Double focal switch and focal plane of cosine-squared Gaussian beams

In order to study the focusing properties of cosine-squared Gaussian beams(CsSGB) through a lens without aperture,the equation for the axial irradiance distribution of focused CsSGB are derived based on the Collins formula,and the analytical expression of beams waist width is presented using the second-order moment method.The double focal switch of axial intensity and the focal shift of focal plane where the real position of beams waist located are studied with numerical method.The dependence of both effects discussed above on the beams parameter b,relative incident separation s' and beams Fresnel number NF are analyzed.Results show that double focal switch can take place only for b1,and the real focal plane has a shift if s'≠1.