Mode Splitting Induced by Mesoscopic Electron Dynamics in Strongly Coupled Metal Nanoparticles on Dielectric Substrates.

Katarzyna Kluczyk-Korch,Lucjan Jacak,Christin David,Witold Aleksander Jacak

doi:10.3390/nano9091206

Abstract

We study strong optical coupling of metal nanoparticle arrays with dielectric substrates. Based on the Fermi Golden Rule, the particle–substrate coupling is derived in terms of the photon absorption probability assuming a local dipole field. An increase in photocurrent gain is achieved through the optical coupling. In addition, we describe light-induced, mesoscopic electron dynamics via the nonlocal hydrodynamic theory of charges. At small nanoparticle size (<20 nm), the impact of this type of spatial dispersion becomes sizable. Both absorption and scattering cross sections of the nanoparticle are significantly increased through the contribution of additional nonlocal modes. We observe a splitting of local optical modes spanning several tenths of nanometers. This is a signature of semi-classical, strong optical coupling via the dynamic Stark effect, known as Autler–Townes splitting. The photocurrent generated in this description is increased by up to 2%, which agrees better with recent experiments than compared to identical classical setups with up to 6%. Both, the expressions derived for the particle–substrate coupling and the additional hydrodynamic equation for electrons are integrated into COMSOL for our simulations.

Highlights

Nanotechnologies strive for higher confinement of both photons and electrons in narrower structures, at sharper tips and in smaller gaps
In order to evaluate the derived equations, we use COMSOL Multiphysics 5.0 with the Wave Optics module implementing the finite element method (FEM) to solve Maxwell’s equations using the modified permittivity Equation (9) for the Si substrate coupled to plasmonic nanoparticles
We study the influence of nanoparticle size and the interparticle separation in order to estimate the range of parameters for which the nonlocal effects significantly change the overall photocurrent gain

Summary

Introduction

Nanotechnologies strive for higher confinement of both photons and electrons in narrower structures, at sharper tips and in smaller gaps. A modified dielectric function of the semiconductor is derived by calculating the photon absorption probability in the presence of the dipole field arising from the plasmon oscillation This enables us to compare with calculations accounting for scattering effects. The light-induced, mesoscopic properties of the electron–electron interaction are derived from the semi-classical hydrodynamic approach [52,57] Both strong coupling and nonlocality are inherently nonlinear effects. Accounting for non-classical electron interaction effects in the dipole field of the metal nanoparticle, we observe a splitting of the local resonance into two sharp resonances which increase both the absorption and scattering cross section around the original local resonance.

Optical Coupling of Nanoparticle and Substrate

Light-Induced Electron Dynamics

Results and Discussion

Conclusions