Calculation of the trapping force in a strongly focused laser beam

We present what is, to the best of our knowledge, the first detailed calculation of the reverse trapping force acting on a dielectric sphere when it is illuminated by a strongly focused laser beam. The calculation is carried out within the geometrical optics approximation. The phenomenon of laser trapping was discovered experimentally by Ashkin et al. [ Opt. Lett.11, 288 ( 1986)] and is of great practical interest in view of the possibility it offers for freely manipulating biological particles, such as viruses and bacteria, in a nondestructive manner. We support our calculations by a qualitative experiment that clearly shows the accessibility of the trapping effect in practice. We use, as an experimental improvement, an objective with a central field stop producing a conical dark field. This enhances the relative contribution from high-N.A. illumination and makes it easier to achieve optical trapping.