Calculation of the intensity at the sharp focus of a cylindrical vector beam by three methods

We conduct a comparative analysis of diffraction fields upon sharply focusing vortex and non-vortex incident beams, calculated using three non-paraxial methods. The methods employed are a finite difference time domain (FDTD) method, a Rayleigh–Sommerfeld integral, and a Richards–Wolf transformation. The Richards–Wolf transformation is used with two apodization functions of the exit pupil, for a spherical lens and a thin diffractive lens. The numerical simulation shows that the Rayleigh–Sommerfeld integral and the Richards–Wolf transformation can produce almost the same result and save time significantly. Meanwhile, the root-mean-square deviation of the results of both methods from the FDTD method can be as low as 2%. If an ultra-short focal length is used, the Richards–Wolf transformation is found to be more accurate, whereas with increasing distance from the initial plane and outside the focal plane, the Rayleigh-Sommerfeld integral is more accurate.