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水下目标发出或反射声波,在传感器周围形成声场变化,声场的变化引起水压的变化,光纤声压传感器通过感知水压变化来获取水声信号。将DC-PCF传感器沉浸在一定深度的海水中,四周环绕的海水会对光纤产生均匀径向压力,此时不存在切向应力[14],如图 1所示。
非耦合型DC-PCF传感器类似于全光纤马赫-曾德尔干涉仪[15],双干涉臂在一根光纤中,单根光纤实现传输与干涉。因两纤芯的传播常数不同,导致出射端双芯有明显相位差,使得光纤出射端干涉透射谱波谷波长发生平移。
自由光谱宽度(free spectral range,FSR)是声压传感器主要性能参量之一,即干涉透射谱的周期,代表着梳状透射谱在一定谱宽下的疏密程度,适当的自由光谱宽度可便于传感信息的读取[16]。
$ R_{\mathrm{FSR}}=\frac{\lambda^{2}}{L \Delta n_{\mathrm{eff}}} $
(1) 由上式可知,器件的自由光谱宽度RFSR与波长λ的平方成正比,与双芯传感臂长度L和双芯有效折射率差Δneff呈反比。通过调整双芯光纤长度和双芯结构参量,改变有效折射率差的变化,最终获得合适的FSR。
利用COMSOL模拟声压加载DC-PCF的受压形变情况,计算DC-PCF存在应力下折射率的改变量,在电磁波频域模块中求得DC-PCF对应有效折射率。在DC-PCF长度已知的情况下,结合均匀径向压力作用下的有效折射率差,可计算双芯传感部分的相位改变量,代入干涉透射谱表达式中计算特定压力下的传输透射谱,再用波谷的波长移动量与光纤所加载的静压力的比值求得DC-PCF的压力传感灵敏度。
$ \begin{aligned} \frac{\Delta \lambda_{p}}{p} =\frac{\lambda_{p}-\lambda_{0}}{p} \end{aligned} $
(2) $ \Delta \lambda_{p} =\frac{\lambda_{p}}{\Delta \lambda} \Delta R_{\mathrm{FSR}} $
(3) 式中,Δλp为某一波谷在压力p作用后的移动量,λ0为波谷移动前的位置,λp为波谷移动后的位置。ΔRFSR为自由光谱宽度在压力p作用后的改变量, Δλ为波长的改变量。
在施加应变后,根据弹性力学原理,分别求取DC-PCF的有效折射率差和长度的改变量,可导出波谷移动量与应力及光纤材料的本质作用关系:
$ \begin{array}{c} \delta_{\lambda}=\left(1+P_{\text {eff }}\right) \varepsilon \lambda \end{array} $
(4) $ P_{\text {eff }}=\left(P_{\text {eff }, 1} n_{\text {eff }, 1}-P_{\text {eff }, 2} n_{\text {eff }, 2}\right) / \Delta n_{\text {eff }} $
(5) 式中,δλ为应变作用后波长移动量,ε为应变大小, Peff, 1和Peff, 2分别为两个纤芯的基模有效折射率弹光系数,neff, 1和neff, 2分别为两个纤芯的有效折射率。由此可知,若双芯结构和材料确定情况下,Peff为定值。波长移动量与应变呈线性关系。
掺杂型双芯光子晶体光纤高灵敏声压传感结构
Design of doped double-core photonic crystal fiber sound pressure sensor with high sensitivity
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摘要: 为了解决石英材料高杨氏模量对光纤传感器均匀径向上灵敏度提升的限制,提出一种掺杂型双芯光子晶体光纤传感结构。该设计将圆形空气孔分列在光纤包层上,构成六边形晶格,在其单侧空气孔环绕的基材区域掺入聚甲基丙烯酸甲酯材料。利用COMSOL分析了均匀应力作用下光纤截面参量对声压灵敏度的影响,得到最优参量匹配结构。结果表明, kPa量级的声压作用下,自由光谱宽度约13nm; MPa量级的声压作用下,自由光谱宽度约2.5465nm, 在1550μm波段下,x偏振声压灵敏度达0.15942nm/kPa; 相比Saganc光子晶体光纤压力传感器,传感尺寸小,均匀径向灵敏度提高了46.6倍。该研究对下一代水下声压传感器的设计有帮助。Abstract: In order to break the limitation of high Young's modulus of quartz material on the sensitivity improvement of fiber optic sensor in uniform radial direction, a doped double-core photonic crystal fiber sensing structure was proposed. The circular air holes were arranged on the fiber cladding to form hexagonal lattice. Polymethyl methacrylate was doped into the base-material area surrounded by the air holes on one side of the double-core photonic crystal fiber. The influence of cross-section parameters on sound pressure sensitivity under uniform stress was analyzed by COMSOL and the optimal structure was obtained. At the kPa level, the free spectral width is about 13nm. At the MPa level, the free spectral width is about 2.5465nm. The results show that the sensitivity of x polarized sound pressure is 0.15942nm/kPa at 1550μm. Compared with the Sagnac PCF pressure sensor, the size of this sensor is smaller, and the sensitivity at uniform radial direction is increased about 46.6 times. This work contributes to the design of the next generation underwater sound pressure sensor.
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