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 simula-tion 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 de-viation 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, where-as with increasing distance from the initial plane and outside the focal plane, the Rayleigh-Sommerfeld integral is more accurate.