针对C_(3v)和C_(4v)对称构型金属纳米多颗粒-薄膜系统的Fano共振光谱低谷的产生机理,运用群论的方法给出了详细的推导。在前期研究成果的基础上,分析证实了当线偏振光电场沿多颗粒所在平面入射时,C_(nv)对称构型多颗粒-薄膜系统共有4个满足相同不可约表示的E模式:在多颗粒所在平面内只有3个局域表面等离激元电偶极矩共振对称模式,其中2个模式位于外围环形多颗粒中,中心颗粒单独具有1个模式,这与Dnh对称构型多颗粒系统的电偶极矩分布完全相同;另外1个模式虽满足对称性相同的要求,但其电偶极矩的方向垂直于多颗粒所在的平面。C_(nv)点群和D_(nh)点群虽然具有相同的光谱线型,但是薄膜基底的存在会使光谱谷(峰)产生一定的红移或蓝移,这就为设计金属纳米多颗粒-薄膜系统的光学性质及其广泛应用提供了一定的参考。 Aiming at the mechanism of Fano resonance spectral trough of metal nano-multiparticulate-thin film system with C_ (3v) and C_ (4v) symmetry, a detailed derivation is given by the method of group theory. Based on the previous research results, it is proved that there are four E modes satisfying the same irreducible representation in the C nn symmetric multipartite-film system when the linearly polarized optical field is incident on the plane where multiple particles are present: There are only three LSPR modes in the plane where the particles reside, of which two modes are located in the outer ring-shaped multiparticulates and the central particle has a single mode, which is consistent with the Dnh symmetric multiparticulate system Of the electric dipole moment distribution is exactly the same; the other one mode to meet the symmetry of the same requirements, but the electric dipole moment direction perpendicular to the plane where the multi-particle. Although the nodal point group and D nh point group have the same spectral line pattern, the existence of thin film base causes a certain red-shift or blue-shift of the spectral valley (peak) - The optical properties of thin film systems and their wide range of applications provide a reference.