Optical forces on interacting plasmonic nanoparticles in a focused Gaussian beam

Zhipeng Li, Mikael Käll, and Hongxing Xu

Phys. Rev. B 77, 085412 – Published 8 February 2008

Abstract

We theoretically analyze optical forces on aggregates of metal nanoparticles in a focused Gaussian beam by extending the generalized Mie theory, which includes higher order multipoles and retardation effects. For two interacting metallic particles, an attractive gradient force, mainly caused by multipole plasmon excitation, exists at short interparticle distances, while induced dipolar fields dominate for separations of the order of the particle radius $R$ or larger. The long-range force component can be either attractive or repulsive depending on the phase of the induced dipoles, as determined by the illumination wavelength and the collective dipolar plasmon resonance. In particular, the repulsive force that occurs for illumination near the plasmon resonance wavelength can be so large that it overcomes the optical trapping effect of the Gaussian beam.

Received 4 September 2007

DOI:https://doi.org/10.1103/PhysRevB.77.085412

Authors & Affiliations

Zhipeng Li¹, Mikael Käll², and Hongxing Xu^1,3,*

¹Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100080, China
²Department of Applied Physics, Chalmers University of Technology, SE-412 96 Göteborg, Sweden
³Division of Solid State Physics, Lund University, P.O. Box 118, Lund S-22100, Sweden

^*Corresponding author. hongxingxu@aphy.iphy.ac.cn

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Issue

Vol. 77, Iss. 8 — 15 February 2008

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Images

Figure 1
(Color online) (a) Field profile of the Gaussian beam in focal plane for $λ = 830 nm$ and $w_{0} = 500 nm$ . The geometry of the 2D optical trapping is shown in the inset. (b) The optical pressure distribution over the surface of a silver sphere $(R = 20 nm)$ positioned at $w_{0} ∕ 2$ along $x$ axis for an incident power $P = 50 mW$ . The colors represent the light intensity. (c) The pressure component along the surface normal around the equator of the sphere in the focal plane.Reuse & Permissions
Figure 2
The transverse optical force (dashed line) and the optical potential (solid line) experienced by a silver nanoparticle $(R = 20 nm)$ in water for the case when the particle is situated in the focal plane of a $x$ -axis polarized Gaussian beam ( $λ = 830 nm$ , $w_{0} = 500 nm$ , $P = 50 mW$ ). The potential is expressed in units of $k_{B} T$ , where $T = 300 K$ .Reuse & Permissions
Figure 3
(Color online) The optical potential experienced by a mobile silver particle (F) close to an identical immobilized particle (I) as a function of the $x$ position of the mobile particle. The right inset in (a) shows the optical trapping configuration for the two-particle system. The radii of spheres are $R = 20$ , 50, and $100 nm$ for (a)–(c), respectively. Different separations, $D = 0$ , 250, and $600 nm$ , between the beam focus and the position of the immobilized particle are represented by dashed, thick solid, and thin solid lines (green for $λ = 514 nm$ and red for $λ = 830 nm$ ), respectively. The surrounding medium is water and $T = 300 K$ . The insets to the left in (a)–(c) are the corresponding van der Waals energies of two silver spheres as a function of the surface separation.Reuse & Permissions
Figure 4
(Color online) Identical plots as in Fig. 3 but for Au particles.Reuse & Permissions
Figure 5
(Color online) Pseudocolor plot of $U − U_{s}$ (see text for description) for silver particles $(R = 50 nm)$ as a function of the $x$ position of particle F and of the illumination wavelength. The immobilized sphere is situated on the $x$ axis at a distance $D = 250 nm$ from the origin. The incident power of the Gaussian beam $(w_{0} = 500 nm)$ is $1 mW$ , the surrounding medium is water, and $T = 300 K$ .Reuse & Permissions
Figure 6
Vector plot of the optical forces exerted on the Ag sphere F in the focal plane of a Gaussian beam $(w_{0} = 500 nm)$ for the case when the incident wavelength is close to the particle plasmon resonance. The immobilized sphere I is situated at $+ x$ axis at $D = 250 nm$ (see right inset in Fig. 3). The radius of the spheres are $100 nm$ and the laser power is $10 mW$ . The surrounding medium is water.Reuse & Permissions

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