Focal switch of cosine-Gaussian beams

The focal switch of cosine-Gaussian (CsG) beams passing through a system with the aperture and lens separated is studied analytically and numerically. It is shown that the focal switch of CsG beams can appear not only for the apertured case, but also for the unapertured case. The necessary condition for the focal switch is that truncation parameter α > α_c and the beam parameter β > β_c, α_c, β_c being the corresponding critical values. There exists a maximum of the relative transition height Δz _sw as α varies, and Δz _sw increases with increasing β and decreasing N _w. The normalized axial intensity minimum I _min / I _max decreases with an increase of α and β, and I _min / I _max remains unchanged as N _w varies.