Theory of trapping forces in optical tweezers

Abstract

Starting from a Debye-type integral representation valid for a laser beam focused through a high numerical aperture objective, we derive an explicit partial-wave (Mie) representation for the force exerted on a dielectric sphere of arbitrary radius, position and refractive index. In the semi-classical limit, the ray-optics result is shown to follow from the Mie expansion, holding in the sense of a size average. The equilibrium position and trap stiffness oscillate as functions of the circumference-to-wavelength ratio, a signature of interference, not predicted by previous theories. We also present comparisons with experimental results.