Topologically protected generation of spatiotemporal optical vortices with nonlocal spatial-mirror-symmetry-breaking metasurface

Recently nonlocal spatial-mirror-symmetry-breaking metasurfaces have been proposed to generate spatiotemporal optical vortices (STOVs), which carry transverse orbital angular momenta. Here we investigate the topological property of the STOV generator and show that spatial mirror symmetry breaking introduces a synthetic parameter dimension associated with the metasurface geometry. Furthermore, we demonstrate that there are well-defined vortices emerging with the synthetic parameter dimension, which can topologically protect the STOV generation robustly against structural perturbations and disorders. Since the vortices are always created' or annihilated’ together in pairs of opposite charges in the $k_x\text{\hspace{0.17em}⁣}-\text{\hspace{0.17em}⁣}\omega$ domain, the total topological charge of these vortices is a conserved quantity. Our studies not only provide a new topological perspective for STOV generation but also lay a solid foundation for potential applications of STOV metasurfaces integrated with other optoelectronic devices, because of their robust immunity to fabrication defects.