Fig. 1: GaP metasurfaces for strong-field light–matter interactions in the mid-infrared.

a Illustration of the high harmonic generation process: resonant GaP metasurfaces show efficient even and odd high harmonic generation (up to order H9) due to the wide direct electronic bandgap, high refractive index, non-centrosymmetric lattice, and intense-field-driven tunneling and Bloch oscillations. b Fabricated GaP metasurfaces: scanning electron microscope images, revealing the substrate (SiO₂), the antenna material (GaP), and the lithography mask (hydrogen silsesquioxane, HSQ). c Calculated local field map \({E}_{{\rm{loc}}}{E}_{{\rm{ext}}}^{-1}\) of the metasurface mode excited by a mid-infrared (mid-IR) pulse with \(\lambda ={\lambda }_{{\rm{res}}}^{(0)}\) and a corresponding induced bound charge map \({\rho }_{b}\) within the GaP antenna revealing an electric dipole mode. d Collimated (normal incidence) transmission spectra of three samples with varying dielectric resonant antenna sizes: largest (upper curve) to the smallest (lower curve) size. The second and third data sets are offset for clarity by +0.4 and +0.8, respectively. e COMSOL simulations of d. The second and third data sets are offset for clarity by +0.5 and +1.0, respectively. Red stars indicate the estimated wavelengths of the maximum local field enhancement.