Fig. 3. Dirac-vortex fibre obtained by continuous Kekulé modulations.

a Example of how an “atom” can be shifted in any direction (arg[δ] = ϕ) with finite amplitude (|δ|) by changing the widths of the three struts. (b1), (c1), (d1) Supercell examples of three coordinated atoms (A1, A2, and A3) with $\mid \mathit{\delta }\mid =\sqrt{3}a/80$, ϕ = 120°; |δ| = 0; and $\mid \mathit{\delta }\mid =\sqrt{3}a/80$, ϕ = 60°, respectively. $\mathrm{\Delta }t=2\sqrt{3}\mid \mathit{\delta }\mid t_0/a=0.012a$. The corresponding band structures are plotted in (b2), (c2), and (d2), respectively. e Structure of a continuous Dirac-vortex PCF, in which every strut is coloured according to its width. f Band diagram of the fibre plotted in reference to the frequency of the original nodal-line (central dashed line). The inset shows the intensity patterns ($\widehat{\mathit{z}}\cdot \mathrm{Re}\left[{\mathit{E}}^{*}\times \mathit{H}\right]$) of the topological mode and one local-defect mode. The single-polarisation topological mode (red line) spans over two octaves