Theory of Nanometric Optical Tweezers

We propose a scheme for optical trapping and alignment of dielectric particles in aqueous environments at the nanometer scale. The scheme is based on the highly enhanced electric field close to a laser-illuminated metal tip and the strong mechanical forces and torque associated with these fields. We obtain a rigorous solution of Maxwell’s equations for the electromagnetic fields near the tip and calculate the trapping potentials for a dielectric particle beyond the Rayleigh approximation. The results indicate the feasibility of the scheme. [S0031-9007(97)03687-9] Optical trapping by highly focused laser beams has been extensively used for the manipulation of submicronsize particles and biological structures [1]. Conventional optical tweezers rely on the field gradients near the focus of a laser beam which give rise to a trapping force towards the focus. The trapping volume of these tweezers is diffraction limited. Near-field optical microscopy enables the optical measurements at dimensions beyond the diffraction limit and makes it possible to optically monitor dynamics of single biomolecules [2]. The potential application of optical near fields to manipulate atoms or nanoparticles has been discussed in Ref. [3]. In this Letter, we present a new methodology for calculating rigorously and self-consistently the trapping forces acting on a nanometric particle in the optical near field and propose a novel high-resolution trapping scheme. The proposed nanometric optical tweezers rely on the strongly enhanced electric field at a sharply pointed metal tip under laser illumination. The near field close to the tip mainly consists of evanescent components which decay rapidly with distance from the tip. The utilization of the metal tip for optical trapping offers the following advantages: (1) The highly confined evanescent fields significantly reduce the trapping volume; (2) the large field gradients result in a larger trapping force; and (3) the field enhancement allows the reduction of illumination power and radiation damages to the sample. High resolution surface modification based on the field enhancement at laser-illuminated metal tips has been recently demonstrated [4]. It is essential to perform a rigorous electromagnetic analysis to understand the underlying mechanism for the field enhancement. Our analysis is therefore relevant not only to optical tweezers, but also to other applications, such as surface modification, nonlinear spectroscopy and near-field optical imaging. To solve Maxwell’s equations in the specific geometry of the tip and its environment, we employ the multiple multipole method (MMP) which recently has been applied to various near-field optical problems [5]. In MMP, electromagnetic fields are represented by a series expansion of known analytical solutions of Maxwell’s equations. To determine the unknown coefficients in the series expansion, boundary conditions are imposed at discrete points on the interfaces between adjacent homogeneous domains. Once the resulting system of equations is solved and the coefficients are determined, the solution is represented by a self-consistent analytical expression. Figure 1 shows our three dimensional MMP simulation of the foremost part of a gold tip (5 nm tip radius) in water for two different monochromatic plane-wave excitations. The wavelength of the illuminating light is l › 810 nm (Ti:sapphire laser), which does not match the surface plasmon resonance. The dielectric constants of tip and water were taken to be « › 224.9 1 1.57i and « › 1.77, respectively [6]. In Fig. 1(a), a plane wave is incident from the bottom with the polarization perpendicular to the tip axis, whereas in Fig. 1( b) the tip is illuminated from the side with the polarization parallel to the tip axis. A striking difference is seen for the two different polarizations: in Fig. 1( b), the intensity