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铌酸锂晶体电场传感器的结构如图1所示,由起偏器、检偏器、1/4波片、铌酸锂晶体组成。起偏器和检偏器的中心轴与铌酸锂晶体的通光方向(晶体光轴为z轴)在同一条直线上,外加电场方向沿铌酸锂晶体y轴,起偏器与检偏器透射光的偏振方向分别与铌酸锂晶体的y轴成45°和−45°。
通过起偏器的光变为线偏振光入射到1/4波片变为圆偏振光,沿z轴入射到晶体中正交分解为沿晶体x轴和y轴振动的两束线偏振光。当外加电场方向与晶体y轴平行时,根据铌酸锂晶体的线性电光效应,铌酸锂晶体x轴和y轴的折射率分别为:
$$ \begin{gathered} n_x' \approx {n_o} + \frac{1}{2}{\gamma _{22}}n_o^3{E_{int}} \\ n_y' \approx {n_o} - \frac{1}{2}{\gamma _{22}}n_o^3{E_{int}} \\ \end{gathered} $$ (1) 式中:γ22为电光系数;no为寻常光的折射率。光通过铌酸锂晶体后产生的相位差为:
$$ \varphi (E) = \frac{{2{\text{π }}}}{{{\lambda _0}}}{\gamma _{22}}n_o^3L{E_{int}} $$ (2) 式中:Eint为晶体内部电场强度;λ0为光的中心波长;L为晶体长度。经电场调制后从铌酸锂晶体中输出的光变化为椭圆偏振光。检偏器将光的偏振态变化转换为光强的变化。铌酸锂晶体电场传感器输出光功率Pout为[15]:
$$ {P_{out}}{\text{ = }}\frac{{{P_{in}}}}{{2\alpha }}\left\{ {1 - b\cos \left[ {{\varphi _0} + \varphi \left( E \right)} \right]} \right\} $$ (3) 式中:Pin为输入光功率;α为传感器光路损耗系数;b为传感器整体消光比;φ0为传感器静态工作点。将公式(2)代入公式(3)中得出:
$$ {P_{out}} = \frac{{{P_{in}}}}{{2\alpha }}\left[ {1 - b\cos \left( {{\varphi _0} + \frac{{2{\text{π }}}}{{{\lambda _0}}}{\gamma _{22}}n_o^3L{E_{int}}} \right)} \right] $$ (4) 因传感器中有1/4波片,令公式(4)中φ0=π/2,将传感器的静态工作点调制到线性工作区域。因2πγ22
$n_o^3 L $ /λ0<<1,所以传感器输出光功率表示为:$$ \begin{gathered} {P_{out}} = \frac{{{P_{in}}}}{{2\alpha }}\left[ {1 + b\sin \left( {\frac{{2{\text{π }}}}{{{\lambda _0}}}{\gamma _{22}}n_o^3L{E_{int}}} \right)} \right] \approx \\ \frac{{{P_{in}}}}{{2\alpha }}\left( {1 + \frac{{2b{\text{π }}}}{{{\lambda _0}}}{\gamma _{22}}n_o^3L{E_{int}}} \right) \\ \end{gathered} $$ (5) 因此,从公式(5)中可以得出传感器输出光功率与晶体内部电场强度成线性关系。
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传感器系统如图2所示,由激光源、铌酸锂晶体电场传感器、光电探测器(Photodetector, PD)、示波器组成。激光源输出的光经通过单模光纤(Single Mode Fiber, SMF)经准直器传输进电场传感器中,因铌酸晶体的线性电光效应,铌酸锂晶体受到外界电场的调制内部传输光的偏振态发生变化。当光通过检偏器时偏振态变化转换为光强度的变化,由准直器将光耦合进SMF传输到光电探测器中,使光强的变化转化为电压的变换。电压信号经射频线传输到示波器中进行信号提取。
传感器系统的输出电压信号Vout为:
$$ {V_{out}} \approx \frac{{A{P_{in}}}}{{2\alpha }}\left( {1 + \frac{{2b{\text{π }}}}{{{\lambda _0}}}{\gamma _{22}}n_o^3L{E_{int}}} \right) $$ (6) 式中:A为光电探测器的电光转换系数。但铌酸锂晶体放置于电场中时,铌酸锂晶体表面会因极化效应产生极化电荷进而形成极化电场Ep[19],且极化电场方向与外加电场方向相反,则晶体内部电场强度可表示为:
$$ \begin{gathered} {E_{int}} = {E_{ext}} - {E_p} = {E_{ext}} - {N_j}{\chi _j}{E_{int}} \\ \end{gathered} $$ (7) 式中:χj为铌酸锂晶体的电极化率;Nj为铌酸锂晶体的极化因子值在0~1之间。由公式(7)可将晶体内外电场比值m可表示为:
$$ m = \frac{{{E_{int}}}}{{{E_{ext}}}} = \frac{1}{{1 + {N_j}{\chi _j}}} $$ (8) 将公式(8)代入到公式(6)中,传感器系统的输出电压信号可写为:
$$ {V_{out}} \approx \frac{{A{P_{in}}}}{{2\alpha }}\left( {1 + \frac{{2b{\text{π }}}}{{{\lambda _0}\left( {1 + {N_j}{\chi _j}} \right)}}{\gamma _{22}}n_o^3L{E_{ext}}} \right) $$ (9) 由公式(9)可将传感器的灵敏度定义为:
$$ S = \frac{{Ab{P_{in}}{\text{π }}}}{{\left( {1 + {N_j}{\chi _j}} \right)\alpha {\lambda _0}}}{\gamma _{22}}n_o^3L $$ (10) 由于公式(10)中Nj值与晶体的几何尺寸相关,理论上当沿外加电场方向即图1中沿y方向的晶体尺寸足够大,同时晶体横截面上沿电场垂直方向即沿图1中沿x轴方向的晶体尺寸足够小时,Nj≈0[19]。此时,由公式(10)可得在晶体长度及其他参数一定的条件下,电场传感器的灵敏度最高。因此,可以通过增加与外加电场平行方向上的晶体尺寸同时减少晶体横截面上与外加电场垂直方向上的晶体尺寸来提高传感器的灵敏度。为此,文中通过仿真并设计制作宽度和厚度不同尺寸的铌酸锂晶体,进一步分析晶体几何尺寸对传感器灵敏度的影响。
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使用 COMSOL Multiphysics仿真软件建立铌酸锂晶体三维仿真模型如图3(a)所示,平行铜板尺寸为350 mm×350 mm×3 mm,间距d=70 mm。将平行铜板右极板接电压为U,频率为50 Hz的交流电,平行铜板左极板接地,则在极板间形成E=U/d的均匀电场。设沿外加电场方向即晶体y轴方向为晶体宽度w=6 mm、晶体横截面上沿外加电场垂直方向即晶体x轴方向为晶体厚度h=6 mm、沿晶体z轴方向为晶体长度L=42.2 mm,并将晶体放置在两块平行铜板的中间,极板正极加U=7 kV的电压,负极接地,平行极板间电场强度分布图,如图3(b)所示。从图3(b)可知,使用域点探针测得平行铜板间电场约为100 kV/m的匀强电场,但由于晶体表面的极化电荷形成与外界电场相反的极化电场,使得晶体内部电场小于极板间电场,晶体表面电场大于极板间电场。
图 3 (a) Comsol仿真结构图;(b) 电场强度分布图
Figure 3. (a) Diagram of Comsol simulation structure; (b) Distribution of electric field intensity
因铌酸锂晶体为单轴晶体,晶体y向和x向的相对介电常数相等且不等于z向相对介电常数,所以分别沿晶体的y向与z向施加电场,并在晶体中心位置设置域点探针,监测晶体内部电场强度变化。如图4(a)所示为铌酸锂晶体L=42.2 mm、w=6 mm,当h从3 mm变化到24 mm时,晶体内部电场强度的变化。从图4(a)可得,当h从3 mm增加到15 mm时,沿晶体y向加电场时,晶体内部电场强度从8570.532 V/m减小到1510.808 V/m;沿晶体z向加电场时,晶体内部电场强度从22388.967 V/m减小到4880.695 V/m。h从15 mm减小到3 mm,晶体内部电场强度提高约5.1倍。并且当h大于15 mm时,电场方向分别沿晶体x向和y向时,晶体内部电场强度变化基本都保持在±200 V/m。由此可知晶体内部电场强度随着厚度的增加而减小并趋于恒定。如图4(b)所示为铌酸锂晶体的L=42.2 mm、h=3 mm,当w从3 mm变化到22 mm时,晶体内部电场强度的变化。从图4(b)可知,沿晶体y向加电场时,晶体内部电场强度从2791.959 V/m增加到38387.549 V/m;沿晶体z向加电场时,晶体内部电场强度从8728.079 V/m增加到95247.030 V/m。内部电场强度约提高约12.3倍。由此得出,晶体内部电场强度与宽度成正比关系。如图4(c)所示,当铌酸锂晶体h=3 mm、w=6 mm,当L从15 mm增加55 mm时,从图4(c)可知,沿晶体x向加电场时,晶体内部电场强度变化基本保持±379 V/m;沿晶体z向加电场时,晶体内部电场强度变化基本保持±12608 V/m。L从15 mm增加55 mm,晶体内部电场强度变化幅度仅约为5%。由此可得晶体长度对晶体内部电场强度的影响较小。综上所述,晶体内部电场强度主要受晶体的厚度和宽度影响。因晶体长度对晶体内部电场的影响较小,所以设置三块长度相同,厚度和宽度不同的晶体来仿真内部电场随外部电场的变化规律。如图4(d)所示,当晶体y轴沿电场方向,右极板上电压从2 kV增加到20 kV,即极板间电场强度从28.571 kV/m增加到285.714 kV/m时,晶体内部电场强度变化与外界电场强度成正比。三种尺寸晶体的内外电场之比分别为0.028、0.090和0.030。分别对比三种尺寸的内外电场比值,尺寸为3 mm×6 mm×42.2 mm的内外电场强度之比是晶体尺寸为3 mm×3 mm×42.2 mm和6 mm×6 mm×42.2 mm的3倍。由此得出晶体越宽越薄,其晶体内部电场强度越高。将三种尺寸下内外电场之比分别代入到公式(10),同时考虑到传感器实验系统中的A=687.936 mV/mW,Pin=2.5 mW,α=1,b=1,γ22= 6.81×10−12 m/V,no=2.212,计算三只传感器的灵敏度分别为0.304、0.976、0.325 mV/(kV·m−1)。因此,在晶体长度一定时,晶体宽度尺寸越大,厚度尺寸越小,其传感器灵敏度越高。
Analysis of influence of lithium niobate crystal structure on sensitivity of electric field sensors
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摘要: 铌酸锂晶体光学电场传感器为全介质结构,具有宽带宽、对被测电场干扰小的优点,但其灵敏度较低。因此,分析了晶体几何尺寸对传感器灵敏度的影响机理,得出通过增加沿外加电场方向的晶体尺寸同时减少晶体横截面上沿外加电场垂直方向的晶体尺寸来提高传感器的灵敏度。使用COMSOL仿真分析了铌酸锂晶体不同厚度、宽度、长度对晶体内部电场强度的影响,得出晶体厚度从15 mm减小到3 mm和宽度从3 mm增加到22 mm时,晶体内部电场强度分别提高约5.1倍和12.3倍;晶体长度从15 mm变化到55 mm时,晶体内部的电场强度变化仅约为5%。设计并研制出晶体尺寸分别为3 mm×3 mm×42.2 mm (x×y×z),3 mm×6 mm×42.2 mm (x×y×z),6 mm×6 mm×42.2 mm(x×y×z)的三只铌酸锂晶体电场传感器,并搭建工频电场测试平台,测试得出三只电场传感器的灵敏度分别为0.243 mV/(kV·m−1)、0.758 mV/(kV·m−1)、0.150 mV/(kV·m−1)。当晶体厚度和长度一定且晶体宽度从3 mm增加到6 mm时,传感器灵敏度提高3倍。当晶体宽度和长度一定且晶体厚度从6 mm减小到3 mm时,传感器灵敏度提高5倍。结合仿真与实验结果得出:在晶体长度一定时,可以通过设计使用宽度更宽、厚度更薄的晶体,研制出高灵敏度的电场传感器。Abstract: The lithium niobate crystal optical electric field sensor has the advantages of wide bandwidth and negligible interference to the original electric field due to its all-dielectric structure. But it has low sensitivity to measure the electric field. The influence mechanism of crystal geometry size on sensor sensitivity is analyzed. The sensitivity of the sensor is improved by increasing the crystal size along the direction of the applied electric field and reducing the crystal size along the vertical direction of the applied electric field on the crystal cross-section. The influence of different thickness, width and length of the crystal on the internal electric field intensity has been analyzed using COMSOL simulation, and it is concluded that the internal electric field intensity of the crystal increases by about 5.1 times and 12.3 times when the thickness decreases from 15 mm to 3 mm and the width of the crystal increases from 3 mm to 22 mm, respectively. When the length of the crystal increases from 15 mm to 55 mm, the internal electric field intensity of the crystal changes by only about 5%. Three lithium niobate crystal electric field sensors with crystal sizes of 3 mm×3 mm×42.2 mm (x×y×z), 3 mm×6 mm×42.2 mm (x×y×z) and 6 mm×6 mm×42.2 mm (x×y×z) have been designed and developed, the sensitivities are 0.243 mV/(kV·m−1), 0.758 mV/(kV·m−1), 0.150 mV/(kV·m−1), respectively. When thickness and length of the crystal are constant, the sensor sensitivity is increased 3 times with the crystal width increased from 3 mm to 6 mm. When width and length of the crystal are constant, the sensor sensitivity is increased 5 times with the crystal thickness decreased from 6 mm to 3 mm. Combining the simulation and experimental results, it is concluded that a higher sensitivity electric field sensor can be developed by designing the crystal with wider width and thinner thickness under a certain crystal length.
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Key words:
- optical engineering /
- electric field sensor /
- crystal structure /
- lithium niobate crystal /
- sensitivity
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