Fig. 1: Topological transition and canalization of polaritons in a hBN metasurface.

a Schematic of a 20-nm-thick hBN metasurface based on a grating made of nanoribbons. b Anisotropic effective dielectric permittivities (real parts) of the metasurface calculated using Eqs. 1–3, εeff,x (red line) and εeff,y (green). Permittivity of unpatterned hBN (εhBN,t, dashed black line) and effective permittivity of the metasurface based on Maxwell–Garnett approximation (\(\varepsilon^{\mathrm{MG}}_{{\mathrm{eff}},x}\), dashed gray line) are provided for comparison. c Simulated PLDOS on the grating metasurface (MS), the effective medium (eff-m) and the unpatterned hBN, respectively. d, f, h Near-field intensity distribution of dipole-launched polaritons at three different frequencies. e, g, i Absolute value of the Fourier transform (FT) of the simulated near-field distribution Ez (see Supplementary Fig. 4). Dotted hyperbola and ellipses are guides to the eye.