Analytical study of Fano phenomenon in plasmonic hexamer and heptamer using characteristic mode theory

Abstract

In this paper, the optical properties of several Plasmonic structures including single nanodisk, Hexamer and Heptamer, using the Characteristic Mode Theory (CMT) are investigated. Single nanodisk and Hexamer have shown a bright mode with Lorentzian response. In Heptamer, a strong interaction is created between the nanoparticles and thus the Fano resonance occurs with a bright and a dark mode. Based on the CMT analysis and the definition of the Fano response, it has been observed that the collision of the modes in the modal significance diagrams is where the Fano response occurs. Due to the characteristic current distributions, bright and dark modes have been observed that are necessary to create a Fano response. So, using CMT, it can be determined whether the structure is capable of generating a Fano response or not. Also, the frequency of bright and dark modes and the Fano minimum can be obtained using CMT. Moreover, according to the characteristic currents, the structure can be modified to achieve a sharper Fano response. We have selected such structures to investigate this method in these types of Heptamers and it has been shown that the proposed method is applicable for such structures.

Introduction

The attractive properties of metal nanoparticles have been extensively studied in recent years. Plasmonics is based on the process of interaction between electromagnetic waves and conducting electrons in nanoscale metals. These near-surface collective electronic oscillations are known as surface Plasmons [1]. Plasmonics are divided into two areas: Surface Plasmon Polaritons (SPPs) and Localized Surface Plasmon (LSPs). SPPs are electromagnetic excitations that propagate at the interface between a metal and a dielectric and they are confined in the vertical direction [2]. LSPs are non-emission excitations of conductive electrons in metal nanoparticles that are coupled to an electromagnetic field. Many of the unique optical properties of Plasmonic structures are due to the interaction of nanoparticle Plasmons. In the last decade, many studies have been performed on the destructive interference of Plasmon modes which makes the Fano resonances [3]. In Plasmonic structures, the Fano resonance arises from the interference between the light that is directly coupled to a bright mode (radiant) and light that is indirectly coupled to a dark mode which is excited by near-field interferences with bright mode [4].

Fano resonances have seen in various dielectric and Plasmonic structures such as Metamaterials [5], nanocavities [6], structures consisting of nanoparticles with different arrangements like Quadrumers [7], Pentamers [8], and nanosphere clusters [9]. In addition, nanoparticles with different shapes in a Plasmonic structure can make a Fano resonance [10]. Sharper Fano resonance has demonstrated by an elliptical nanoring resonator array on a gold conducting layer [11]. By connecting two nanodisks with a functional metal dielectric nanowire in a four-member system, it has been shown that it is possible to excite the Fano resonance and charge transfer Plasmons in an optical device [12]. Moreover, in [13], an all-dielectric cluster is suggested which has the ability to support distinct Fano line-shapes.

Due to its sharp spectral characteristic and strong field enhancement, Fano resonances have an extraordinary ability for applications such as switches, modulators, sensors, and nonlinear applications [14]. Plasmonic sensors with Fano response are very suitable for detecting the concentration of nanoparticles in liquid and gas, so they will have many applications in medicine, health, and safety [15], [16]. Another importance of Fano response is in applications related to SERS as a promising and sensitive tool for detecting a single molecule and chemically sensitive imaging [17].

Accurate modeling of Plasmonic structures is important for understanding the physical processes affecting near- and far-field optical response. Recently, a new method called Characteristic Mode Theory (CMT) has been proposed for the analysis of the intrinsic properties of Plasmonic structures [18]. CMT is based on the numerical Method of Moments which is used to solve surface integral equations (SIE). It is used for analyzing the resonant behavior of a radiation structure that is independent of excitation [19]. In this way, the resonant frequencies of the basic modes as well as the higher-order modes are obtained which can be used for optimizing structures for a specific purpose.

In 2016, the mathematical relationships of CMT were improved and its validity was also proven for some Plasmonic structures [20]. Plasmonic structures can be modeled with high accuracy as a penetrable homogeneous lossy object with a negative real part permittivity, and the existing relationships for SIE can be used with a little modification [20], [21]. These equations were modified in 2018 to address the challenge of eliminating non-physical modes [22]. In one of the most recent studies in this field, the CMT has been used to optimize a Plasmonic nano-antenna [23].

Here, it is shown for the first time that the Fano phenomenon can be observed and analyzed with CMT. This article contains several sections. In Section II, the mathematical relations of CMT are shown. Next, in Section III, a FEKO-based in-house code and commercial electromagnetic software CST are used to analyze the data. This section consists of three sub-section:

• First, a gold nanodisk was used as a basic structure to check the accuracy of the in-house code and compare the results with CST.

• Hexamer has been studied in this section. CMT has been used for this structure and then, the optical spectra and near-field distribution are shown and the results are compared with CMT.

• In the last step, the optical response of Heptamer is investigated. It is shown that in this structure a Fano resonance occurs which can be justified using CMT.

In short, three conventional structures are selected for this study to show that we can predict the Fano response frequency and occurrence by analyzing the surface current with CMT techniques. We have chosen such structures to investigate the Fano response with CMT analysis in these types of Heptamers and it has been shown that the proposed method is applicable for such structures. Moreover, to our best knowledge, this is the first time that the Fano phenomenon has been analyzed with CMT. This study can be used for chiral structure and controlling the surface current can be noticed for modifying the Fano response in chiral structure to obtain sharper diagram.