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–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). This framework provides a consistent and computationally efficient description of 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, driven mainly by filling fraction. The analysis reveals that polarization-dependent effects arise from variations in boundary-condition coupling rather than distinct localized resonances, 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 EMT–TMM predictions. No full-wave simulations or experiments are presented; all results derive from analytical-numerical modeling. Rather than proposing new excitation mechanisms, this study provides a validated theoretical framework for understanding how polarization and nanostructural filling fraction jointly modulate SPR coupling in thin-film metasurfaces. The results offer a foundation for rational design and optimization of plasmonic coatings and SPR sensors with tunable surface sensitivity.