Baoli Yao’s research team demonstrate the possibility of creating multiple spherical spots in 4π; focusing system with a radially polarized beam. Using spherical waves to expand the plane wave factor in the Richards–Wolf integral, it is found that a proper spatial modulation in the amplitude of input filed with radial polarization can form multiple spherical spots with a focusing system satisfying the Herschel condition. These spots are distributed symmetrically about the focus on the optical axis with variable positions and intensity. Although they consider only the case of three spherical spots in this paper, the generalization to multiple spots case will present no difficulty.

（Original research article: Journal of the Optical Society of America A Vol. 27, Issue 9, pp. 2033-2037 (2010) . https://doi.org/10.1364/JOSAA.27.002033）