• Photonics Research
  • Vol. 13, Issue 1, 49 (2025)
Haixiang Ma1,†, Fu Feng1,2,5,†,*, Jie Qiao1..., Jiaan Gan3 and Xiaocong Yuan1,4,6,*|Show fewer author(s)
Author Affiliations
  • 1Research Center for Frontier Fundamental Studies, Zhejiang Lab, Hangzhou 311100, China
  • 2State Key Laboratory of Extreme Photonics and Instrumentation, College of Optical Science and Engineering, Zhejiang University, Hangzhou 310058, China
  • 3Institute of Modern Optics, Tianjin Key Laboratory of Micro-scale Optical Information Science and Technology, Nankai University, Tianjin 300350, China
  • 4Nanophotonics Research Center, Institute of Microscale Optoelectronics & State Key Laboratory of Radio Frequency Heterogeneous Integration, Shenzhen University, Shenzhen 518061, China
  • 5e-mail: fufeng@zhejianglab.com
  • 6e-mail: xcyuan@zhejianglab.com
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    DOI: 10.1364/PRJ.530406 Cite this Article Set citation alerts
    Haixiang Ma, Fu Feng, Jie Qiao, Jiaan Gan, Xiaocong Yuan, "Positioning spherical nanoantennas with picometer precision," Photonics Res. 13, 49 (2025) Copy Citation Text show less

    Abstract

    Accurate positioning of nanoantennas is critical for their efficient excitation and integration. However, since nanoantennas are subwavelength nanoparticles, normally smaller than the diffraction limit, measuring their positions presents a significant challenge. This is particularly true for locating the nanoantenna along the z-direction, for which no suitable method currently exists. Here, we have theoretically developed and experimentally validated a novel light field capable of measuring the 3D positions of nanoantennas accurately. This field’s polarization chirality transitions from right-handed to left-handed along a predefined 3D direction at a subwavelength scale. For a spherical single-element nanoantenna, the polarization components of the scattering field change significantly as the nanoantenna moves, due to the rapid polarization transformation in the excitation light field. By analyzing the polarization components of the scattering field, we can achieve positional accuracy of the nanoantenna along the specified direction close to 20 pm. This work improves the accuracy of transversely distinguishing nanoantennas from 100 pm in conventional methods to 20 pm. Moreover, the positioning of the nanoantenna along three dimensions is all available as polarization transitions can be predefined along arbitrary 3D direction, which is significant for precision measurement and nanoscale optics.
    E=exp(ikαρcosϕf)exp(ikβρsinϕf)  exp(ikγf2ρ2f),

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    g=ILIRIL+IR.

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    Ein(ρ)=[EReRELeL]=[EeREeL],

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    {exp(ikαρcosϕf)=exp(ikαcosϕsinθ)exp(ikβρsinϕf)=exp(ikβsinϕsinθ)exp(ikγf2ρ2f)=exp(ikγcosθ).

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    ε=atan(A2A1)sign(Δψ),

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    Eout(r,φ,z)=ikf22π0α02πcosθ[22[EL(cosθ1)(cosϕ+isinϕ)2+(cosθ+1)ER]eR22[ER(cosθ1)(cosϕisinϕ)2+(cosθ+1)EL]eL[(ER+EL)cosϕ+i(EREL)sinϕ]sinθez]×exp{ik[zcosθ+rsinθcos(φϕ)]}sinθdθdϕ,(A1)

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    Eout(r,φ,z)=ikf22π0α02πcosθ[22E(cosθ+1)eR22E(cosθ1)(cosϕ+isinϕ)2eL]×exp[ikzcosθ+ikrsinθcos(φϕ)]sinθdθdϕ=ikf22π0α02πcosθ[22(cosθ+1)eR22[(cosθ1)(cosϕ+isinϕ)2]eL]×exp{ik(zγ)cosθ+ikrsinθ[(xα)cosϕ+(yβ)sinϕ]}sinθdθdϕ.(A2)

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    es=j=1n(gjg^j)2/(n2)j=1n(xjx¯)2,(A3)

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    e=Des/s,(A4)

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    s=j=1n(xjx¯)(gjg¯)j=1n(xjx¯)2,(A5)

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    {xj=jDx¯=n+12D.(A6)

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    e=Dj=1n(2jn1)2(gjg^j)2/(n2)j=1n(2jn1)(gjg¯).(A7)

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    E=Exex+Eyey=ikf22π0α02πcosθ[[(ER+EL)(cos2ϕcosθ+sin2ϕ)+i(EREL)cosϕsinϕ(cosθ1)]ex[(ER+EL)sinϕcosϕ(cosθ1)+i(EREL)(sin2ϕcosθ+cos2ϕ)]ey]×exp{ik[zcosθ+rsinθcos(φϕ)]}sinθdθdϕ,(A8)

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    γ=12atan2|Ex||Ey|cos(Δψ)|Ex|2|Ey|2.(A9)

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    {E1=Excosγ+EysinγE2=Exsinγ+Eycosγ.(A10)

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    {A1=|E1|A2=|E2|.(A11)

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    ε=atan(A2A1)sign(Δψ),(A12)

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    Haixiang Ma, Fu Feng, Jie Qiao, Jiaan Gan, Xiaocong Yuan, "Positioning spherical nanoantennas with picometer precision," Photonics Res. 13, 49 (2025)
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