图 1  (a) 金属纳米粒子的双圆环阵列示意图; (b) 阵列结构参数图; (c) 激发场参数图

Fig. 1.  (a) Schematic diagram of the double ring array of metallic nanoparticles; (b) structure diagram and the parameter definitions; (c) definition of the excitation field.

图 2  4种特殊的双圆环金属纳米粒子阵列结构

Fig. 2.  Four special arrangement of the double ring array of metallic particles.

图 3  (a) 由单圆环粒子阵列构造双圆环粒子阵列; (b) 双圆环阵列的归一化增强因子随结构参数$ {{\Delta \theta } \mathord{\left/ {\vphantom {{\Delta \theta } \theta }} \right. } \theta } $和$ {{\Delta r} \mathord{\left/ {\vphantom {{\Delta r} r}} \right. } r} $的变化, 图中展现出两种共振结构(用红色虚线标出)随着$ {{\Delta \theta } \mathord{\left/ {\vphantom {{\Delta \theta } \theta }} \right. } \theta } $变化而逐渐简并的情形. 在仿真中, 金属纳米粒子使用的是半径为40 nm的银球, 激发波长为650 nm, 其他参数为N = 12和r = 200 nm

Fig. 3.  (a) Transform to double ring structure from single ring array by varying two parameters $ \Delta \theta /\theta $ and $ {{\Delta r} \mathord{\left/ {\vphantom {{\Delta r} r}} \right. } r} $; (b) normalized enhancement factor ($\beta $) as a function of the two parameters. Two resonant structures are displayed via red dashed arrows, which gradually degenerate as the $ \Delta \theta /\theta $ turns large. In the calculation, the metallic particles are silver sphere of 40 nm in radius, and the incident wavelength is 650 nm, other parameters are N = 12 and r = 200 nm.

图 4  双圆环粒子阵列(图2(c)结构)的增强因子$\beta $随结构参数r₁/r₂和粒子数N的改变

Fig. 4.  Enhancement factor $\beta $ of the double ring array as shown in Fig. 2(c) as a function of the structural parameter r₁/r₂ and the particle number N of a single ring.

图 5  4种基于图2(c)结构的双圆环阵列的增强因子$\beta $随结构参数r₁/r₂和激发波长$ \lambda $的变化情况

Fig. 5.  Enhancement factor $\beta $ of the four different double ring array based on the model shown in Fig. 2(c) as a function of the structural parameter r₁/r₂ and the incident wavelength $ \lambda $.

图 6  两种双圆环粒子阵列结构的局域场分布　(a), (c) xz平面上的场分布, 最大传输距离为150 nm; (b), (f) 距离阵列40 nm处xy平面上的场分布; (c), (g) 距离阵列80 nm处xy平面上的场分布; (d), (h) 距离阵列120 nm处xy平面上的场分布. 仿真区域的边长为600 nm, 蓝色箭头标识了横向能流的方向

Fig. 6.  Radiation field of two double ring array: (a), (c) Field distribution on the xz plane, where the largest propagation distance is 150 nm; (b), (f) field distribution plot the transverse distribution on the xy plane of 40 nm away from the array; (c), (g) field distribution on the xy plane at 80 nm from the array; (d), (h) field distribution on the xy plane at 120 nm distance from the array. The simulation area is a square of 600 nm wide, and the blue arrows show the transversal energy flux.

图 7  双圆环粒子阵列的共振效应　(a) 完全共振结构与作为对比的部分共振结构参数; (b) 完全共振结构的增强因子; (c) 在不同激发外场下, 两种共振结构在不同传输距离处的局域场分布与横向能流分布

Fig. 7.  Resonant characteristics of the double ring particle array: (a) Structural parameters of the full resonant and partial resonant array; (b) enhancement factor of the full resonant structure; (c) radiation field of the two structures at different propagation distance under different excitation.