We investigate the intensity distribution of sharply focused Laguerre-Gaussian beams in relation to the uniform (linear and circular) polarization of the beam and the order of the vortex phase. It is shown that to the greatest extent the polarization state affects the longitudinal component of the electric vector of the light field. The greatest visual difference in the total intensity patterns for different polarization types is observed when using a first-order phase vortex. The use of a diffractive axicon improves focusing when compared with an aplanatic lens.