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为了设计表面等离子体共振预警装置,首先需要获取合适的各项系统参量,以便于后续装置中模块的选择。本文中基于表面等离子体共振原理设计装置传感参量选取图形用户界面(graphical user interface, GUI)模块,通过总反射率公式,得出入射波长、入射角、介电常数之间的关系并求解出最佳参量。
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利用表面等离子体共振进行检测的主要描述为:结合菲涅耳定理及麦克斯韦方程[10]可知,当p偏振光在金属薄膜与棱镜的界面处发生全反射并产生水平波矢,激发金膜表面的自由电子产生表面等离子体,入射光波的水平波数和表面等离子体的波数分别为:
$ {k_{\rm{s}}} = \frac{{2{\rm{ \mathit{ π} }}}}{\lambda }{\varepsilon _0}{\rm{sin}}\theta $
(1) $ {k_{\rm{p}}} = \frac{{2{\rm{ \mathit{ π} }}}}{\lambda }\sqrt {\frac{{{\varepsilon _2}{\varepsilon _3}}}{{{\varepsilon _2} + {\varepsilon _3}}}} $
(2) 式中,λ为入射光波长,θ为光波的入射角,ε是介电常数, 下标0, 1, 2, 3分别代表棱镜、传感玻片、金膜和油品。
当光波的入射角满足一定条件时,表面等离子波与入射光水平分量的频率相等,二者将发生共振。
利用反射公式:
$ \begin{array}{l} {r_{12}} = \frac{{{E_{1, p}}\mathit{'}}}{{{E_{1, p}}}} = \frac{{{n_2}{\rm{cos}}{\theta _1} - {n_1}{\rm{cos}}{\theta _2}}}{{{n_2}{\rm{cos}}{\theta _1} + {n_1}{\rm{cos}}{\theta _2}}} = \\ \;\;\;\;\;\;\;\;\;\;\;\;\frac{{{\varepsilon _2}{k_{1, p, z}} - {\varepsilon _1}{k_{2, p, z}}}}{{{\varepsilon _2}{k_{1, p, z}} + {\varepsilon _1}{k_{2, p, z}}}} \end{array} $
(3) $ \begin{array}{l} {r_{23}} = \frac{{{E_{2, p}}\mathit{'}}}{{{E_{2, p}}}} = \frac{{{n_3}\rm{cos}{\theta _2} - {n_2}\rm{cos}{\theta _3}}}{{{n_3}\rm{cos}{\theta _2} + {n_2}\rm{cos}{\theta _3}}} = \\ \;\;\;\;\;\;\;\;\;\;\;\;\frac{{{\varepsilon _3}{k_{2, p, z}} - {\varepsilon _2}{k_{3, p, z}}}}{{{\varepsilon _3}{k_{2, p, z}} + {\varepsilon _2}{k_{3, p, z}}}} \end{array} $
(4) 式中,E为入射振幅分量,E′为反射振幅分量, n为折射率,r为相邻介质层振幅反射比。入射光在z方向的波数ki, p, z为:
$ \begin{array}{l} {k_{i, }}_{p, z} = \sqrt {\frac{{{\omega ^2}}}{{{c^2}}}{\varepsilon _i} - {k_{0, p, x}}^2} = \\ \frac{{2{\rm{ \mathit{ π} }}}}{\lambda }\sqrt {{\varepsilon _i} - {\varepsilon _0}{\rm{si}}{{\rm{n}}^2}\theta } , (i = 0, 1, 2, 3) \end{array} $
(5) 式中,c为光在真空中的速度,ω为波矢振荡角频率。
总反射率公式为:
$ R = {r_{13}} = \frac{{{r_{12}} + {r_{23}}{\rm{exp}}(2{\rm{i}}{\mathit{d}_{\rm{2}}}{\mathit{k}_{{\rm{2}},\mathit{p,z}}})}}{{1 + {r_{12}}{r_{23}}{\rm{exp}}(2{\rm{i}}{\mathit{d}_{\rm{2}}}{\mathit{k}_{{\rm{2}},\mathit{p,z}}})}} $
(6) 式中,光波在传感玻片、传感金膜和待测介质中沿z方向的波数分别为k1, p, z, k2, p, z, k3, p, z, d2为金膜厚度。
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为了获取合适的各项参量值,保证实验平台设计的合理性和可靠性,利用MATLAB中的GUI设计器,设计了一个参量求取软件进行参量仿真与求解,GUI模块如图 1所示。
经过MATLAB的GUI仿真[11-12],表面等离子体共振海上溢油预警装置采用波长650nm±5nm的光源,其功率为5mW,工作温度-10℃~40℃。选用金膜介电常数ε2=-12.2275+1.05i[13],棱镜与传感玻片采用相同材质的ZF13重火石玻璃,其介电常数ε0=ε1=1.78472[14]。
表面等离子体共振海上溢油预警实验装置设计
Design of experimental device of marine oil spill warning based on surface plasmon resonance
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摘要: 为了实现对早期、小规模溢油检测及预警, 采用对外界介质折射率微小变化敏感的表面等离子体共振传感技术, 设计搭建了一套小型溢油检测实验装置, 创建了一个基于表面等离子体共振设计的GUI界面用于选取传感参量, 并通过C++编译了一套具有数据采集、存储、处理以及显示功能的软件用于数据处理以及提前预警, 进行了理论分析和实验验证, 取得了折射率为1.4451, 1.4774, 1.5299的原油样品的表面等离子体共振响应数据。结果表明, 实验数据与仿真结果相符, 该装置可用于海上溢油检测实验研究, 其软件设计满足预警需求。这一结果对海上溢油检测是有帮助的。Abstract: In order to realize the early and small-scale oil spill detection and warning, surface plasmon resonance (SPR) sensing technology, which was sensitive to small changes in refractive index of external media, was used. A set of small oil spill detection experimental device was designed and built. A GUI interface based on SPR was created to select sensing parameters. A set of software with functions of data acquisition, storage, processing and display was compiled by C++ for data processing and early warning. The theoretical analysis and experimental verification were carried out. SPR data of crude oil samples with refractive index of 1.4451, 1.4774 and 1.5299 were obtained. The results show that the experimental data are in agreement with the simulation results. The device can be used in the experimental study of oil spill detection at sea. Its software design meets the needs of early warning. This result is helpful to the detection of oil spill at sea.
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