1.Guangdong Provincial Key Laboratory of Optical Fiber Sensing and Communications, Institute of Photonics Technology, Jinan University, Guangzhou 510632, China 2.Guangdong Provincial Key Laboratory of Nanophotonic Functional Materials and Devices, School of Information and Optoelectronic Science and Engineering, Guangzhou 510632, China 3.Institute of Modern Optics, Nankai University, Tianjin 300350, China
Fund Project:Project supported by the National Natural Science Foundation of China (Grant No. 61875093) and the Research Fund Program of Guangdong Provincial Key Laboratory of Nanophotonic Functional Materials and Devices, China.
Received Date:13 November 2018
Accepted Date:04 February 2019
Available Online:23 March 2019
Published Online:05 April 2019
Abstract:The nano groove can highly improve the transmittance of coaxial nanoring aperture due to the excitation of surface plasmon polariton (SPP). The total angular momentum carried by incident beam is reserved in the whole process and transferred to the SPP, thus the vortex SPP carrying orbital angular momentum is generated. The enhanced transmittance of nano aperture by vortex SPP has a wide range of applications, but its physical mechanism has been ignored for a long time. Here we study the process of the enhanced transmittance of the coaxial nanoring aperture and provide a model to describe the process of photon transmission. When the incident light irradiates on the coaxial nanoring aperture and nano groove, the vortex SPP induced by the groove propagates to coaxial nanoring aperture. Some of the photons in the SPP are coupled into the coaxial nanoring aperture and some are reflected back. The reflected photons travel back and forth multiple times between the coaxial nanoring aperture and nano groove. The vortex SPP interacts with the incident beam at the round of coaxial nanoring aperture, which determines the intensity at the round of the coaxial nano aperture, and thus affecting the transmittance. We systematically study the influence of optical angular momentum and the radius of the nano groove on the transmittance of coaxial nanoring aperture by using theoretical analysis and numerical simulations. The results show that the optical angular momentum and radius of the nano groove both affect the radial propagation phase of vortex SPP from nano groove to coaxial nanoring aperture, hence affecting the intensity of the electric field at the round of coaxial nanoring aperture and consequently determine the transmittance. The transmittance peaks of incident beams with different optical angular momenta will appear at different radii of the nano grooves, which provides a potential way to modulate the transmittance by adjusting the radius of the nano groove. This study is instructive for designing the enhanced optical transmission nano device based on vortex SPP. Keywords:optical angular momentum/ enhanced transmission/ surface plasmon polariton
研究的结构示意图如图1所示, 厚度为D = 150 nm的金膜上刻蚀有宽度为100 nm、深度为100 nm的环形凹槽, 其半径为R; 在凹槽的中心处有环形纳米孔, 环形纳米孔的内外半径分别为rin = 250 nm和rout = 300 nm, 深度h与金膜的厚度相等, 即h = D = 150 nm, 从而形成穿孔. 当入射光照射在金膜上时, 一部分光直接照射在环形纳米孔上, 其电场复振幅用符号$ \tilde \alpha $表示; 另外照射在凹槽上的入射光部分转化为表面等离极化激元并汇聚在环形纳米孔附近, 其电场复振幅表示为$ {\tilde \beta }$; 在表面等离极化激元中被环形纳米孔反射回来的光子在环形凹槽与环形纳米孔之间来回传播, 再次传播到环形纳米孔附近时的电场复振幅表示为$ {\tilde \gamma }$. 图 1 纳米结构示意图. 厚度为D = 150 nm的金膜上刻蚀有宽度为100 nm、深度为100 nm的环形凹槽, 半径为R; 在凹槽的中心处有环形纳米孔, 环形纳米孔的内外半径分别为rin = 250 nm和rout = 300 nm, 深度与金膜的厚度相等, 形成穿孔 Figure1. The schematic of nano structure: An annular nano groove having a width of 100 nm and a depth of 100 nm is etched on the gold film having a thickness of D = 150 nm, the coaxial nanoring aperture with the inner and outer radii are rin = 250 nm and rout = 300 nm is located in the center of the nano groove.
在时域有限差分法的仿真模拟中, 我们所采用的光源为携带不同轨道角动量的左旋圆偏振光的聚焦光束, 其携带的自旋角动量的拓扑荷数为ls = –1, 轨道角动量的拓扑荷数分别为lo = 1, 2, 3, 4, 携带的光子总角动量为自旋角动量和轨道角动量的拓扑荷数之和, 即L = ls + lo = 0, 1, 2, 3. 计算中采用的入射光波长范围为600—1000 nm, 其中图2(a)—(d)所示为波长800 nm时的光源的光强分布(物镜的数值孔径为0.4), 可以看出随着轨道角动量的拓扑核数目逐渐增大, 光斑尺寸逐渐变大. 图2(e)—(h)给出了这四种左旋圆偏振光中电场分量Ex的相位分布情况. 图 2 波长为800 nm时, 携带不同轨道角动量的左旋圆偏振入射光(ls = –1)的强度分布情况及电场分量Ex的相位分布情况 (a) lo = 1对应的强度分布; (b) lo = 2对应的强度分布; (c) lo = 3对应的强度分布; (d) lo = 4对应的强度分布; (e) lo = 1对应的相位分布; (f) lo = 2对应的相位分布; (g) lo = 3对应的相位分布; (h) lo = 4对应的相位分布.随着携带的轨道角动量拓扑核数逐渐增加, 入射光光斑逐渐变大 Figure2. The intensity distribution and the phase distribution of the Ex component of the incident beams (ls = –1) at the wavelength of 800 nm: (a) The intensity distribution (lo = 1); (b) the intensity distribution(lo = 2); (c) the intensity distribution(lo = 3); (d) the intensity distribution(lo = 4); (e) the phase distribution (lo = 1); (f) the phase distribution (lo = 2); (g) the phase distribution (lo = 3); (h) the phase distribution (lo = 4). The light spot is increasing with the topological number of the orbital angular momentum
其中CL表示自由光子耦合为表面等离极化激元的耦合效率, kr为涡旋表面等离极化激元中光子沿径向的传播常数, JL为第L级贝塞尔函数. 当波长为650 nm、L = 3时, 由(3)式计算得到的涡旋表面等离极化激元的电场分量$E_z^{{\rm{spp}}}$的相位分布如图3(a)所示, 其中白色虚线表示等相位面, 其呈螺旋状分布. 由惠更斯-菲涅耳原理可知, 光的传播方向与等相位面垂直, 表面等离极化激元的传播方向由kspp表示, 大小为${k_{{\rm{spp}}}} = {k_0}\sqrt {{{{\varepsilon _{\rm{m}}}{\varepsilon _{\rm{d}}}} / {\left( {{\varepsilon _{\rm{m}}} + {\varepsilon _{\rm{d}}}} \right)}}} $, 其中${\varepsilon _{\rm{m}}}$为金的介电常数, 其数值参量来自于Johnson 和 Christy的文章[22], ${\varepsilon _{\rm{d}}}$为空气的介电常数${\varepsilon _{\rm{d}}} = 1$. 在极坐标下将kspp分解为沿着径向分量kr和角向分量$ k_\varphi$, 对于金膜上表面上的任意一个观察点(r,$\varphi$), 表面等离极化激元沿角向传播为一周时, 角向传播相位与表面等离极化激元携带的涡旋相位的拓扑核数目成正比, 即${k_\varphi }2{\text{π}}r = 2L{\text{π}}$, 沿角向的传播常数可表示为 图 3 波长为650 nm时 (a)入射光携带有光子总角动量L = 3 (ls = –1, lo = 4)时, 在金膜上表面激发的涡旋表面等离极化激元中电场分量$E_z^{{\rm{spp}}}$的相位图; (b)在选定的四种左旋圆偏振的照射下, 激发的涡旋表面等离极化激元在金膜上表面的传输时的径向传播相位φr Figure3. (a) The phase distribution of the $E_z^{{\rm{spp}}}$ component of the surface plasmon polariton when the topological number of the total angular momentum carried by the incident beam at the wavelength of 650 nm equals to 3 (ls = –1, lo = 4); (b) the radical propagation phase φr of the surface plasmon polariton(SPP) when the nanostructure is irradiated by the selected four incident beams (ls = –1, lo = 1, 2, 3, 4).
利用商用软件 Lumerical FDTD solutions对选定的四种左旋圆偏振光照射环形凹槽包围环形纳米孔结构的进行了仿真模拟. 仿真模拟时, 纳米结构置于真空中, 涡旋光束从上方垂直照射在纳米结构上, 在纳米结构的下方设置了用于探测透射率的探测器, 在纳米结构上设置了大小为10 nm的细化网格, 完美吸收层包围着整个计算区域. 图4(a)—(d)分别给出了改变凹槽半径时, 携带不同轨道角动量的左旋圆偏振入射光(L = 0, 1, 2, 3)的透射率变化情况. 由图中可以观察到当入射光的波长逐渐变大, 透射率的极大值所对应的凹槽半径也逐渐增大, 该现象是由于表面等离极化激元波长随入射光波长的增大所致. 图4(b)—(d)为入射光携带的光子角动量拓扑核数L = 1, 2, 3时的透射率变化情况, 透射率极大值随凹槽半径的变化周期${\rm{d}}{R_{2,3,4}} \approx $${{{\lambda _{{\rm{spp}}}}} / 2}$, 这说明环形纳米孔入射端附近的电场复振幅主要由表面等离极化激元中的光子决定. 对比透射率与波长的变化可以发现在波长分别为900, 780 nm和650 nm时, 透射率大于周围波长, 这种透射率与波长的关系是受环形纳米孔本征模式的影响, 当环形纳米孔的本征模式与表面等离极化激元模式相匹配和环形纳米孔内传输的光子满足谐振条件时透射率才能显著增强[21]. 图 4 (a)—(d)在选定的四种左旋圆偏振光(ls = –1, lo = 1, 2, 3, 4)的照射下, 透射率与环形凹槽半径和波长的变化关系; (e)波长为650 nm时, 透射率随凹槽半径的变化曲线; (f)光子总角动量为3(ls = –1, lo = 4)的光束透射率与光子总角动量为2(ls = –1, lo = 3)的光束透过率之间的差值 Figure4. (a)?(d) The relation of the transmittance to wavelength of incident beams and radius of the nano groove; (e) the curves of the transmission with radius of the nano groove when wavelength equals to 650 nm; (f) the difference between transmittance of total angular momentum topological number of 3 (ls = –1, lo = 4)and 2 (ls = –1, lo = 3)
图 1 纳米结构示意图. 厚度为D = 150 nm的金膜上刻蚀有宽度为100 nm、深度为100 nm的环形凹槽, 半径为R; 在凹槽的中心处有环形纳米孔, 环形纳米孔的内外半径分别为rin = 250 nm和rout = 300 nm, 深度与金膜的厚度相等, 形成穿孔
图 2 波长为800 nm时, 携带不同轨道角动量的左旋圆偏振入射光(ls = –1)的强度分布情况及电场分量Ex的相位分布情况 (a) lo = 1对应的强度分布; (b) lo = 2对应的强度分布; (c) lo = 3对应的强度分布; (d) lo = 4对应的强度分布; (e) lo = 1对应的相位分布; (f) lo = 2对应的相位分布; (g) lo = 3对应的相位分布; (h) lo = 4对应的相位分布.随着携带的轨道角动量拓扑核数逐渐增加, 入射光光斑逐渐变大
图 3 波长为650 nm时 (a)入射光携带有光子总角动量L = 3 (ls = –1, lo = 4)时, 在金膜上表面激发的涡旋表面等离极化激元中电场分量
图 4 (a)—(d)在选定的四种左旋圆偏振光(ls = –1, lo = 1, 2, 3, 4)的照射下, 透射率与环形凹槽半径和波长的变化关系; (e)波长为650 nm时, 透射率随凹槽半径的变化曲线; (f)光子总角动量为3(ls = –1, lo = 4)的光束透射率与光子总角动量为2(ls = –1, lo = 3)的光束透过率之间的差值
