Analytical surface-impedance modeling of disordered dielectric metasurface monolayers

This work presents a compact, closed-form surface-impedance framework for statistically disordered all-dielectric monolayer metasurfaces under normal incidence. Dynamic Mie polarizabilities, combined with a disorder-averaged interaction constant, yield collective electric and magnetic responses that are mapped to an equivalent sheet admittance and sheet impedance. Coherent reflection and transmission are obtained via an ABCD-matrix embedding, while diffuse scattering is estimated from single-particle Mie theory and linked to the specular channel through a single correlation weight. The formulation enforces passivity and energy conservation and provides direct access to the corresponding electric and magnetic surface-current distributions. Validation for silicon-nanosphere metasurfaces shows good agreement with ensemble-averaged full-wave simulations (FDTD) and illustrates an ultrathin antireflection coating on crystalline silicon. By connecting microscopic resonances to macroscopic sheet parameters, the framework provides an efficient and physically transparent tool for modeling and design of disordered metasurfaces.