Extended Data Fig. 9: Cross-sectional polar maps.

a, Polarization maps along the ordered [010]_pc direction. The projection of a cycloidal and helical modulated vortex array into the [001]_pc–[010]_pc plane shows that the domain topology is retained. b, The projection of the modulated vortex array into the [001]_pc–[100]_pc plane shows that the cycloidal modulation allows the polar vector to rotate in plane, similar to the experimental polar map, whereas the helical modulation does not.