Theory of trapping forces in optical tweezers

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.