Comparative analysis of theories accounting for quantum effects in plasmonic nanoparticles

Abstract

Understanding and accounting for quantum effects in nanoplasmonics is essential for accurate modeling and design of nanophotonic devices. In this paper, we investigate the influence of such quantum effects as spatial nonlocality and splitting of the wave function of conduction electrons near the surface of plasmonic nanoparticles on the extinction cross-section and the field enhancement factor. We apply the theory of generalized nonlocal optical response (GNOR) to describe the spatial nonlocality of noble metal particles. To consider the behavior of electrons near the metal–dielectric interface, mesoscopic boundary conditions are used, including the surface response functions (SRF) - the Feibelman parameters. We use the discrete source method (DSM), allowing for numerical analysis of the scattering problems taking into account quantum effects in the frame of both theories. The application of both GNOR and SRF approaches leads to a decrease in the amplitude of the plasmon resonance compared to the classical Maxwell theory and its shift to the shorter wavelength region (blue shift). The simulation results demonstrate significant differences between the two theories explaining the quantum effects arising in non-spherical plasmonic nanoparticles located in a dense environment. Specifically, compared with GNOR theory, SRF predicts a larger field enhancement. We found that quantum nonlocal effects are more significant for the enhancement factor at the particle surface than for the extinction cross-section. In addition, it was discovered that a denser environment leads to a significant increase in the blue shift of the plasmonic peak.