A forced damped harmonic oscillator model of the dipole plasmon mode is illustrated by the theoretical derivation and the simulation based on the metal ellipsoids. The analytical expression of the restoring force is derived. The displacement of the oscillator, which is the phenomenological relative displacement of the free negative and positive charge systems in solids, can be represented by the accumulated charges on the surface of the nanoparticles based on the derived results. With the help of the finite-difference time-domain method, the dependence of the resonance wavelengths and the surface charge distributions on the geometric parameters and the materials has been verified by the ellipsoids evolved from 10 nm radius spheres. As an essential feature of an oscillator, the phase shifts, which are between the accumulated surface charges (the displacement of the oscillator) and the electric field of the incident light, are also illustrated by the numerical simulation. For the silver nanoparticle with the radius of 10 nm, the phase shifts are consistent with the feature of a forced damped harmonic oscillator. For the large silver nanoparticle with the radius of 50 nm, the magnitudes of the phase shifts have some deviations due to the nonuniform electric field along the light propagation. By this oscillator model, we confirm that localized surface plasmon resonance arises from the collective motion of free charges modulated by the bound charges of the lattice background and the dielectric medium. The forced damped harmonic oscillator model is a clear picture for the dipole localized surface plasmon resonance.

通过理论推导和基于金属椭球的仿真，说明了偶极等离子体激元模式的强迫阻尼谐振子模型。得出恢复力的解析表达式。振荡器的位移，即固体中自由的负电荷和正电荷系统的现象学上的相对位移，可以根据得出的结果由纳米粒子表面上的累积电荷表示。借助于时域有限差分法，共振波长和表面电荷分布对几何参数和材料的依赖性已通过从半径为10 nm的球体演化而来的椭圆体得到了验证。作为振荡器的基本特征，相移 数值模拟也说明了在累积的表面电荷（振荡器的位移）和入射光的电场之间的电导率。对于半径为10 nm的银纳米粒子，相移与强制阻尼谐波振荡器的特征一致。对于半径为50 nm的大银纳米粒子，由于沿光传播的电场不均匀，相移的大小会有一些偏差。通过此振荡器模型，我们确认局部表面等离子体激元共振是由晶格背景和介电介质的束缚电荷调制的自由电荷的集体运动引起的。强制阻尼谐波振荡器模型清楚地显示了偶极子局部表面等离子体激元共振。