Spatially variant arbitrary polarization shaping for optical skyrmions generation

Polarization is fundamental degree of freedom of light, crucial for applications from imaging to quantum optics. Although numerous methods can spatially manipulate the polarization orientation, e.g., for generating vector beam, achieving simultaneous, spatially resolved control of both the orientation ({\psi}) and ellipticity (\c{hi}) remains challenging. Here, we present an efficient and compact platform to generate spatially variant arbitrary polarization states, e.g., optical skyrmions, in free space, using cascaded spatially variant waveplates in a single silica glass plate via ultrafast laser direct writing. We propose two configurations: (1) a spatially variant half-waveplate (S-HWP) and followed by a quarter-waveplate (S-HWP); and (2) two cascaded spatially variant quarter-waveplates (S-QWPs). Design rules linking the target polarization parameters (orientation {\psi} and ellipticity \c{hi}) to the fast-axis distributions enable spatially resolved arbitrary polarization control. Using these devices, we realize N\'eel-, Bloch-, and anti-skyrmions of different orders (e.g., second and fourth) and n-{\pi} textures (2{\pi} and 3{\pi}), with polarization-resolved measurements in excellent agreement with simulations. We further demonstrate 3 by 3 arrays comprising either identical or hybrid skyrmions. This approach enables the realization of spatially variant arbitrary polarization state and scalable skyrmion lattices.