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共振光隧穿效应(ROTE)是在光学隧穿效应[12](受抑全内反射)的基础上提出来的一种新型的光学现象。光学隧穿效应是指光线从高折射率层照射到低折射率层,并且入射角大于临界角时,在界面处会发生全反射,当低折射率层的厚度足够小(小于入射光波长)时,光线将穿过低折射率层,即穿过经典几何光学中光线不能穿过的“壁垒”,形成透射(隧穿光线)。而共振光隧穿效应是在满足光学隧穿效应的前提下,促使隧穿光线在微米级的谐振腔中形成共振的一种光学效应[13-14]。
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基于ROTE的加速度传感器结构如图 1所示。包括中间的圆柱形质量块和两根弹性悬臂梁与外边框相连。传感元件采用ROTE结构,如图 2所示。包含在中间的圆形质量块中。通过仿真分析,圆柱形质量块的半径设为0.775mm,其高度定为0.1mm,并根据仿真结果设计悬臂梁和外边框的几何尺寸。另外,关于传感元件ROTE结构的模型参量如表 1所示。表 1中, dλ和gλ均被量化为入射光中心波长的倍数。
Table 1. Parameters of ROTE model[14]
parameters symbols values s polarizer p polarizer static incident angle θ 22.5884° 22.5884° tunneling gap dλ 1.4700 1.4700 width of resonant cavity gλ 10.0023 10.0790 refractive index of input and output space n1 3.420 3.420 refractive index of resonant cavity n1 3.420 3.420 refractive index of tunneling gap n2 1.000 1.000 该加速度计可以通过标准硅微加工技术集成在硅片上,利用深反应离子刻蚀技术[15]可以使传感器每一部分的尺寸达到相对高的精度。并且通过热氧化法[16]、激光改进技术[17]、氢退火技术[18]等方法可以降低质量块的外表面和隧穿层的侧壁粗糙度。通过以上分析,确定了加速度计器件设计的可行性。
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根据仿真结果,宽谱光源与水平方向的夹角设定为β=105°。当一个垂直的面内加速度作用到传感器上时,惯性力会促使中心质量块相对于外边框产生一个向上或向下的位移量,如图 3所示。以图 3a为例,入射光在质量块外表面发生折射后,将在输入层和第1层隧穿层的分界面产生初始入射角α0。当受到朝上的加速度作用时,中心质量块会产生向上的位移ΔH,由于光源位置不变,所以入射角由α0变为α1。同理,当加速度方向向下时,中心质量块会产生向下的位移ΔH,入射角由α1变为α0。由几何关系得到位移量ΔH与入射角(包括α0, α1)满足以下关系式:
$ \begin{align} & \Delta H\text{=}R\left( \sin {{\gamma }_{0}}-\sin {{\gamma }_{1}} \right)+R\cdot \\ & \tan \left( \text{ }\pi\text{ -}\beta \right)\cdot \left( \cos {{\gamma }_{0}}-\cos {{\gamma }_{1}} \right) \\ \end{align} $
(1) $ {{\alpha }_{0}}={{\gamma }_{0}}-\frac{\text{ }\!\!\pi\!\!\text{ }}{2}-\arcsin \left[ \frac{\sin \left( {{\gamma }_{0}}-\beta \right)}{{{n}_{\text{Si}}}} \right] $
(2) $ {{\alpha }_{1}}={{\gamma }_{1}}-\frac{\text{ }\!\!\pi\!\!\text{ }}{2}-\arcsin \left[ \frac{\sin \left( {{\gamma }_{1}}-\beta \right)}{{{n}_{\text{Si}}}} \right] $
(3) 式中,R(775μm)为圆形质量块的半径,γ0和γ1均是入射光经过圆形块外表面时的法线与水平x轴的夹角。由此可以发现,当质量块产生面内的位移量时,入射光在质量块的外表面发生折射后,进入到质量块中的光透射强度T也会发生改变,以此可以实现加速度传感。
图 4描述的是不同偏振态下透射光强度与中心质量块相对位移的关系。图中C点和D点分别对应s偏振和p偏振下的初始透射光强度。比较两曲线容易发现,s偏振光的陡峭程度要比p偏振光大得多,即s偏振光对于位移变化更加敏感,因此,该传感器在s偏振光的条件下将会有更优秀的表现。另外,法布里-珀罗(Fabry-Pérot,F-P)谐振腔作为经典的光学模型,其随位移变化的透射曲线也被绘制在图 4中。其中棱镜反射率设为95%,入射角设为3.335°,根据表 1中的参量,F-P谐振腔的腔长设置为12.94λ (λ为入射光的中心波长),基本等于ROTE模型的有效腔长。相比较而言,基于ROTE的传感器具有更高的灵敏度。另外,F-P谐振腔已经被证实具有小于5nm的位移分辨率[19],所以基于ROTE的s偏振光加速度计有望实现更高精度的测量。
基于共振光隧穿效应的加速度传感器
Acceleration sensors based on resonant optical tunneling effect
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摘要: 为了设计新型的加速度传感器,将共振光隧穿结构应用于传感元件,利用COMSOL软件对传感器的频率响应、灵敏度性能等关键要素进行了模拟仿真分析,搭建了实验平台,验证了共振光隧穿原理。结果表明,基于共振光隧穿效应结构的加速传感器在100Hz~3000Hz范围内、加速度为500m/s2的情况下,灵敏度可达到6.7dB/g。该传感器小巧轻便、结构简单,且具有较高的灵敏度,这为光学传感器的研究提供了新的方法和思路,具有广阔的应用前景。Abstract: In order to design a new acceleration sensor, resonant optical tunneling effect(ROTE) structure was applied to design the optical sensor. The key factors, such as frequency response and sensitivity performance of the sensor, were simulated and analyzed by using COMSOL software. The experimental platform was built to verify the principle of resonant optical tunneling effect. The results show that the sensitivity of ROTE acceleration sensor is 6.7dB/g when acceleration is 500m/s2 in the range of 100 Hz to 3000Hz. The sensor is deft, simple and has high sensitivity. The study provides a new idea and method for optical sensor and has broad application prospects.
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Table 1. Parameters of ROTE model[14]
parameters symbols values s polarizer p polarizer static incident angle θ 22.5884° 22.5884° tunneling gap dλ 1.4700 1.4700 width of resonant cavity gλ 10.0023 10.0790 refractive index of input and output space n1 3.420 3.420 refractive index of resonant cavity n1 3.420 3.420 refractive index of tunneling gap n2 1.000 1.000 -
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