  Symmetry governs many electronic and photonic phenomena in optics and
condensed matter physics. Skyrmions and merons are prominent topological
structures in magnetic materials, with the topological features determined by
the interplay between anisotropy of a material and its magnetization. Here we
theoretically show and experimentally demonstrate that the symmetry of the
electromagnetic field determines the spin topological properties of the guided
modes via spin-orbit coupling and may only result in either hexagonal
spin-skyrmion or square spin-meron lattices. We also show that in the absence
of spin-orbit coupling these spin topologies are degenerated in dynamic
field-skyrmions, unifying description of electromagnetic field topologies. The
results provide new understanding of electromagnetic field topology and its
transformations as well as new opportunities for applications in quantum
optics, spin-optics and topological photonics.
