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本文中采用长度不同的非对称矩形石墨烯纳米片二聚体(分别表示为Ⅰ和Ⅱ)为阵列单元,如图 1a和图 1b所示。两纳米片的宽度均为25 nm,长度分别为L1和L2,中间间隔为5 nm;两个纳米片错位放置,底边错开的长度设为a;纳米片二聚体成周期性分布,x和y方向的周期长均为100 nm。石墨烯纳米片沉积在基底上,如图 1b所示,基底的介电常量设为εs=3.9。整个模型置于空气中(εm=1.0)。而石墨烯纳米片,作为单原子层材料,当它和电磁场作用时,可以用表面电流密度来进行描述:
$ J_{\mathrm{s}}=\sigma_{\mathrm{g}} E_{/ /} $
(1) 式中,σg是石墨烯的表面电导率,E//是平行于石墨烯平面的电场。石墨烯的表面电导率σg由带间电导率σintra和带内电导率σinter两部分构成,分别对应石墨烯的带间和带内光电子散射,其表达式为:
$ \sigma_{\mathrm{g}}=\sigma_{\text {intra }}+\sigma_{\text {inter }} $
(2) 其中:
$ \begin{gathered} \sigma_{\text {intra }}= \\ -\mathrm{i} \frac{e^2 k_{\mathrm{B}} t}{\mathsf{π} \hbar\left(\omega-\mathrm{i} \tau^{-1}\right)}\left\{\frac{E_{\mathrm{F}}}{k_{\mathrm{B}} t}+2 \ln \left[\exp \left(-\frac{E_{\mathrm{F}}}{K_{\mathrm{B}} t}\right)+1\right]\right\} \end{gathered} $
(3) 当$\hbar \omega \gg k_{\mathrm{B}} t$和$\left|E_{\mathrm{F}}\right| \gg k_{\mathrm{B}} t$时,σinter可表示为:
$ \sigma_{\text {inter }}=-\frac{\mathrm{i} e^2}{4 \mathsf{π} \hbar} \ln \left[\frac{2\left|E_{\mathrm{F}}\right|-\hbar\left(\omega-\mathrm{i} \tau^{-1}\right)}{2\left|E_{\mathrm{F}}\right|+\hbar\left(\omega-\mathrm{i} \tau^{-1}\right)}\right] $
(4) 式中,e为电子电荷,kB为玻尔兹曼常数,EF为费米能级,τ为弛豫时间,取τ=4 ps,$\hbar$为约化普朗克常量,ω为角频率,温度t=300 K。
为了详细分析石墨烯纳米片二聚体阵列与电磁波的相互作用,本文中利用有限元分析法进行数值模拟。光吸收率为A=1-T-R,其中T为透射率,R为反射率。当偏振方向为x方向的线偏光沿着-z方向射向石墨烯纳米片二聚体阵列时,产生强烈的表面等离激元法诺共振,如图 1c、图 1d和图 1e所示。由图可知,在中红外波段出现4个明显的非对称法诺共振峰,其中,图 1c为反射谱,图 1d为透射谱, 图 1e为吸收谱。
图 1 a—石墨烯纳米片二聚体的结构及参数 b—模型单元结构图 c~e—石墨烯纳米片二聚体阵列在偏振方向为x的线偏光激发下的法诺共振谱(L1=70 nm, L2=40 nm, a=0 nm, EF=0.5 eV)
Figure 1. a—structure and parameters of graphene nanosheet heterodimer b—schematic of each cell unite c~e—the resonance spectra of the graphene nanosheet heterodimer array excited with x-polarized incident light (L1=70 nm, L2=40 nm, a=0 nm, EF=0.5 eV)
石墨烯纳米片阵列的表面等离激元法诺共振
Plasmonic Fano resonance based on the graphene nanosheet array
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摘要: 为了在中红外波段获得多阶表面等离激元法诺共振, 设计了结构简单、制备方便的非对称石墨烯纳米片二聚体阵列超表面。采用有限元分析方法, 对各阶法诺共振峰产生的物理机制, 费米能级、纳米片结构及相对位置等因素对法诺共振的影响进行了理论分析。结果表明, 随着费米能级的增加, 法诺共振发生蓝移; 表面等离激元共振效应增强, 同时增强了近场的局域效应; 随着纳米片二聚体的大小和位置的不对称性增加, 法诺线型的非对称性也随之增加; 这种结构简单的多阶表面等离激元法诺共振有望在生物传感及相关领域得到广泛应用。该研究为进一步的实验研究提供了理论参考。
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关键词:
- 光电子学 /
- 表面等离激元法诺共振 /
- 杂化分析 /
- 非对称纳米块二聚体 /
- 石墨烯
Abstract: In order to obtain strong multiple Fano resonances, a metasurface composed of asymmetric nanosheet heterodimer was designed in the paper. Based on the finite element analysis method, the physical mechanism of Fano resonances was analyzed by the hybridization theory, and the different Fano responses resulted from different Fermi levels, structures parameters were analyzed. Results show that when the Fermi level of the graphene nanosheet increases, the Fano resonance peaks blue shift, and the intensity of graphene responses is enhanced, which causes that the local effect and absorption are enhanced accordingly. At the same time, with the increase of the asymmetry of the size and position of the nanosheet heterodimer, the asymmetry of Fano resonances also increases. The Fano resonances based on the simply graphene nanosheet heterodimer array are expected to be widely used in biosensor and related fields. The study provides theoretical reference for further experimental research. -
图 1 a—石墨烯纳米片二聚体的结构及参数 b—模型单元结构图 c~e—石墨烯纳米片二聚体阵列在偏振方向为x的线偏光激发下的法诺共振谱(L1=70 nm, L2=40 nm, a=0 nm, EF=0.5 eV)
Figure 1. a—structure and parameters of graphene nanosheet heterodimer b—schematic of each cell unite c~e—the resonance spectra of the graphene nanosheet heterodimer array excited with x-polarized incident light (L1=70 nm, L2=40 nm, a=0 nm, EF=0.5 eV)
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