Hybrid topological guiding mechanisms for photonic crystal fibers.

We create hybrid topological-photonic localisation of light by introducing concepts from the field of topological matter to that of photonic crystal fiber arrays. S-polarized obliquely propagating electromagnetic waves are guided by hexagonal, and square, lattice topological systems along an array of infinitely conducting fibers. The theory utilises perfectly periodic arrays that, in frequency space, have gapped Dirac cones producing band gaps demarcated by pronounced valleys locally imbued with a nonzero local topological quantity. These broken symmetry-induced stop-bands allow for localised guidance of electromagnetic edge-waves along the crystal fiber axis. Finite element simulations, complemented by asymptotic techniques, demonstrate the effectiveness of the proposed designs for localising energy in finite arrays in a robust manner.