fig6

Figure 6. (A) The sketch of the in-plane dispersion around the Dirac nodal ring (the upper left panel), the experimental setup (the upper right panel), the transmission spectra of the PC to observe the Dirac nodal ring (the lower left panel, the situation of the TM mode is similar), and the double-bowl state for the truncated PC (the lower right panel, the situation of the TM mode is similar), quoted with permission from Hu et al.^[37]; (B) The schematic of PC without the inversion symmetry (the upper left panel), the gapped ridge state (the upper right panel), and the toroidal-shaped Berry fluxes for vortexes for two structures (the lower panel), quoted with permission from Deng et al.^[120]; (C) The degree of freedom of rotation and translation in the hypercrystal; (D) The bilateral drumhead surface state (the upper panel) is pinned by a pair of reflection-phase topological charges (the middle panel), and the charge pair approaches each other, but cannot annihilate completely, which forms a quasi-BIC (the lower panel), quoted with permission from Hu et al.^[122]. PC: Photonic crystal; TM: transverse magnetic; BIC: bound state in the continuum.