Analytical-Numerical Modeling of Filling-Fraction-Dependent Plasmonic Coupling in Nanostructured Metasurfaces Under Kretschmann Configuration

Surface plasmon resonance (SPR) sensors based on nanostructured metasurfaces offer enhanced sensitivity through engineered electromagnetic responses. In this study, we present an analytical and numerical investigation of the plasmonic behavior of gold nanopillar (Au-NP) and nanohole (Au-NH) arrays under both p- and s-polarized illumination, employing the Effective Medium Theory (EMT) in combination with the Transfer Matrix Method (TMM). The study combines Effective Medium Theory (EMT) and the Transfer Matrix Method (TMM) to describe the macroscopic optical response of multilayer plasmonic systems. For p-polarization, the nanostructure geometry strongly modulates the real and imaginary parts of the effective permittivity, with nanoholes supporting stronger SPR coupling and reduced optical losses compared to nanopillars. Under s-polarization, the effective permittivity remains largely invariant, primarily driven by the filling fraction. The analysis reveals that polarization-dependent behavior arises from boundary-condition-mediated coupling mechanisms governing surface plasmon excitation, aligning with classical plasmonic theory. Benchmarking against analytical dispersion relations and published experimental data for Au/BK7 systems shows close agreement within ±2°, confirming the physical consistency of the EMT–TMM framework. These results provide a systematic description of how polarization and filling fraction jointly modulate SPR coupling. The results offer a foundation for the rational design of plasmonic coatings and SPR-supporting metasurfaces by elucidating macroscopic coupling trends; however, no quantitative sensor performance metrics, such as refractive index sensitivity or figure of merit, are evaluated in this work.