Continuous spectral and coupling-strength encoding with dual-gradient metasurfaces.

To control and enhance light-matter interactions at the nanoscale, two parameters are central: the spectral overlap between an optical cavity mode and the material's spectral features (for example, excitonic or molecular absorption lines), and the quality factor of the cavity. Controlling both parameters simultaneously would enable the investigation of systems with complex spectral features, such as multicomponent molecular mixtures or heterogeneous solid-state materials. So far, it has been possible only to sample a limited set of data points within this two-dimensional parameter space. Here we introduce a nanophotonic approach that can simultaneously and continuously encode the spectral and quality-factor parameter space within a compact spatial area. We use a dual-gradient metasurface design composed of a two-dimensional array of smoothly varying subwavelength nanoresonators, each supporting a unique mode based on symmetry-protected bound states in the continuum. This results in 27,500 distinct modes and a mode density approaching the theoretical upper limit for metasurfaces. By applying our platform to surface-enhanced molecular spectroscopy, we find that the optimal quality factor for maximum sensitivity depends on the amount of analyte, enabling effective molecular detection regardless of analyte concentration within a single dual-gradient metasurface. Our design provides a method to analyse the complete spectral and coupling-strength parameter space of complex material systems for applications such as photocatalysis, chemical sensing and entangled photon generation.