Limits of the Effective Medium Theory in Particle Amplified Surface Plasmon Resonance Spectroscopy Biosensors

The resonant wave modes in monomodal and multimodal planar Surface Plasmon Resonance (SPR) sensors and their response to a bidimensional array of gold nanoparticles (AuNPs) are analyzed both theoretically and experimentally, to investigate the parameters that rule the correct nanoparticle counting in the emerging metal nanoparticle-amplified surface plasmon resonance (PA-SPR) spectroscopy. With numerical simulations based on the Finite Element Method (FEM), we evaluate the error performed in the determination of the surface density of nanoparticles σ when the Maxwell-Garnett effective medium theory is used for fast data processing of the SPR reflectivity curves upon nanoparticle detection. The deviation increases directly with the manifestations of non-negligible scattering cross-section of the single nanoparticle, dipole-dipole interactions between adjacent AuNPs and dipolar interactions with the metal substrate. Near field simulations show clearly the set-up of dipolar interactions when the dielectric thickness is smaller than 10 nm and confirm that the anomalous dispersion usually observed experimentally is due to the failure of the effective medium theories. Using citrate stabilized AuNPs with a nominal diameter of about 15 nm, we demonstrate experimentally that Dielectric Loaded Waveguides (DLWGs) can be used as accurate nanocounters in the range of surface density between 20 and 200 NP/µm², opening the way to the use of PA-SPR spectroscopy on systems mimicking the physiological cell membranes on SiO₂ supports.