D3h和D4h等离激元超分子的Fano共振光谱的子集合分解解释

Subgroup decomposition analyses of D_(3h) and D_(4h) plasmonic metamolecule Fano resonance spectrum

针对D_(3h)和D_(4h)对称构型金属纳米多颗粒集合即等离激元超分子表面等离激元共振光谱的子集合分解及其相对应的Fano共振光谱低谷的产生机理,本文运用群论的方法做出了详细的分析研究.运用与群论中求解分子简正振动模式类似的方法,推导证实了在线偏振光入射时,Dnh环形多颗粒只有2个电偶极表面等离激元共振模式,增加中心颗粒会使模式增加1个.对D_(3h)和D_(4h)等离激元超分子的表面等离激元共振模式进行不可约表示基向量正交分解分析表明,Fano共振光谱低谷是由于两个起主要作用的相邻模式包含有共同的正交基向量,并形成相消干涉而产生.这进一步验证了Fano共振光谱低谷的起源除传统观点(即源自于宽频超辐射亮模式和窄频低辐射暗模式之间的耦合)之外的另一种解释视角.

In recent decades, research about surface plasmon polariton（SPP） has earned its popularity in nanotechnology with many theoretical achievements, much progress in metal nanostructure manufacturing, spectral analyzing, biomedicine ultrasensing, etc. Group theory is an effective tool for analyzing the spectra of symmetrical organized multiparticles（dubbed as plasmonic metamolecule）. Recently, SPP Fano resonance in nanostructure either from plasmonic metamolecules or from symmetry-breaking has attracted much attention. Regarding to the subgroup decomposition analysis of the D3h and D4h plasmonic metamolecule surface plasmon resonance spectra and the mechanism of forming the Fano resonance spectral dip, this paper proposes an explanation method based on group theory.By using a similar group theory approach to constructing the molecular vibration normal modes, the method to build the dipolar SPP symmetric modes of plasmonic metamolecules is established. It is confirmed that under the linear polarization excitation there exists only two dipolar SPP symmetric modes for a ring shaped Dnhplasmonic metamolecule, while adding the center particle will merely add an extra independent symmetric mode. For the D3hand D4h plasmonic metamolecule, it is found that there are two dominant eigenmodes i.e., one is composed by adding two symmetric modes and the other by subtracting two symmetric modes. The decomposition analysis further reveals that the negative coefficient of the symmetric mode for forming the short wavelength eigenmode for D3h tetramer plasmonic metamolecules is much smaller than that for D4h pentamer plasmonic metamolecules, thereby explaining that the Fano resonance dip of the pentamer is sharper than that of the tetramer. It is worth noting that the group theory can provide some guidance for building the symmetric modes and the SPP eigenmodes, but is unable to determine the coefficient of each symmetric mode.As for the origin of Fano resonance dip, so far there have existed two different perspectives： one is the traditional viewpoint, i.e., the Fano resonance dip is formed due to the coupling of the wideband superradiant bright mode with the narrowband subradiant dark mode, and the other is that the Fano resonance dip is formed by the destructive interference between two neighboring eigenmodes. The decomposition analysis described in this paper actually can unify these two perspectives.