Theory of optical tweezers

We derive an exact partial-wave (Mie) expansion of the axial force exerted on a transparent sphere by a laser beam focused through a high numerical aperture objective. The results hold throughout the range of interest for practical applications, as well as in the Rayleigh and geometrical optics limits. They allow, in principle, an absolute calibration of optical tweezers. Starting from the Mie result, we derive a closed analytic representation for the size-averaged short-wavelength limit that takes into account the Abbe sine condition. Numerical plots show large deviations from geometrical optics near the focal region and around the edge of the sphere, and oscillatory behavior of the force as a function of the size parameter. The oscillations are explained in terms of a simple interferometer picture derived from the Mie expansion. The few existing experimental data look more consistent with the present model than with previous ones.