A four-quadrant phase filter for creating two focusing spots

We present a design method of four-quadrant pure phase filter and phase modulation functions for creating two focusing spots. With the combination of a high numerical aperture objective and a four-quadrant pure phase filter, a radially polarized incident plane wave can be focused into two focusing spots with the spacing of several wavelengths along the optical axis. The filter with the phase modulation functions are verified effective by numerical simulation. The distance of the two focuses and the position of each focus can be controlled and adjusted by changing the phase modulation functions. The beam quality and longitudinally polarization purity of these two focusing spots are calculated and discussed and thus the centrally obstructed four-quadrant phase filters are proposed to improve the beam quality.