A Highly Efficient Superresolving Phase Filter for a Radially Polarized Beam

We simulate the focal intensity distribution of a radially polarized beam, in view of the vector diffraction theory. We summarize two important rules: (i) the marginal ray of the aperture determines the focal size on the focal plane; (ii) the ratio of the longitudinal component to the transversal component affects the shape of the focus. We design a continuous phase filter using these rules for a confocal system. We chose the tangent of the semi-aperture angle to build up the phase function, because it is sensitive to the marginal rays, which have large aperture angles. To achieve a flexible modulation, we use a quadratic function for unwrapping the phase. We optimize the parameters of the quadratic function and achieve a transverse superresolving focus. Aiming at different Strehl ratios, we obtain a series of superresolution phase filters. Compared with others, the filter proposed has the advantages of superior superresolution effect and higher energy utilization ratios. The phase-filter design is universal and proved to be valid. It can be employed in either high or low NA systems, superresolving or donut focus applications.