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[en] An optical-trap method based on the illumination of a double-ring-shaped radially polarized beam (R-TEM11*) is proposed. The numerical results based on the vector diffraction theory show that a highly focused R-TEM11* beam not only can produce a bright spot but also can form an optical cage in the focal region by changing the truncation parameter β, defined as the ratio of the radius of the aperture to the waist of the beam. The radiation forces acting on Rayleigh particles are calculated by using the Rayleigh scattering theory. The bright spot generated by the R-TEM11* beam with a β value close to 2 can three-dimensionally trap a particle with a refractive index larger than that of the ambient. An optical cage or three-dimensional dark spot generated by the R-TEM11* beam with a β value close to 1.3 can three-dimensionally trap a particle with refractive index smaller than that of the ambient. Because the adjustment of the truncation parameter can be actualized by simply changing the radius of a circular aperture inserted in the front of the lens, only one optical-trap system in the present method can be used to three-dimensionally trap two types of particles with different refractive indices.