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当PCF施加压力后,PCF横截面将会发生几何形变,产生各向异性的应力分布。同时,由于弹光效应的存在,将会改变原有的折射率,并改变相位模式双折射。
当PCF静态时,模式双折射为:
$ B_{0}=\left|n_{\mathrm{eff}, x}-n_{\mathrm{eff}, y}\right| $
(1) 式中,neff, x和neff, y为两个正交偏振模式的有效折射率,可由COMSOL仿真得到。
当PCF施加压力后,通过COMSOL可得到PCF横截面的应力分布和几何形变。此时,空气孔折射率不发生改变,SiO2折射率由下式决定:
$ \left\{\begin{array}{l}{n_{x}=n_{0}+C_{1} \sigma_{x}+C_{2}\left(\sigma_{y}+\sigma_{z}\right)} \\ {n_{y}=n_{0}+C_{1} \sigma_{y}+C_{2}\left(\sigma_{x}+\sigma_{z}\right)} \\ {n_{z}=n_{0}+C_{1} \sigma_{z}+C_{2}\left(\sigma_{x}+\sigma_{y}\right)}\end{array}\right. $
(2) 式中,弹光系数C1和C2与波长没有关系,C1=6.5×10-13m2/N,C2=4.2×10-12m2/N。聚碳酸脂[11]的弹性模量E=2.412GPa,泊松比ν=0.37,弹光系数C1=2.45×10-11m2/N,C2=9.38×10-11m2/N。
在COMSOL仿真时,通过(2)式将结构力学中的应力分布转化为PCF材料施加压力后的折射率输入到电磁波频域中,即可得到施加压力后两个正交偏振基模的有效折射率,再根据(1)式可得出施加压力后的相位模式双折射为:
$ B_{p}=\left|n_{\mathrm{eff}, x, p}-n_{\mathrm{eff}, y, p}\right| $
(3) 式中,neff, x, p和neff, y, p为施加压力后的两个正交偏振基模有效折射率。
通过静态时相位模式双折射B0和施加压力后得到的相位模式双折射Bp可得到相位模式双折射B。相位模式双折射灵敏度为:
$ \frac{\Delta B}{\Delta p}=\frac{B_{p}-B_{0}}{p} $
(4) 式中,p为外部施加的压力, ΔB表示双折射的变量,Δp表示压力变化量。可得到压力偏振相位灵敏度为:
$ K_{p}=\frac{2 \pi}{\lambda}\left(\frac{\Delta B}{\Delta p}+B l_{p}\right) $
(5) 式中,λ为曲空间波长,在测量横向压力时,压力诱导PCF的轴向伸长lp是很小的,且相位模式双折射B也很小,因此在计算(5)式中的第2项时,可以忽略轴向伸长lp对偏振相位灵敏度的影响,整理(5)式得:
$ K_{p}=\frac{2 {\rm{ \mathsf{ π} }}}{\lambda} \frac{\Delta B}{\Delta p} $
(6)
光子晶体光纤高灵敏度压力传感特性研究
Study on high sensitivity pressure sensing characteristics of photonic crystal fiber
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摘要: 为了提高压力传感器的灵敏度,利用光子晶体光纤理论及其高双折射特性和可灵活设计的结构特点,设计了一种新型边孔高双折射光子晶体光纤压力传感结构。采用全矢量有限元法并结合COMSOL软件对传感结构的受力和模场分布进行仿真分析,获得压力传感特性随几何结构和自由空间波长的变化关系,通过优化设计得到最优结构参量,进一步获得高压力灵敏度。结果表明,在最优结构下,自由空间波长为1.55μm、压力为200MPa时,偏振相位灵敏度为166.2rad/(MPa·m),所能施加的最大压力为720MPa,相位模式双折射灵敏度保持在4.1×10-5MPa-1左右。该研究对提高压力传感器的灵敏度是有帮助的。Abstract: In order to improve the sensitivity of a pressure sensor, a novel pressure sensing structure of photonic crystal fiber with side hole and high birefringence was designed, based on the theory of photonic crystal fiber and its high birefringence and flexible design structure. The force and mode field distribution of sensing structure were simulated and analyzed by using full vector finite element method and COMSOL software. The dependence of pressure sensing characteristics on geometrical structure and free space wavelength was obtained. The optimum structural parameters were obtained by optimum design. The high pressure sensitivity was further obtained. The results show that, under the optimal structure, when free space wavelength is 1.55μm and pressure is 200MPa, polarization phase sensitivity is 166.2rad/(MPa·m) and maximum pressure that can be applied is 720MPa. The sensitivity of phase mode birefringence is maintained at about 4.1×10-5MPa-1. The research is helpful to improve the sensitivity of pressure sensors.
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