Calculation of optical trapping forces on a dielectric sphere in the ray optics regime produced by a radially polarized laser beam

We calculated the optical trapping forces on a microscopic particle in the ray optics regime for the case where a radially polarized laser beam is applied. A higher axial trapping efficiency than for a circularly polarized doughnut beam was predicted due to the large p polarization component. Three-dimensional optical trapping was expected for particles with a larger index of refraction and for objectives with a smaller numerical aperture.