It is necessary to study characteristics of axial intensity distributions, such as focal depth and focal shift, which influence the maximum energy efficiency obtained and the assembling error at the receiving plane. The rigorous electromagnetic characteristic must be considered for diffractive optical elements (DOEs) whose features are on the order of or smaller than the wavelength of the incidence illumination. The rigorous electromagnetic analysis of diffractive micro-cylindrical lenses that are finite in extent using a two dimensional finite-difference time-domain (FDTD) method is presented. Compared with the scalar theory, the axial intensity distributions of lenses with different F-numbers are analyzed rigorously, considering different incidence polarizations (transverse electric polarization and transverse magnetic polarization) and different profile structures (continuous profile, 16-level profile and 8-level profile) of lenses, respectively. It is shown that focal shifts calculated by the rigorous method are larger than those made by the scalar theory, and focal depths calculated by these two methods are consistent basically, furthermore, focal depth and focal shift increase when F-number increases for both the rigorous electromagnetic method and the scalar method.