• Advanced Photonics
  • Vol. 3, Issue 3, 034001 (2021)
Yuanjie Yang1、*, Yu-Xuan Ren2、*, Mingzhou Chen3、*, Yoshihiko Arita3、4, and Carmelo Rosales-Guzmán5、6、*
Author Affiliations
  • 1University of Electronic Science and Technology of China, School of Physics, Chengdu, China
  • 2University of Hong Kong, Department of Electrical and Electronic Engineering, Hong Kong SAR, China
  • 3University of St Andrews, SUPA, School of Physics and Astronomy, St Andrews, United Kingdom
  • 4Chiba University, Molecular Chirality Research Center, Chiba, Japan
  • 5Centro de Investigaciones en Óptica, A.C., León, Guanajuato, Mexico
  • 6Harbin University of Science and Technology, Wang Da-Heng Collaborative Innovation Center for Quantum Manipulation and Control, Harbin, China
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    Abstract

    Optical trapping describes the interaction between light and matter to manipulate micro-objects through momentum transfer. In the case of 3D trapping with a single beam, this is termed optical tweezers. Optical tweezers are a powerful and noninvasive tool for manipulating small objects, and have become indispensable in many fields, including physics, biology, soft condensed matter, among others. In the early days, optical trapping was typically accomplished with a single Gaussian beam. In recent years, we have witnessed rapid progress in the use of structured light beams with customized phase, amplitude, and polarization in optical trapping. Unusual beam properties, such as phase singularities on-axis and propagation invariant nature, have opened up novel capabilities to the study of micromanipulation in liquid, air, and vacuum. We summarize the recent advances in the field of optical trapping using structured light beams.
    F=14Re(αp)|E|2+σ(αp)2cRe(E×H*)+σ(αp)c×(ϵ04ωiE×E*),(1)

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    αp=α01iα0k3/6πϵm,(2)

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    Fgrad=2πnmr3c(η21η2+2)I(r),(3)

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    Fscat=8πnmk4r63c(η21η2+2)2I(r)z^,(4)

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    Γ0x˙=κ0x+Fth,(5)

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    Sx(f)=4Γ0kBT/κ021+f2/fc2,(6)

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    0Sx(f)df=x2=kBTκ0.(7)

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    LGp(ρ,φ,z)=ω0ω(z)2p!π(||+p)!(2ρω(z))||Lp||[2(ρω(z))2]×exp[i(2p+||+1)ξ(z)]×exp[(ρω(z))2]exp[ikρ22R(z)]exp(iφ),(8)

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    B(ρ,φ,z)=E0J(ktρ)exp(ikzz)exp(φ),(9)

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    B(ρ,φ,0)=J(ktρ)exp[(ρω0)2]exp(iφ).(10)

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    V(ρ,θ)=exp(ρρ0Δρ2)eiθ,(11)

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    [2ξ2+2η2+f2kt22(cosh2ξcos2η)]uT(ξ,η)=0.(12)

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    Mme(ξ,η,z;q)=CmJem(ξ;q)cem(η;q)exp(ikzz),(13)

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    Mmo(ξ,η,z;q)=SmJom(ξ;q)sem(η;q)exp(ikzz).(14)

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    MGme(ξ˜,η˜,z;q)=exp(ikt22kzμ)Mme(ξ˜,η˜,z;q)exp(r2μω02)exp(ikz)μ,(15)

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    MGmo(ξ˜,η˜,z;q)=exp(ikt22kzμ)Mmo(ξ˜,η˜,z;q)exp(r2μω02)exp(ikz)μ.(16)

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    A(sx,sy,ξ)=Ai[sx(ξ2)2]Ai[sy(ξ2)2]exp[iξ2(sx+syξ33)],(17)

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    A0(sx,sy,ξ)=Ai[sx(ξ2)2+ibξ]Ai[sy(ξ2)2+ibξ]×exp[b(sx+sy)bξ2+ibξ2ξ36+iξ(sx+sy)2],(18)

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    F1{A0(sx,sy)}exp[b(kx2+ky2)]exp[i(kx3+ky3)3],(19)

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    IGp,me(r,ϵ)=Cω0ω(z)Cpm(iξ,ϵ)Cpm(η,ϵ)exp(r2ω2(z))exp{i[kz+k22R(z)(p+1)ξ(z)]},(20)

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    IGp,mo(r,ϵ)=Sω0ω(z)Spm(iξ,ϵ)Spm(η,ϵ)exp(r2ω2(z))exp{i[kz+k22R(z)(p+1)ξ(z)]},(21)

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    ψ(r,φ)=φ(Kr/ro),(22)

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    U(r)=u1(r)eiδ1e^R+u2(r)eiδ2e^L,(23)

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    U(r)=12(LGp11eiδ1e^R+LGp22eiδ2e^L).(24)

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    U(r)=12(LG0e^R+LG0eiδe^L).(25)

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    UTE(r)=12(LG01e^R+LG01e^L),(26)

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    UTM(r)=12(LG01e^RLG01e^L),(27)

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    UHEo(r)=12(LG01e^L+LG01e^R),(28)

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    UHEe(r)=12(LG01e^LLG01e^R).(29)

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    Ef(ρ)=k2πfeiθ(ρ)d2rEin(r)eikr·ρ/f,(30)

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    R(θ)=aλNA[1+10dφ(θ)dθ],(31)

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    Raλ/NA(1+/0),(32)

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    uγ,(r,z)=m=[γk]||mγ2Jm(qmR)exp[i(m)γz]exp(imθ)Jm(qmr),(33)

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    R0(s)=R(cos(sR)cosβ,sin(sR),cos(sR)sinβ),(34)

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    E(r0)=0Tg(t)exp[ik2f2uz(t)r02]exp[ikfr0R(t)]dt,(35)

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    E˜(r,z=uz(t))=iλexp[ikuz(t)]f0Tg(t)δ[1f(R(t)r)]dt.(36)

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    Ψ(t)=2πS(T)S(t),(37)

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    S(t)=0t|c(τ)|dτ.(38)

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    E(r)=1T0TΦ(r,t)φ(r,t)|c2(t)|dt(39)

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    Φ(r,t)=exp{iρ2[yx0(t)xy0(t)]}exp[i2πmS(T)S(t)],(40)

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    S(t)=0t[x0(τ)y0(τ)y0(τ)x0(τ)]dτ,(41)

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    φ(r,t)=exp{iπ[xx0(t)]2+[yy0(t)]2λf2z0(t)},(42)

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    bn(τ)=(1τ)3Ps(n)+3τ(1τ)2Ts(n)+3τ2(1τ)2Te(n)+τ3Pe(n),(43)

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    c(t)={b1(τ),b2(τ),,bm(τ)},(44)

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    mx¨=Γ0x˙κ0x+Fth,(45)

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    Sx(ω)=kBTπmΓ0(ω2Ω02)2+ω2Γ02,(46)

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    x2=kBTCMmΩ02.(47)

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    Copy Citation Text
    Yuanjie Yang, Yu-Xuan Ren, Mingzhou Chen, Yoshihiko Arita, Carmelo Rosales-Guzmán. Optical trapping with structured light: a review[J]. Advanced Photonics, 2021, 3(3): 034001
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    Category: Reviews
    Received: Dec. 1, 2020
    Accepted: Mar. 25, 2021
    Published Online: Jun. 3, 2021
    The Author Email: Yang Yuanjie (dr.yang2003@uestc.edu.cn), Ren Yu-Xuan (yxren@ustc.edu.cn), Chen Mingzhou (mingzhou.chen@st-andrews.ac.uk), Rosales-Guzmán Carmelo (carmelorosalesg@cio.mx)