Gradient force pattern of cosine-squared Gaussian beams through lens without aperture

The intensity distribution and gradient force pattern of cosine-squared Gaussian beams focused by a thin lens without aperture were derived based on the Collins formula. Through the numerical simulation, the influence of the beams parameter, relative incident separation and beams Fresnel number on the distribution of gradient force pattern, the number, position and size of the optical traps were discussed. The results indicated that the bigger the beams parameter b, the more the optical traps; the position of optical trap changed with the beams relative incident separation, and the size decreased with the increase of Fresnel number of the system while the position stayed unchanged.