Radiation forces of a highly focused radially polarized beam on spherical particles

A radially polarized beam focused by a high-numerical-aperture (na) objective has a strong longitudinal and nonpropagating electric field in the focal region, which implies that it is suitable for axial optical trapping. in this paper, we use the vectorial diffraction integral to represent the field distribution of the radially polarized beam focused by a high-na objective and then employ the t-matrix method to compute the radiation forces on spherical particles. effects of different parameters, such as the size of the sphere, the inner radius of the radially polarized beam, and the na of the objective, on the radiation forces are presented.