielectric particles, intriguing aspects of light-matter interactions in single chiral nanostructures is lacking. Here, we unveil that extraordinary multipoles can be simultaneously superpositioned in a chiral nanocylinder, such as two toroidal dipoles with opposite moments, and electric and magnetic sextupoles. The induced optical lateral forces and their scattering cross sections can thus be either significantly enhanced in the presence of those multipoles with high- $Q$ factors, or suppressed by the bound states in the continuum. This work for the first time reveals the complex correlation between multipolar effects, chiral coupling, and optical lateral force, providing a distinct way for advanced optical manipulation.

Received 27 February 2020
Accepted 22 June 2020

DOI:https://doi.org/10.1103/PhysRevLett.125.043901

Physics Subject Headings (PhySH)

Classical optics Light-matter interaction Metamaterials Nanophotonics

Atomic, Molecular & Optical

Authors & Affiliations

Tongtong Zhu ^1,2, Yuzhi Shi^3,4,*, Weiqiang Ding⁵, Din Ping Tsai ⁶, Tun Cao¹, Ai Qun Liu⁴, Manuel Nieto-Vesperinas ⁷, Juan José Sáenz⁸, Pin Chieh Wu ⁹, and Cheng-Wei Qiu ^2,†

¹School of Optoelectronic Engineering and Instrumentation Science, Dalian University of Technology, Dalian 116024, China
²Department of Electrical and Computer Engineering, National University of Singapore, Singapore 117583
³School of Mechanical Engineering, Xi’an Jiaotong University, Xi’an 710049, China
⁴School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798
⁵Department of Physics, Harbin Institute of Technology, Harbin 150001, China
⁶Department of Electronic and Information Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China
⁷Instituto de Ciencia de Materiales de Madrid, Consejo Superior de Investigaciones Científicas, Campus de Cantoblanco, Madrid 28049, Spain
⁸Donostia International Physics Center, 20018 Donostia-San Sebastián, Spain
⁹Department of Photonics, National Cheng Kung University, Tainan 70101, Taiwan

^*Corresponding author. shiyuzhi1990@gmail.com
^†Corresponding author. eleqc@nus.edu.sg

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Issue

Vol. 125, Iss. 4 — 24 July 2020

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Images

Figure 1
Superposition of electromagnetic modes and enhanced optical lateral force from chiral nanocylinders at the water-air interface. (a) Illustration of the chiral nanocylinder under the illumination of an obliquely incident $s$ -polarized beam with an incident angle of $θ$ . Two multipole modes are excited when the radius and length of the cylinder change. TD: toroidal dipole. ES: electric sextupole. MS: magnetic sextupole. (b) Two TD with opposite momentums appear in the upper and lower part of the cylinder when $x_{coe} = 0.982$ and $l_{coe} = 0.634$ ( $r 1$ ). The cylinder has two ES on both sides and a MS in the middle when $x_{coe} = 0.708$ and $l_{coe} = 0.624$ ( $r 2$ ). (c) Optical lateral force with the relation of the aspect ratio and incident angle when $x_{coe} = 0.982$ . (d) Superpositions of ES and MS with different kappa and incident angles when $x_{coe} = 0.708$ and $l_{coe} = 0.624$ . Sextupole (SP). The lateral force $F_{y}$ is enhanced significantly in two resonance modes. Illustration of the Poynting vectors in the $y − z$ plane indicating (e) a negative lateral force $F_{y}$ in system 1 and (f) a positive $F_{y}$ in system 2. Scale bars in (e) and (f) equal 100 nm.
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Figure 2
Dispersion of modes and optical lateral force in a high-index chiral cylinder. (a) Scattering cross sections with dispersion modes in a high-index chiral pillar. The nanocylinder with $ϵ = 80$ and $κ = 0.4$ is under the illumination of an $s$ -polarization beam with $θ = 50 °$ . (b) Dispersion of modes near a BIC point. (c) Optical lateral forces near the BIC point. Scale bar equals 100 nm.
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Figure 3
Characterization of the multipole modes supported by a dielectric chiral cylinder. (a) Spectra of scattering cross section and optical torques of the chiral nanocylinders near the BIC point. The solid lines and dashed lines represent the spectra and optical torques, respectively. The $ϵ$ and $κ$ of the nanocylinder are 80 and 0.4, respectively. (b) Comparison of optical forces in the $x$ and $y$ directions on the nanocylinders near the BIC point.
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Figure 4
Field distribution in different layers in nanocylinders in system 1 and system 2. (a) Upper row: Map of magnetic field in the $z$ direction and arrow of magnetic flux density showing the toroidal dipole in different $x − y$ planes with momentum $T$ turns between $T > 0$ and $T < 0$ . Lower row: Three-dimensional displacement density. And $x_{coe} = 0.982$ ; $l_{coe} = 0.634$ . (b) Upper row: Map of normalized electric field and arrow of displacement current density in different $x − y$ planes. Lower row: Map of magnetic field in the $z$ direction and arrow of magnetic flux density. And $x_{coe} = 0.708$ ; $l_{coe} = 0.624$ .
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