Reflection compensation mediated by electric and magnetic resonances of all-dielectric metasurfaces

All-dielectric nanostructures have recently emerged as a promising alternative to plasmonic devices, as they also possess pronounced electric and magnetic resonances and allow effective light manipulation. In this work, we study optical properties of a composite structure that consists of a silicon nanoparticle array (metasurface) and high-index substrate aiming at clarifying the role of substrate on reflective properties of the nanoparticles. We develop a simple semi-analytical model that describes interference of separate contributions from nanoparticle array and the bare substrate to the total reflection. Applying this model, we show that matching the magnitudes and setting the {\pi}-phase difference of the electric and magnetic dipole moments induced in nanoparticles, one can obtain a suppression of reflection from the substrate coated with metasurface. We perform numerical simulations of sphere and disk nanoparticle arrays for different permittivities of the substrate. We find full agreement with the semi-analytical results, which means that the uncoupled-element model adequately describes nanostructure reflective properties, despite the effects of induced bi-anisotropy. The model explains the features of the reflectance spectrum, such as a number of dips and their spectral positions, and show why it may not coincide with the spectral positions of Mie resonances of the single nanoparticles forming the system. We also address practical aspects of the antireflective device engineering: we show that the uncoupled-element model is applicable to the structures on top of silicon substrates, including lithographically defined nanopillars. The reflectance suppression from nanoparticle array on top of the silicon substrate can be achieved in a broad spectral range with disordered nanoparticle array and for a wide range of incidence angles.