Fig. 1: Hetero-bilayer WS₂/MoS₂ van der Waals hexagonal nanoantennas sustaining anapole states.

a Schematic of the dual-layer van der Waals (vdW) nanoantenna positioned on a SiO₂ substrate, composed of a bottom MoS₂ layer (blue) and a top WS₂ layer (red), each ~100-nm thick. Inset shows the second harmonic generation process where the absorption of two photons at the fundamental frequency ω leads to the generation of a frequency-doubled photon at 2ω. b Illustration of the in-plane TMDC crystalline honeycomb symmetry. Metal atoms are depicted in blue and chalcogenide ones in yellow. c Illustration of the interface between the two TMDC layers aligned at zero degrees, showing broken inversion symmetry region resulting in the second order non-linear signal. d Real and imaginary parts of the in-plane dielectric function for WS₂ (red) and MoS₂ (blue). Adapted from ref. ²⁷. e Far field illustration of an electric dipole (top) and a toroidal dipole (bottom) whose interference generates the anapole state. f Numerical FDTD simulations of the electric field intensity, \({(| E| /| {E}_{0}| )}^{2}\), at the anapole wavelength for a WS₂/MoS₂ disk with layer thicknesses of 92 nm and 115 nm, respectively, and radius of 280 nm. The data is displayed along the z-plane of the WS₂/MoS₂ interface (left panel) and the center of the structure, along the vertical plane at x = 0 (right panel). Scale bar: 200 nm. g Numerical FDTD simulations of the normalized scattering cross section (in red) exhibiting a minima, and the normalized internal electromagnetic energy (in blue) exhibiting a maximum at the anapole wavelength. h Numerical FDTD simulations of the normalized scattering cross section for a WS₂/MoS₂ disk on a glass substrate, with radial size from 260 nm to 360 nm, and height of 92 nm for the MoS₂ layer and 115 nm for the WS₂ one. The sample is illuminated with normal incidence light from the air side. The dashed white line indicates the dip in far-field scattering attributed to the anapole state