Tightly focused optical skyrmions and merons formed by electric-field vectors with prescribed characteristics.

Optical skyrmions, which are topological quasi-particles with nontrivial electromagnetic textures, have garnered escalating research interest recently for their potential in diverse applications. In this paper, we present a method for generating tightly focused optical skyrmion and meron topologies formed by electric-field vectors under 4-focusing system, where both the topology types (including Néel-, Bloch-, intermediate- and anti-skyrmion/meron) and the normal direction of the two-dimensional topology projection plane can be tailored at will. By utilizing time-reversal techniques, we analytically derive the radiation pattern of a multiple concentric-ring array of dipoles (MCAD) to obtain the required illumination fields on the pupil planes of the two high numerical aperture lenses. The Deby vector diffraction integral theory is employed to calculate the corresponding tightly focused field, and their topology characteristics are quantitatively evaluated by the electric-field vector distribution. The results demonstrate that arbitrary electric-field based skyrmion and meron can be conveniently generated by adjusting the oscillation direction of each dipole in the MCAD and the normal direction of the dipole array. The generated optical topologies with fully controllable degrees of freedom provide potential applications in optical information processing, transmission, and storage.