Creating axial bifocal spots by solving the binary phase zone plate in inverse in 4Pi focusing system

We propose an approach to obtain bifocal spots with variable axial distance in 4Pi focusing system. The approach is to inversely solve the radii of a binary phase zone plate (BPZP) according to the conceived 4Pi focal field distribution. The ring radius of the BPZP solved in reverse has an analytic expression by the Richards-Wolf vector diffraction theory, which is directly related to the axial offset distance of the bifocal spots. With the BPZP designed by the analytic expression to modulate the incident radially polarized beam, bifocal spots with variable axial distance can be achieved in the 4Pi focusing region, and two focal spots have the same size. Moreover, some special focal fields, such as optical chain and optical cage, can also be created by selecting suitable axial offset distance to design the BPZP for modulating radially polarized beam. In addition, axial multi-spherical spots can also be generated by superposition of a BPZP and an annular obstruction.