中文摘要：

当金属纳米粒子形成规则分布且阵列周期与单粒子的共振波长近似匹配时，会形成一种特殊的阵列共振，这种共振比单粒子的局域表面等离子体共振具有更窄的共振线宽和更高的共振强度．基于修正的长波近似方法，讨论了矩形阵列的消光截面与阵列因子和单粒子的极化率之间的关系；并详细研究了在不同偏振的入射光照射下，阵列因子随着电偶极子方向的改变而产生的变化，以及这一效应对阵列共振和消光截面所产生的影响．结果表明，大型的方阵是偏振无关的；在矩形阵列中，沿着阵列两个轴向的相邻粒子之间的耦合形成了阵列因子的两个极值，并且分别对应了散射截面的最小值．

英文摘要：

A special lattice resonance can be observed when the array period of a metal nanoparticle array matches the resonant wavelength of the localized plasmon resonance of an isolated particle. The lattice resonance is sharper and its linewidth is narrower than the localized plasmonics resonance of a single particle. According to the modified long wavelength approximation approach, we discuss the extinction cross-section of the rectangular array ill terms of the array factor and the particle polarizability. In this paper we emphasize the polarization characteristics of the regular array when the laser is incident vertically under different polarizations, and we also discuss in detail the variation of the array factor with the direction of electric dipole, and its influence on extinction cross section of the particle array. The square lattice with big size is polarization independent, while the rectangular lattice is polarization dependent. The coupling between the neighboring particle dipoles along the two lattice vectors of the regular array gives rise to a maximum value of its array factor, which determines a minimum value of the extinction cross section. When the incident light is polarized along one of the lattice vectors, the dipole coupling along that direction can be ignored since the particles are located in the far field of its neighboring particles, and the relevant peak in the array factor disappears.