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Chinese Optics Letters
Vol. 14, Issue 1, 011405 (2016)

Optically trapping Rayleigh particles by using focused partially coherent multi-rotating elliptical Gaussian beams

Xi Peng^1、2, Chidao Chen^1、2, Bo Chen^1、2, Yulian Peng^1、2, Meiling Zhou^1、2, Xiangbo Yang¹, and Dongmei Deng^1、2、*

Author Affiliations

¹Guangdong Provincial Key Laboratory of Nanophotonic Functional Materials and Devices, South China Normal University, Guangzhou 510631, China

²CAS Key Laboratory of Geospace Environment, University of Science & Technology of China, Chinese Academy of Sciences, Hefei 230026, China

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DOI: 10.3788/COL201614.011405 Cite this Article Set citation alerts

Xi Peng, Chidao Chen, Bo Chen, Yulian Peng, Meiling Zhou, Xiangbo Yang, Dongmei Deng. Optically trapping Rayleigh particles by using focused partially coherent multi-rotating elliptical Gaussian beams[J]. Chinese Optics Letters, 2016, 14(1): 011405 Copy Citation Text

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Abstract

By investigating the cross-spectral density of partially coherent multi-rotating elliptical Gaussian beams (REGBs) that propagate through a focusing optical system, we obtain the radiation force on a Rayleigh particle. The radiation force distribution is studied under different beam indexes, coherence widths, and elliptical ratios of the partially coherent multi REGBs. The transverse and the longitudinal trapping ranges can increase at the focal plane by increasing the beam index or decreasing the coherence width. The range of the trapped particle radii increases as the elliptical ratio increases. Furthermore, we analyze the trapping stability.

E_{0} (x^{'}, y^{'}) = A_{0} \exp [- (\frac{x^{' 2}}{w_{x}^{2}} + \frac{y^{' 2}}{w_{y}^{2}} + \frac{i x^{'} y^{'}}{R_{0}})],

(1)

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g (r_{1}^{'} - r_{2}^{'}) = \exp [- \frac{{(r_{1}^{'} - r_{2}^{'})}^{2}}{δ^{2}}],

(2)

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W^{0} (x_{1}^{'}, y_{1}^{'}, x_{2}^{'}, y_{2}^{'}; z = 0) = \frac{1}{C_{0}} \sum_{m = 1}^{M} \frac{{(- 1)}^{m - 1}}{m} (\begin{matrix} M \\ m \end{matrix}) E_{1}^{*} E_{2} g (r_{1}^{'} - r_{2}^{'}) = \frac{A_{0}^{2}}{C_{0}} \sum_{m = 1}^{M} \frac{{(- 1)}^{m - 1}}{m} (\begin{matrix} M \\ m \end{matrix}) \exp [- (\frac{x_{1}^{' 2}}{w_{x}^{2}} + \frac{y_{1}^{' 2}}{w_{y}^{2}} + i \frac{x_{1}^{'} y_{1}^{'}}{R_{0}}) - (\frac{x_{2}^{' 2}}{w_{x}^{2}} + \frac{y_{2}^{' 2}}{w_{y}^{2}} - i \frac{x_{2}^{'} y_{2}^{'}}{R_{0}}) - (\frac{x_{1}^{' 2} + x_{2}^{' 2} - 2 x_{1}^{'} x_{2}^{'} + y_{1}^{' 2} + y_{2}^{' 2} - 2 y_{1}^{'} y_{2}^{'}}{2 m δ^{2}})],

(3)

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(\begin{matrix} A & B \\ C & D \end{matrix}) = (\begin{matrix} 1 & z \\ 0 & 1 \end{matrix}) (\begin{matrix} 1 & 0 \\ - 1 / f & 1 \end{matrix}) = (\begin{matrix} 1 - z / f & z \\ - 1 / f & 1 \end{matrix}) .

(4)

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W (x_{1}, y_{1}, x_{2}, y_{2}; z) = {(\frac{k}{2 π B})}^{2} \int \int \int \int d x_{1}^{'} d x_{2}^{'} d y_{1}^{'} d y_{2}^{'} W^{0} \times \exp {\frac{i k}{2 B} [(A x_{2}^{' 2} - 2 x_{2}^{'} x_{2} + D x_{2}^{2}) + (A y_{2}^{' 2} - 2 y_{2}^{'} y_{2} + D y_{2}^{2}) - (A x_{1}^{' 2} - 2 x_{1}^{'} x_{1} + D x_{1}^{2}) - (A y_{1}^{' 2} - 2 y_{1}^{'} y_{1} + D y_{1}^{2})]},

(5)

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W (r, r; z) = \frac{A_{0}^{2}}{Δ} \frac{1}{C_{0}} \sum_{m = 1}^{M} \frac{{(- 1)}^{m - 1}}{m} (\begin{matrix} M \\ m \end{matrix}) \exp (Y_{1}),

(6)

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Δ = \sqrt{(A^{2} + \frac{4 B^{2}}{k^{2}} X_{1}) (A^{2} + \frac{4 B^{2}}{k^{2}} X_{2})},

(7)

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X_{1} = {(\frac{1}{w_{x}^{2}})}^{2} + \frac{1}{m δ^{2} w_{x}^{2}} - {(\frac{i}{2 R_{0}})}^{2},

(8)

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X_{2} = {(\frac{1}{w_{y}^{2}})}^{2} + \frac{1}{m δ^{2} w_{y}^{2}} - {(\frac{i}{2 R_{0}})}^{2},

(9)

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Y_{1} = - \frac{2}{Δ^{2}} [ϵ_{x} \frac{x^{2}}{w_{x}^{2}} - \frac{2 B A}{k R_{0}} (\frac{1}{w_{x}^{2}} + \frac{1}{w_{y}^{2}}) x y + ϵ_{y} \frac{y^{2}}{w_{y}^{2}}],

(10)

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ϵ_{x} = A^{2} + \frac{4 B^{2}}{k^{2}} [{(\frac{1}{w_{y}^{2}})}^{2} + \frac{1}{m δ^{2} w_{y}^{2}} - \frac{w_{x}^{2}}{w_{y}^{2}} {(\frac{i}{2 R_{0}})}^{2}],

(11)

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ϵ_{y} = A^{2} + \frac{4 B^{2}}{k^{2}} [{(\frac{1}{w_{x}^{2}})}^{2} + \frac{1}{m δ^{2} w_{x}^{2}} - \frac{w_{y}^{2}}{w_{x}^{2}} {(\frac{i}{2 R_{0}})}^{2}] .

(12)

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I_{out} (r; z) = W (r, r; z) .

(13)

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{F⃗}_{scat} (r⃗; z) = {e⃗}_{z} n_{m} α_{0} I_{out} / c,

(14)

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{F⃗}_{grad} (r⃗; z) = 2 π n_{m} β_{0} \nabla I_{out} / c,

(15)

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| F_{b} | = \sqrt{12 π η a K_{B} T},

(16)

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Figures&Tables (7)

References (31)

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Xi Peng, Chidao Chen, Bo Chen, Yulian Peng, Meiling Zhou, Xiangbo Yang, Dongmei Deng. Optically trapping Rayleigh particles by using focused partially coherent multi-rotating elliptical Gaussian beams[J]. Chinese Optics Letters, 2016, 14(1): 011405

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