Inverse-Designed Metasurfaces for Compact Optical Skyrmion Generation with High Topological Fidelity

Abstract: Optical skyrmions are structured vector fields with nontrivial polarization topology and subwavelength-scale features. One common approach to generating optical skyrmions is the superposition of a zeroth-order Bessel beam and a higher-order Bessel beam carrying orbital angular momentum, with each beam possessing an orthogonal circular polarization state. However, creating such complex beams typically requires bulky free-space optical setups; therefore, recent efforts have focused on compact optical skyrmion generators based on metasurfaces. Nevertheless, achieving the degrees of freedom required for simultaneous phase and polarization control remains challenging because of the limited design flexibility of conventional meta-atoms. Here, we address this challenge by employing an inverse-design approach and demonstrate a single-layer metasurface that generates high-fidelity optical skyrmions. We employ an adjoint-based topology-optimization method to design a silicon metasurface that converts an incident beam into an optical skyrmion without the need for additional optical components. The optimized metasurface generates an optical skyrmion with skyrmion number $(N_\mathrm{sk}) = 0.970$. This work demonstrates that inverse design can be a promising route to compact skyrmion generators, and our approach provides a basis for near-field particle manipulation and the generation of independent topological bits in dense photonic integration.