Fig. 1: Non-local photonic mode-driven polaritonic topologies.

a, A comparison between polaritonic topologies generated via conventionally used wavelength-dependent coupling structures^17,24 (left) and our topology-generating metasurface (right). While previous platforms relied on circularly polarized incident light and polariton wavelength-dependent offsets to compensate for the phase mismatch at each edge, our approach enables the generation of HPhPs in regular polygons. b, An illustration of the topology-generating metasurface introduced in this work, consisting of hexagonal amorphous silicon resonators on a CaF₂ substrate that supports the non-local qBIC resonance. c, The simulated real part Re(E_z) (left) and phase φ_z (right) of the out-of-plane electric field at the qBIC resonance. The optical phase on the surface of each resonator is uniform and does not contain any singularities. d, A schematic of a dielectric resonator covered by hBN and illuminated with linearly polarized light. The excitation launches HPhPs at the edges of the resonator. e, The real part of the in-plane permittivity of hBN (orange curve) ε_r,|| and reflectance spectra (blue curves) of the qBIC metasurface simulated for various resonator sizes, from smaller (light blue) to larger (dark blue). For the modelling of the permittivity of hBN and the calculated dispersion, see Supplementary Notes 1 and 2 and Supplementary Fig. 3, respectively. f, The qBIC resonances lie spectrally within the in-plane RS-band of hBN to excite HPhPs (grey shaded area in e), allowing for the in-phase generation of HPhPs at each resonator edge, resulting in photonic skyrmion lattices. g–i, Our approach contrasts with the use of local modes, such as a dipolar resonance in single resonators (g), which do not generate uniform field distributions (h) and therefore no notable topological configurations can be observed (i). Simulations of the out-of-plane electric fields were conducted at ω = 1,560 cm⁻¹, within the RS-band of hBN.