Analytical modeling of substrate-wave interference in periodic antireflection metasurfaces

Antireflection (AR) metasurfaces have been known for decades as “artificial dielectrics.” By subwavelength periodic patterning, a quarter-wave film with a controllable effective refractive index is realized to achieve classic AR effects. Metasurfaces inscribed in high-index materials may support propagating substrate waves causing reduced surface reflection. Here, we provide new analytical models substantiated by rigorous numerical simulations elucidating the attendant physical mechanisms. Accordingly, we present a comprehensive model for substrate-wave interference in periodic AR metasurfaces. It is demonstrated that AR spectral bands originate in lattice diffraction and corresponding constructive interference (CI) effects sustained in transmitted substrate waves. By analyzing one-dimensional (1D) and two-dimensional (2D) metasurfaces, we derive analytical solutions for CI conditions of these substrate waves using effective medium theory. For 1D structure, we identify distinct interference mechanisms between the zero-order and first-order diffracted waves, revealing paired high transmission bands that contribute to broad AR regions. In 2D metasurfaces, our model employs quasi-equivalent 1D gratings with effective refractive indices for both TM and TE modes, successfully predicting complex AR properties. The analytical results correspond well with numerical simulations and illustrate the formation of broad AR regions through the interplay of multiple CI conditions. This work provides fundamental insights into the physics of periodic AR metasurfaces and establishes a theoretical foundation for their optimal design.