Engineering Plasmonic Surface Lattice Resonances via a Nanoparticle Filling Factor

The theory of dielectric photonic crystals (PCs) has been extensively developed, with band diagrams providing key insights into their eigenmodes. Under certain conditions, the band structures are scale-invariant; i.e., the relative positions of the bands do not change if the lattice geometry is uniformly scaled. This implies that the PC can operate similarly across different size regimes. In contrast, arrays of metallic nanoparticles exhibit dispersive behavior, but for surface lattice resonance (SLR) modes in the coherent coupling regime, their behavior appears to be similar to that of dielectric PCs. In this work, we combine experimental studies with finite-difference time-domain (FDTD) simulations to investigate the influence of the filling factor (ratio of the nanoparticle surface area to that of the unit cell) in determining the SLR wavelength. We demonstrate that two distinct 2D nanoparticle periodic arrays with identical filling factors and lattice periods along the propagation direction of the Rayleigh anomaly support SLRs at the same wavelength in the coherent coupling regime. Insight into the filling factor in SLRs provides a simple geometrical rule to control plasmonic resonances, enabling the rational design of substrates for sensing, photocatalysis, and surface-enhanced spectroscopies.