Interacting plasmonic nanostructures beyond the quasi-static limit: a “circuit” model

Xuezhi Zheng,Victor V Moshchalkov,Guy A E Vandenbosch,Vladimir Volskiy,Jeremy J Baumberg,Ventsislav K Valev,Niels Verellen

doi:10.1364/oe.21.031105

Abstract

The interaction between individual plasmonic nanoparticles plays a crucial role in tuning and shaping the surface plasmon resonances of a composite structure. Here, we demonstrate that the detailed character of the coupling between plasmonic structures can be captured by a modified "circuit" model. This approach is generally applicable and, as an example here, is applied to a dolmen-like nanostructure consisting of a vertically placed gold monomer slab and two horizontally placed dimer slabs. By utilizing the full-wave eigenmode expansion method (EEM), we extract the eigenmodes and eigenvalues for these constituting elements and reduce their electromagnetic interaction to the structures' mode interactions. Using the reaction concept, we further summarize the mode interactions within a "coupling" matrix. When the driving voltage source imposed by the incident light is identified, an equivalent circuit model can be constructed. Within this model, hybridization of the plasmonic modes in the constituting nanostructure elements is discussed. The proposed circuit model allows the reuse of powerful circuit analysis techniques in the context of plasmonic structures. As an example, we derive an equivalent of Thévenin's theorem in circuit theory for nanostructures. Applying the equivalent Thévenin's theorem, the well-known Fano resonance is easily explained.

Highlights

Localized surface plasmon resonances (LSPR) in nanoparticles have found many applications spanning from the realm of life sciences, including biomedicine, bio-sensing, cancer treatment [1,2,3,4], to the conventional research domain of electrical engineering, such as the design of nanocircuits, nanofilters and nanoantennas [5,6,7,8]
By assuming the size of constituent nanoparticles much smaller than the wavelengths of the incident light, a dipole-interaction model is conceived and applied to the spectral splitting of nanoparticle pairs [18]
By considering the influence of higher order resonances, the coupling between surface plasmon modes is modeled by hybridization theory, similar to molecular hybridization theory where the atomic orbitals mix and form new molecular orbitals

Summary

Introduction

Localized surface plasmon resonances (LSPR) in nanoparticles have found many applications spanning from the realm of life sciences, including biomedicine, bio-sensing, cancer treatment [1,2,3,4], to the conventional research domain of electrical engineering, such as the design of nanocircuits, nanofilters and nanoantennas [5,6,7,8]. Based on the nanoparticles’ electrostatic resonances [20], a methodology of systematically designing and analyzing the optical properties of an ensemble of nanoparticles is presented in [21,22] All these models are constructed within the quasi-static limit. Utilizing a dolmen-like nanostructure (dimensions, materials and depth profile are shown in Fig. 1), we illustrate that in contrast to the electrostatic modal analysis [20] where the material contribution is the only factor affecting the resonances, in a full-wave eigenmode analysis the radiation, as the result of retardation effects, comes into the picture and plays a crucial role in determining the resonances of surface plasmon modes. We develop an equivalent of Thevenin’s theorem [32] for composite nanostructures and use it to explain the well-known Fano interference [33,34,35,36,37,38,39] in the dolmen structure

The eigenvalue problem for a nanoscatterer

The hybridization between monomer and dimer eigenmodes: a “circuit” model

Fano resonance in the dolmen structure: a Thévenin’s theorem viewpoint

Conclusion