Fig. 4: Analysis of M0 and M1 modes.

a Numerically calculated band structure of HPhP in the Fourier crystal across the upper Reststrahlen band of hBN. The same model is used as in Fig. 3c. b Independently calculated band structures of M0 (left) and M1 (right) modes, where the Fourier crystal with hBN is modeled as a 2D sheet of spatially modulated conductivity according to the analytical dispersion of modes in hBN over a conductive surface. Band structures in (a and b) are calculated for the direction of surface corrugation. c Numerically calculated near-field amplitude profiles independently generated by M0 (left) and M1 (right) modes. Here, the hBN slab is modeled as a 2D sheet of uniform conductivity which supports only one desired eigenmode, placed over a metallic Fourier surface. d Same as in (c), but for the near-field phase. Both (c and d) demonstrate that experimentally and numerically obtained near-field patterns correspond to the M0 mode.