Optical trapping of dielectric nanoparticles in resonant cavities

Juejun Hu, Shiyun Lin, Lionel C. Kimerling, and Kenneth Crozier

Phys. Rev. A 82, 053819 – Published 16 November 2010

Abstract

We theoretically investigate the opto-mechanical interactions between a dielectric nanoparticle and the resonantly enhanced optical field inside a high $Q$ , small-mode-volume optical cavity. We develop an analytical method based on open system analysis to account for the resonant perturbation due to particle introduction and predict trapping potential in good agreement with three-dimensional (3D) finite-difference time-domain (FDTD) numerical simulations. Strong size-dependent trapping dynamics distinctly different from free-space optical tweezers arise as a consequence of the finite cavity perturbation. We illustrate single nanoparticle trapping from an ensemble of monodispersed particles based on size-dependent trapping dynamics. We further discover that the failure of the conventional dipole approximation in the case of resonant cavity trapping originates from a new perturbation interaction mechanism between trapped particles and spatially localized photons.

Received 20 August 2009

DOI:https://doi.org/10.1103/PhysRevA.82.053819

Authors & Affiliations

Juejun Hu^1,2,*, Shiyun Lin³, Lionel C. Kimerling¹, and Kenneth Crozier³

¹Microphotonics Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
²Department of Materials Science & Engineering, University of Delaware, Newark, Delaware 19716, USA
³School of Engineering and Applied Science, Harvard University, Cambridge, Massachusetts 02138, USA

^*hujuejun@udel.edu

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Issue

Vol. 82, Iss. 5 — November 2010

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Images

Figure 1
Schematic illustration of a 1D Bragg cavity used to demonstrate the resonant cavity trapping principles. For the specific example in this figure, each Bragg mirror consists of three high-index silicon layers and the whole device is immersed in water.Reuse & Permissions
Figure 2
(a) Optical force exerted on a spherical particle located in the cavity illustrated in Fig. 1. Particle is offset by 90 nm from the center of the cavity along the $z$ axis. Right-side axis gives the dimensionless parameter Re( $α$ ) $Q$ / $ɛ_{c}$ $V$ $_{c}$ : the deviation between dipole approximation and the open cavity analysis Eq. (7) scales with its magnitude. (b) Optical trapping potential profile experienced by particles of different radii, given in $k_{B}$ T $~$ 0.026 eV; the solid lines correspond to the open cavity analysis, and the solid symbols are FDTD simulation results, calculated by integrating the optical force along the $z$ axis.Reuse & Permissions
Figure 3
(a) Single-particle trapping potential in 1D cavities with different numbers of Bragg mirror pairs $N$ and hence different $Q$ factors. (b) Trapping potential in a cavity shown in Fig. 1 ( $N$ $=$ 3) as a function of particle radius; the detuning is given as the relative shift between the cavity resonant wavelength and the excitation wavelength, and is expressed as the fraction of resonant peak full width at half maximum (FWHM).Reuse & Permissions
Figure 4
(a) Optical force exerted on a 40-nm-radius particle located in a cavity structure shown in Fig. 1 when another identical particle is also present in the resonant cavity, plotted as a function of the two particles’ positions along the $z$ axis. (b) Two cross sections of the plot (a), showing the optical force applied on the second particle when the first particle is in the cavity center and in the cavity edge, respectively.Reuse & Permissions
Figure 5
Optical force exerted on a spherical particle located in the cavity illustrated in Fig. 1. Particle is offset by 90 nm from the center of the cavity along the $z$ axis. Thesolid circles give the force results calculated by dipole approximation along with the application of a quadrupole approximation [21]. We see that the discrepancy between the dipole approximation and the Maxwell stress tensor method is not eliminated by the introduction of a quadrupole term, which suggests that the cavity perturbation effect we discuss in this manuscript is fundamentally different from excitation of multipoles.Reuse & Permissions
Figure 6
Resonant wavelength shift of a 1D cavity shown in Fig. 1 ( $N$ $=$ 3) induced by introduction of a particle into the cavity center, calculated 3D FDTD and using different cavity perturbation formalisms; clearly, Eq. (C6) gives theoretical predictions in good agreement with FDTD simulation results.Reuse & Permissions

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