Abstract
Periodic nanoparticle arrays with lower loss or high-quality (<i>Q</i>) factor resonances have made great advances in numerous applications. Such arrays can support narrow resonance modes by the hybridization of plasmonic-photonic modes, known as lattice plasmon modes (LPMs). The LPMs arise from the diffraction-induced coupling between localized surface plasmon resonances (LSPRs) of nanoparticles in symmetric or quasi-symmetric refractive index environment. To date, the great majority of researches have focused on the coupling of dipolar modes to in-plane orthogonal diffraction waves in nanoparticle arrays, resulting in dipolar lattice plasmon modes (DLPMs). However, there are few studies about quadrupolar lattice plasmon modes (QLPMs) for parallel coupling in symmetric environment, especially for high <i>Q</i>-factor QLPMs. In this work, we explore the sharp QLPMs of the silver nanodisk arrays by <i>x</i>-polarized light at normal incidence. In the first place, the scattering cross-section and near-field electric field distribution of single silver nanodisk indicate the existence of dipolar and quadrupolar LSPRs, thus, the optical responses of silver nanodisk arrays exhibit the peak-and-dip profiles of DLPMs and QLPMs at different wavelengths. Also, the electromagnetic field distributions confirm that the parallel propagating electric field introduces QLPM and results in electric field delocalization, while DLPM is existent in another way in periodic silver nanodisk arrays. Moreover, the position, linewidth and lineshape of the QLPM strongly depend on the role of lattice period. We enable these resonance modes to be selectively accessed and individually optimized by tuning lattice periods in the <i>x</i>- or <i>y</i>-direction. By changing the lattice period in the <i>x</i>-direction from 300 to 550 nm in steps of 50 nm, the dip of transmission intensity increases gradually, and when periods in the two directions are equal, the transmission dip exhibits a narrow-band QLPM resonance with a linewidth of 0.4 nm, corresponding quality factor is as high as <i>Q</i> = 1815 under the <i>x</i>-polarized light. In particular, by varying periods in the <i>y</i>-direction, the QLPM can also be manipulated in a range from an asymmetric Fano-like lineshape peak to a dip. The acquisition of these results may provide a design strategy for high-<i>Q</i> factor resonance in nanolaser, sensing, and nonlinear optics.
Highlights
Periodic nanoparticle arrays with lower loss or high-quality
The lattice plasmon modes (LPMs) arise from the diffractioninduced coupling between localized surface plasmon resonances
the great majority of researches have focused on the coupling of dipolar modes
Summary
近年来, 研究人员发现在阵列结构中金属纳米 粒子的 LSPRs 与瑞利异常 (rayleigh anomalies, RAs) 衍射之间的耦合能产生表面晶格共振 [5−11](surface lattice resonances, SLRs), 这种共振由于能有效地 图 2 (a) 高度 h = 100 nm, 直径 d = 160 nm 的单个银纳 米粒子散射截面光谱 ; 插图为偶极与四偶极 LSPRs 在 xz 平面对应的电场强度与方向 (箭头) 分布, 纳米圆柱的侧 面轮廓用白色框表示 , “ +” 与 “ – ” 符号表示正负电荷 ; (b) 银纳米圆柱阵列在 x 偏振光照射下的透射谱, 插图为 QLPM 的 放 大 图 ; (c) 银纳米圆柱阵列极化率倒数 ( 1/α ) 与 格 点 和 (S), 黑色虚线表示瑞利异常衍射, 粉色虚线表示 DLPM 共振波长 点位置为 SLR, 出现在 803 nm 处 (如图 2(c) 中粉 色虚线标记 ), 相较于前述的 LSPR, Im(1/α) 与 Im(S)符号相同, 并且 Im(1/α − S) 明显变小, 此时 消光截面最大, Q 值增加, 共振增强; 如果共振位 置向衍射模式靠近, 那么将会有更多的光能局限在 阵列表面, 粒子损耗降低, Im(1/α − S) 进一步变 小, 导致一个窄线宽共振模式出现 [9].
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