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长周期光纤光栅由周期性的折射率调制组成, 光在LPFG中发生模式耦合。根据模式耦合原理,LPFG采用前向传输的纤芯基模同各阶包层膜间耦合的方式,其满足相位匹配条件为[14]:
$ \beta_{\mathrm{co}}-\beta_{\mathrm{cl}, m}=2 \mathsf{π} / \mathit{\Lambda} $
(1) $ \beta=2 \mathsf{π} n_{\text {eff }} / \lambda $
(2) 式中,βco是纤芯基模的传播常数;βcl, m为m阶包层模的传播常数;β为传播常数,neff为有效折射率;λ为波长。
由(1)式、(2)式得到LPFG的谐振波长为:
$ \lambda_{0, m}=\left(n_{\mathrm{co}}-n_{\mathrm{cl}, m}\right) \mathit{\Lambda} $
(3) 式中,nco为纤芯基模有效折射率;ncl, m为m阶包层膜有效折射率;λ0, m为m阶谐振波长。nco同纤芯、包层折射率和纤芯半径有关; ncl, m同纤芯、包层、外界折射率和包层半径有关,且与外界折射率具有非线性关系。
应力和温度使LPFG的有效折射率发生改变。应力影响谐振峰波长是由纤芯和包层弹光系数决定的, 而温度影响谐振峰波长是由纤芯和包层热光系数决定的[19]。
LPFG透射的中心波长λ0的变化可以表示为:
$ \Delta \lambda_0 / \lambda_0=K_{\varepsilon} \Delta \varepsilon+K_T \Delta T $
(4) 式中, Kε为应变灵敏度,KT为温度灵敏度,ε为应变,T为温度。
当温度保持恒定时,透射中心波长只跟应力有关。
当LPFG两端存在应变ε时,可以得到LPFG的Kε为:
$ K_{\varepsilon}=\mathrm{d} \lambda / \mathrm{d} \varepsilon=\left(p_{\mathrm{cl}} n_{\mathrm{cl}, m}-p_{\mathrm{co}} n_{\mathrm{co}}\right) \mathit{\Lambda} $
(5) 式中, pco和pcl是纤芯和包层弹光系数。
随着LPFG浸入在溶液中,其所受应变力为:
$ F=\rho g V $
(6) $ \sigma=F / S=E \varepsilon $
(7) 式中, ρ为液体密度,g为重力加速度,V为体积,F为LPFG的受力,σ为LPFG的应力,S为光纤截面积,E为杨氏模量[19]。
光栅的透射中心波长的变化量为:
$ \Delta \lambda_0=k \lambda_0 \Delta l $
(8) 式中, k=Kερg/E,Δl为LPFG浸入液体中的长度变化量。
LPFG的透射光谱由一系列以纤芯-包层模式耦合波长为中心的衰减带组成。透射功率最小值和衰减带宽度由纤芯、包层和光纤光栅的长度间的耦合效率决定。透射功率的最小值与LPFG的长度有关[16]:
$ T(L)=\sin ^2(\kappa L) $
(9) 式中, L是LPFG的长度,κ是耦合系数。LPFG衰减带的中心波长的折射率灵敏度来源于包层模式的有效折射率与周围材料的折射率。基于波长的变化和LPFG光谱中衰减带的最小透射值的变化,LPFG可以作为折射率传感器使用。当一个LPFG部分浸入液体中时,它可以被认为是两个独立的光纤光栅处于外界环境为空气和液体中。对于每个包层模式,透射光谱将包含两个衰减带,其中衰减带A的中心位于空气接口影响下的芯模与包层模式的耦合波长处,衰减带B的中心位于液体影响下的芯模与相同包层模式的耦合波长处。两个光栅的有效长度由液体的高度决定,光谱中衰减带的最小透射值和宽度取决于液体的高度。通过(9)式,对于一个长度为L的LPFG,它可以展示出衰减带A和B的最小透射值与长周期光纤光栅浸入在液体中长度的相关性,并由相关公式表示出来:
$ T_{\mathrm{A}}(l, L) \propto \sin ^2[(\mathsf{π} / 2) l / L] $
(10) $ T_{\mathrm{B}}(l, L) \propto \sin ^2[(\mathsf{π} / 2)(L-l) / L] $
(11) 式中, l为LPFG浸入液体中的长度, 0 < l < L[20]。
为验证使用LZM-110M制作LPFG这种方法是否有效,利用MATLAB对LPFG的透射光谱进行仿真,仿真结果会出现不同阶次的波峰,现只对波长在1540 nm~1620 nm范围内的一个波峰进行观察,当传感器完全置于空气中时,其透射光谱的谱型如图 4a所示[21],只显示单个波峰,波峰位置在1586 nm。利用(10)式进行不同液位条件下的LPFG的透射功率的变化趋势仿真分析,如图 4b所示。由仿真结果可以看出, 液位l的变化对透射光谱产生影响。随着l的增大,衰减带A的透射值逐渐增大,其所对应的变化趋势如图 4b所示。
基于长周期光纤光栅的光纤液位传感器
Optical fiber liquid level sensor based on long period fiber grating
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摘要: 为了测量液位在警戒值附近变化的情况, 采用新款光纤熔接机制作了一种基于锥形结构的长周期光纤光栅测量液位的光纤传感器, 对传感器进行了理论分析, 搭建了液位传感实验系统, 根据传感器对外界环境的折射率灵敏度, 测量浸没在液体中的光纤长度。结果表明, 在0 mm~12 mm的液位测量范围内, 光纤液位传感器的峰值波长灵敏度和透射功率灵敏度分别是0.700 nm/mm和1.377 dB/nm。该传感器对液位变化测量较为准确, 且采用刻栅方式可有效解决传统长周期光纤光栅中存在的非对称模耦合和偏振依赖性高等问题, 同时具有制作简单、成本低和应用前景广泛等优点。Abstract: In order to measure the change of liquid level near the warning value, a new optical fiber fusion splicer was used to fabricate a fiber optic sensor for measuring liquid level based on long-period fiber grating with tapered structure. The refractive index sensitivity of the liquid level sensing experimental system was built to measure the length of the optical fiber immersed in the liquid. The results show that in the liquid level measurement range of 0 mm~12 mm, the peak wavelength sensitivity and transmission power sensitivity of the optical fiber liquid level sensor were 0.700 nm/mm and 1.377 dB/nm, respectively. The sensor is more accurate in measuring the liquid level change, and the grating method mentioned above can effectively solve the problems of asymmetric mode coupling and high polarization dependence in the traditional long-period fiber grating, and it has the advantages of simplicity, low cost and wide application prospects.
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