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Advanced Photonics
Vol. 3, Issue 3, 034001 (2021)

Optical trapping with structured light: a review | Article Video , EIC Choice Award

Yuanjie Yang^1、*, Yu-Xuan Ren^2、*, Mingzhou Chen^3、*, Yoshihiko Arita^3、4, and Carmelo Rosales-Guzmán^5、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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DOI: 10.1117/1.AP.3.3.034001 Cite this Article Set citation alerts

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 Copy Citation Text

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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.

Keywords

optical angular momentum optical trapping structured beams vortex beam

Video Introduction to the Article

⟨ F ⟩ = \frac{1}{4} Re (α_{p}) \nabla {| E |}^{2} + \frac{σ (α_{p})}{2 c} Re (E \times H^{*}) + σ (α_{p}) c \nabla \times (\frac{ϵ_{0}}{4 ω i} E \times E^{*}),

(1)

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α_{p} = \frac{α_{0}}{1 - i α_{0} k^{3} / 6 π ϵ_{m}},

(2)

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F_{grad} = - \frac{2 π n_{m} r^{3}}{c} (\frac{η^{2} - 1}{η^{2} + 2}) \nabla I (r),

(3)

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F_{scat} = \frac{8 π n_{m} k^{4} r^{6}}{3 c} {(\frac{η^{2} - 1}{η^{2} + 2})}^{2} I (r) \hat{z},

(4)

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Γ_{0} \dot{x} = - κ_{0} x + F_{th},

(5)

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S_{x} (f) = \frac{4 Γ_{0} k_{B} T / κ_{0}^{2}}{1 + f^{2} / f_{c}^{2}},

(6)

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\int_{0}^{\infty} S_{x} (f) d f = ⟨ x^{2} ⟩ = \frac{k_{B} T}{κ_{0}} .

(7)

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{LG}_{p}^{ℓ} (ρ, φ, z) = \frac{ω_{0}}{ω (z)} \sqrt{\frac{2 p!}{π (| ℓ | + p)!}} {(\frac{\sqrt{2} ρ}{ω (z)})}^{| ℓ |} L_{p}^{| ℓ |} [2 (\frac{ρ}{ω (z)})^{2}] \times \exp [i (2 p + | ℓ | + 1) ξ (z)] \times \exp [- {(\frac{ρ}{ω (z)})}^{2}] \exp [- \frac{i k ρ^{2}}{2 R (z)}] \exp (i ℓ φ),

(8)

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B (ρ, φ, z) = E_{0} J_{ℓ} (k_{t} ρ) \exp (i k_{z} z) \exp (ℓ φ),

(9)

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B (ρ, φ, 0) = J_{ℓ} (k_{t} ρ) \exp [- {(\frac{ρ}{ω_{0}})}^{2}] \exp (- i ℓ φ) .

(10)

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V_{ℓ} (ρ, θ) = \exp (- \frac{ρ - ρ_{0}}{Δ ρ^{2}}) e^{i ℓ θ},

(11)

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[\frac{\partial^{2}}{\partial ξ^{2}} + \frac{\partial^{2}}{\partial η^{2}} + \frac{f^{2} k_{t}^{2}}{2} (\cosh 2 ξ - \cos 2 η)] u_{T} (ξ, η) = 0 .

(12)

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M_{m}^{e} (ξ, η, z; q) = C_{m} J e_{m} (ξ; q) c e_{m} (η; q) \exp (i k_{z} z),

(13)

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M_{m}^{o} (ξ, η, z; q) = S_{m} J o_{m} (ξ; q) s e_{m} (η; q) \exp (i k_{z} z) .

(14)

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M G_{m}^{e} (\tilde{ξ}, \tilde{η}, z; q) = \exp (- \frac{i k_{t}^{2}}{2 k} \frac{z}{μ}) M_{m}^{e} (\tilde{ξ}, \tilde{η}, z; q) \exp (- \frac{r^{2}}{μ ω_{0}^{2}}) \frac{\exp (i k z)}{μ},

(15)

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M G_{m}^{o} (\tilde{ξ}, \tilde{η}, z; q) = \exp (- \frac{i k_{t}^{2}}{2 k} \frac{z}{μ}) M_{m}^{o} (\tilde{ξ}, \tilde{η}, z; q) \exp (- \frac{r^{2}}{μ ω_{0}^{2}}) \frac{\exp (i k z)}{μ} .

(16)

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A (s_{x}, s_{y}, ξ) = Ai [s_{x} - {(\frac{ξ}{2})}^{2}] Ai [s_{y} - {(\frac{ξ}{2})}^{2}] \exp [\frac{i ξ}{2} (s_{x} + s_{y} - \frac{ξ^{3}}{3})],

(17)

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A_{0} (s_{x}, s_{y}, ξ) = Ai [s_{x} - {(\frac{ξ}{2})}^{2} + i b ξ] Ai [s_{y} - {(\frac{ξ}{2})}^{2} + i b ξ] \times \exp [b (s_{x} + s_{y}) - b ξ^{2} + i b ξ^{2} - \frac{ξ^{3}}{6} + \frac{i ξ (s_{x} + s_{y})}{2}],

(18)

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F^{- 1} {A_{0} (s_{x}, s_{y})} \propto \exp [- b (k_{x}^{2} + k_{y}^{2})] \exp [\frac{i (k_{x}^{3} + k_{y}^{3})}{3}],

(19)

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{IG}_{p, m}^{e} (r, ϵ) = \frac{C ω_{0}}{ω (z)} C_{p}^{m} (i ξ, ϵ) C_{p}^{m} (η, ϵ) \exp (\frac{- r^{2}}{ω^{2} (z)}) \exp {i [k z + \frac{k^{2}}{2 R (z)} - (p + 1) ξ (z)]},

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{IG}_{p, m}^{o} (r, ϵ) = \frac{S ω_{0}}{ω (z)} S_{p}^{m} (i ξ, ϵ) S_{p}^{m} (η, ϵ) \exp (\frac{- r^{2}}{ω^{2} (z)}) \exp {i [k z + \frac{k^{2}}{2 R (z)} - (p + 1) ξ (z)]},

(21)

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ψ (r, φ) = ℓ φ (K - r / r_{o}),

(22)

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U (r) = u_{1} (r) e^{i δ_{1}} {\hat{e}}_{R} + u_{2} (r) e^{i δ_{2}} {\hat{e}}_{L},

(23)

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U (r) = \frac{1}{\sqrt{2}} ({LG}_{p_{1}}^{ℓ_{1}} e^{i δ_{1}} {\hat{e}}_{R} + {LG}_{p_{2}}^{ℓ_{2}} e^{i δ_{2}} {\hat{e}}_{L}) .

(24)

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U (r) = \frac{1}{\sqrt{2}} ({LG}_{0}^{ℓ} {\hat{e}}_{R} + {LG}_{0}^{- ℓ} e^{i δ} {\hat{e}}_{L}) .

(25)

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U_{TE} (r) = \frac{1}{\sqrt{2}} ({LG}_{0}^{1} {\hat{e}}_{R} + {LG}_{0}^{- 1} {\hat{e}}_{L}),

(26)

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U_{TM} (r) = \frac{1}{\sqrt{2}} ({LG}_{0}^{1} {\hat{e}}_{R} - {LG}_{0}^{- 1} {\hat{e}}_{L}),

(27)

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U_{HE}^{o} (r) = \frac{1}{\sqrt{2}} ({LG}_{0}^{1} {\hat{e}}_{L} + {LG}_{0}^{- 1} {\hat{e}}_{R}),

(28)

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U_{HE}^{e} (r) = \frac{1}{\sqrt{2}} ({LG}_{0}^{1} {\hat{e}}_{L} - {LG}_{0}^{- 1} {\hat{e}}_{R}) .

(29)

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E^{f} (ρ) = \frac{k}{2 π f} e^{i θ (ρ)} \int d^{2} r E^{in} (r) e^{- i k r \cdot ρ / f},

(30)

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R (θ) = a \frac{λ}{NA} [1 + \frac{1}{ℓ_{0}} \frac{d φ (θ)}{d θ}],

(31)

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R_{ℓ} \approx a λ / NA (1 + ℓ / ℓ_{0}),

(32)

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u_{γ, ℓ} (r, z) = \sum_{m = [ℓ - γ k]}^{| ℓ |} \frac{ℓ - m}{γ^{2}} J_{m} (q_{m} R) \exp [\frac{i (ℓ - m)}{γ} z] \exp (i m θ) J_{m} (q_{m} r),

(33)

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R_{0} (s) = R (\cos (\frac{s}{R}) \cos β, \sin (\frac{s}{R}), \cos (\frac{s}{R}) \sin β),

(34)

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E (r_{0}) = \int_{0}^{T} g (t) \exp [- \frac{i k}{2 f^{2}} u_{z} (t) r_{0}^{2}] \exp [\frac{i k}{f} r_{0} R (t)] d t,

(35)

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\tilde{E} (r, z = u_{z} (t)) = - \frac{i λ \exp [i k u_{z} (t)]}{f} \int_{0}^{T} g (t) δ [\frac{1}{f} (R (t) - r)] d t .

(36)

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Ψ (t) = \frac{2 π ℓ}{S (T)} S (t),

(37)

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S (t) = \int_{0}^{t} | c^{'} (τ) | d τ .

(38)

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E (r) = \frac{1}{T} \int_{0}^{T} Φ (r, t) φ (r, t) | c_{2}^{'} (t) | d t

(39)

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Φ (r, t) = \exp {\frac{i}{ρ^{2}} [y x_{0} (t) - x y_{0} (t)]} \exp [\frac{i 2 π m}{S (T)} S (t)],

(40)

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S (t) = \int_{0}^{t} [x_{0} (τ) y_{0}^{'} (τ) - y_{0} (τ) x_{0}^{'} (τ)] d τ,

(41)

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φ (r, t) = \exp {i π \frac{{[x - x_{0} (t)]}^{2} + {[y - y_{0} (t)]}^{2}}{λ f^{2}} z_{0} (t)},

(42)

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b_{n} (τ) = {(1 - τ)}^{3} P_{s}^{(n)} + 3 τ {(1 - τ)}^{2} T_{s}^{(n)} + 3 τ^{2} {(1 - τ)}^{2} T_{e}^{(n)} + τ^{3} P_{e}^{(n)},

(43)

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c (t) = {b_{1} (τ), b_{2} (τ), \dots, b_{m} (τ)},

(44)

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m \ddot{x} = - Γ_{0} \dot{x} - κ_{0} x + F_{th},

(45)

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S_{x} (ω) = \frac{k_{B} T}{π m} \frac{Γ_{0}}{{(ω^{2} - Ω_{0}^{2})}^{2} + ω^{2} Γ_{0}^{2}},

(46)

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⟨ x^{2} ⟩ = \frac{k_{B} T_{CM}}{m Ω_{0}^{2}} .

(47)

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References (264)

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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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