Fig. 3: Magnetic fields of toroidal and supertoroidal light pulses.

a, b Isoline and arrow plots of the magnetic fields in the x–z plane for a the fundamental TLP and b the STLP of α = 5, in logarithmic scale. Magnetic field singularities are marked by black dots with red arrows correspondingly marking the saddle or vortex style of the vector singularities. Panels a1 and b1 present the zoom-in plots corresponding to regions of blue boxes in (a) and (b), respectively. Panels a2 and b2 present transverse distributions of magnetic amplitude (in logarithmic scale) and normalized magnetic vectors at z = 0 planes, the positions marked by the black dashed lines in (a) and (b), respectively, where the magnetic fields vanish along the circular solid black lines with red arrows marking the styles of singularities (vortex for a2 and saddle for b2). Skyrmionic structures in magnetic fields of toroidal and supertoroidal light pulses: c Various textures of Néel-type skyrmionic structure observed at various transverse planes (see dashed purple lines in a and b) for the fundamental TLP (c1–c2) and the STLP of α = 5 (c3–c6), which are demonstrated by the arrows with color-labeled longitudinal component value of magnetic field. The up-right insert of each panel shows the basic texture of the skyrmionic structure. Unit for coordinates: q₁.