Extended Data Fig. 4: Structure of fused heliknotons reconstructed numerically and experimentally.

a, Simulated midplane cross-sections of a fused heliknoton colored according to director orientations corresponding to the \({{\mathbb{S}}}^{2}\) sphere in the right column. Parameters used: sample thickness 20 μm, pitch 5 μm, applied voltage 2.8 V. White and black loops visualize the north- and south-pole preimages (with director orientations colinear to cell normal \(\hat{z}\)) of the director field, respectively. b, Experimental (top) and numerical (bottom) POM images of the fused heliknotons shown in a. White arrows indicate crossed polarizer orientations. c, Reconstructed experimental (top) and numerical (bottom) nonlinear fluorescence images obtained using circularly polarized laser excitation. Dark regions correspond to north- and south-pole preimages while bright regions are coplanar with director orientations confined to the cross-sectional plane. d, North- and south-pole preimages extracted from experimental 3PEF-PM imaging (top) and corresponding numerical simulations (bottom). Preimages are colored according to the \({{\mathbb{S}}}^{2}\) -based scheme shown in a.