This theoretical study deals with the effect of bi-particle interaction on the surface plasmon resonance (SPR) in a dimer which includes two identical metal nanoparticles (NPs). Considering the dipole-dipole interaction in a Drude-like model, an appropriate equation is derived for the permittivity of each NP. The restoration force related to the classical confinement originating from the finite size of NPs is considered, and an appropriate adjustment coefficient is considered for this term through analyzing experimental data. Two different polarizations are considered for the laser beam electric field, and it is shown that the orientation of the electric field has an essential role in the linear optical properties of a dimer. Numerical investigation is accomplished for a dimer of gold NPs with two different diameters of 4 nm and 20 nm. For the parallel polarization, dipole-dipole interaction leads to the redshift of SPR wavelength and increase in its peak value, while for the perpendicular polarization, the absolute opposite results are derived. For all cases, it is shown that SPR wavelength functionality with respect to the geometric factor a/d (NP radius to the separation) can be presented by a cubic equation that fits better than an exponential one suggested by the earlier studies which demonstrates the dipole-dipole characteristic of the interaction. Qualitatively, our results are in good agreement with the other experimental studies.

这项理论研究处理了包含两个相同金属纳米颗粒（NPs）的二聚体中双粒子相互作用对表面等离振子共振（SPR）的影响。考虑到像德鲁德模型中的偶极子-偶极子相互作用，为每个NP的介电常数导出了一个合适的方程。考虑了由NP的有限大小引起的与经典约束有关的恢复力，并通过分析实验数据为该项考虑了适当的调整系数。对于激光束电场，考虑了两种不同的偏振，并且显示出电场的方向在二聚体的线性光学性质中起着至关重要的作用。对具有两个不同直径的4 nm和20 nm的金NP的二聚体进行了数值研究。对于平行极化，偶极-偶极相互作用导致SPR波长发生红移并增加其峰值，而对于垂直极化，则得出绝对相反的结果。在所有情况下，均显示出SPR波长功能相对于几何因子a / d（分离的NP半径）可以由三次方程表示，该三次方程的拟合度比早期研究建议的指数方程更好，后者证明了相互作用的偶极-偶极特性。定性地，我们的结果与其他实验研究吻合良好。