Spatiotemporal Hermite-Gaussian skyrmions

Recently, optical skyrmions with polarization topological structures have been extended from the spatial domain to spatiotemporal dimensions. However, previously reported spatiotemporal Laguerre-Gaussian (STLG) skyrmions are limited to a single skyrmion unit, and their topological texture degrades during propagation. Here, we theoretically propose and numerically investigate spatiotemporal Hermite-Gaussian (STHG) skyrmions, characterized as a multiunit skyrmion array within the spatiotemporal plane. Numerical results show that the central skyrmion array, excluding the outermost units, maintains an average skyrmion number above 0.8 over 10 Rayleigh lengths, and that the STHG skyrmions exhibit self-healing ability against partial obstructions, with the topological texture recovering after 1-1.5 Rayleigh lengths of propagation.