Theory of Optical Tweezers

We derive a 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. The ray optics limit is shown to follow from the Mie expansion by size averaging. Numerical plots show large deviations from ray optics near the focal region and oscillatory behavior (explained in terms of a simple interferometer picture) of the force as a function of the size parameter. Available experimental data favor the present model over previous ones.