Focal shift of radially laguerre polarized Bessel Gaussian beams induced by cosine phase masks are investigated theoretically by vector diffraction theory. Results show that when the radially polarized laguerre Bessel Gaussian beam with cosine phase plate is focused, the focal pattern differs considerably with frequency parameter (C) in the cosine function term. Increasing the value of frequency parameter in the cosine part of the phase mask, focal shift may occur, simultaneously, the focal shift direction may change. Moreover, by altering frequency parameter of the phase mask will change the energy distributions of maximum intensity peak and other small intensity peaks.
