The optical trapping of nanoparticles is important in the assembly of nanostructured materials and in fundamental studies of plasmonics and coupled light-matter interactions. These applications demand an accurate model of the trapping force and the ability to manipulate nanoparticles at high speeds over long distances. The trapping force is most simply modeled using a dipole approximation for particles much smaller than the wavelength, resulting in a force proportional to particle volume. For metallic nanoparticles, it was previously thought to be more accurate to replace the full particle volume with an effective volume based on a spherical shell with thickness equal to the metallic skin depth. The resulting optical trapping force is then proportional to surface area rather than volume. However, experimental studies have generally failed to find forces that scale with surface area, with qualitative explanations such as enhanced radiation pressure displacing particles from the beam focus or the presence of spherical aberration. Here we show through comparison to rigorous Mie theory that the complex permittivity of the metal fully accounts for the skin effect in metallic nanoparticles, and it is more accurate to use the full volume with a radiation reaction correction rather than an effective volume based on the skin depth. We compare these predictions to experiments, where we also show particularly high-speed (>0.1 mm/s) and long-distance (1 mm) manipulation of gold, silver, and polystyrene nanoparticles using a high-powered laser and low-aberration optical tweezer. We hope that that these results will help to enable high-speed nano-assembly.
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