Diffraction of a Gaussian beam on the generalized lens

We consider diffraction of a Gaussian beam on the generalized parabolic lens with an arbitrary degree in paraxial approach using the stationary phase method. It is shown, that the method in this case corresponds to local approximation of any phase function of an optical element by the linear axicon with a varying angle of an inclination. Comparison of diffraction of a Gaussian beam and the bounded plane wave has shown, that suppression axial intensity oscillations at Gaussian apodization leads generally to reduction of longitudinal extent of focal area and to spreading of the central light spot.