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图 1为紫外准分子激光经过相位掩模板照射在待刻光纤上。沿掩模板的平行和法线方向分别建立x轴和z轴,沿光纤的平行和法线方向分别建立s轴和t轴。激光的发散(会聚)角为Δθ;激光束整体与掩模板的夹角为θ0; 光纤与掩模板的夹角为φ0; 激光的波矢为KUV,掩模板的光栅波矢为G,掩模板后第m级次衍射光波矢为Km。
理想情况下,激光束平行,并与掩模板垂直,此时:
$ {\mathit{\boldsymbol{K}}_{_{{\rm{UV}}}}}{\rm{ = (}}{\mathit{K}_{_{{\rm{UV}}}}}{\rm{, 0, 0) = }}\left( {\frac{{{\rm{2 \mathit{ π} }}}}{\mathit{\lambda }}{\rm{, 0, 0}}} \right) $
(1) $ \mathit{\boldsymbol{G}}{\rm{ = (}}\mathit{G}{\rm{, 0, 0) = }}\left( {\frac{{{\rm{2 \mathit{ π} }}}}{\mathit{\Lambda }}{\rm{, 0, 0 }}} \right) $
(2) $ \left| {{\mathit{\boldsymbol{K}}_\mathit{m}}} \right|{\rm{ = }}\left| {{\mathit{\boldsymbol{K}}_{_{{\rm{UV}}}}}} \right| $
(3) $ \left( {{\mathit{\boldsymbol{K}}_\mathit{m}} - {\mathit{\boldsymbol{K}}_{_{{\rm{UV}}}}} - \mathit{m}\mathit{\boldsymbol{G}}} \right) \times \mathit{z}{\rm{ = 0}} $
(4) 式中,λ为紫外准分子激光的波长;Λ为占空比是0.5的相位掩模板周期。由(1)式~(4)式可得:
$ {\mathit{\boldsymbol{K}}_\mathit{m}}{\rm{ = [}}\mathit{mG}{\rm{,0,}}\sqrt {{\mathit{K}_{{\rm{UV}}}}^{\rm{2}}{\rm{ - (}}\mathit{mG}{{\rm{)}}^{\rm{2}}}} {\rm{]}} $
(5) 实际情况中,紫外准分子激光存在发散或会聚情况,与掩模板并不垂直。由此,(1)式中KUV修正为:
$ {\mathit{\boldsymbol{K}}_{{\rm{UV}}}}{\rm{ = [}}{\mathit{K}_{{\rm{UV}}}}{\rm{sin}}\left( {{\mathit{\theta }_{\rm{0}}}{\rm{ + }}\mathit{\theta }} \right){\rm{, }}{\mathit{K}_{{\rm{UV}}}}{\rm{cos(}}{\mathit{\theta }_{\rm{0}}}{\rm{ + }}\mathit{\theta }{\rm{)]}} $
(6) 式中,θ为区间[-Δθ/2, Δθ/2]内的任意值。从而,(5)式中Km修正为:
$ \begin{array}{c} {\mathit{\boldsymbol{K}}_\mathit{m}} \approx \left[ {\mathit{mG}{\rm{ - }}{\mathit{K}_{{\rm{UV}}}}{\rm{sin(}}{\mathit{\theta }_{\rm{0}}}{\rm{ + }}\mathit{\theta }{\rm{),}}\sqrt {{\mathit{K}_{{\rm{UV}}}}^{\rm{2}}{\rm{ - (}}\mathit{mG}{{\rm{)}}^{\rm{2}}}} {\rm{ + }}} \right.\\ \left. {\frac{{\mathit{mG}{\mathit{K}_{{\rm{UV}}}}{\rm{sin(}}{\mathit{\theta }_{\rm{0}}}{\rm{ + }}\mathit{\theta }{\rm{)}}}}{{\sqrt {{\mathit{K}_{{\rm{UV}}}}^{\rm{2}}{\rm{ - (}}\mathit{mG}{{\rm{)}}^{\rm{2}}}} }}} \right] \end{array} $
(7) 光纤与掩模板并不平行,m阶衍射光Km映射到光纤上,即在s-t坐标轴中,
$ \begin{array}{c} {\mathit{\boldsymbol{K}}_{\mathit{m,s,t}}}{\rm{ = }}\\ \left\{ {{\rm{[}}\mathit{mG}{\rm{ - }}{\mathit{K}_{{\rm{UV}}}}{\rm{sin(}}{\mathit{\theta }_{\rm{0}}}{\rm{ + }}\mathit{\theta }{\rm{)]cos}}{\mathit{\varphi }_{\rm{0}}}{\rm{ - }}} \right.\\ \left[ {\sqrt {{\mathit{K}_{{\rm{UV}}}}^{\rm{2}}{\rm{ - (}}\mathit{mG}{{\rm{)}}^{\rm{2}}}} {\rm{ + }}\frac{{\mathit{mG}{\mathit{K}_{{\rm{UV}}}}{\rm{sin(}}{\mathit{\theta }_{\rm{0}}}{\rm{ + }}\mathit{\theta }{\rm{)}}}}{{\sqrt {{\mathit{K}_{{\rm{UV}}}}^{\rm{2}}{\rm{ - (}}\mathit{mG}{{\rm{)}}^{\rm{2}}}} }}} \right]{\rm{sin}}{\mathit{\varphi }_{\rm{0}}}{\rm{,}}\\ {\rm{[}}\mathit{mG}{\rm{ - }}{\mathit{K}_{{\rm{UV}}}}{\rm{sin(}}{\mathit{\theta }_{\rm{0}}}{\rm{ + }}\mathit{\theta }{\rm{)]sin}}{\mathit{\varphi }_{\rm{0}}}{\rm{ + }}\\ \left. {\left[ {\sqrt {{\mathit{K}_{{\rm{UV}}}}^{\rm{2}}{\rm{ - (}}\mathit{mG}{{\rm{)}}^{\rm{2}}}} {\rm{ + }}\frac{{\mathit{mG}{\mathit{K}_{{\rm{UV}}}}{\rm{sin(}}{\mathit{\theta }_{\rm{0}}}{\rm{ + }}\mathit{\theta }{\rm{)}}}}{{\sqrt {{\mathit{K}_{{\rm{UV}}}}^{\rm{2}}{\rm{ - (}}\mathit{mG}{{\rm{)}}^{\rm{2}}}} }}} \right]{\rm{cos}}{\mathit{\varphi }_{\rm{0}}}} \right\} \end{array} $
(8) 1阶衍射光的光强最大,且在刻栅过程中起主要作用,在此只讨论±1阶衍射光相互干涉情况,干涉光的电场强度为:
$ \begin{array}{c} {\rm{d}}{\mathit{E}_\mathit{\theta }}\left( {\mathit{s}{\rm{, }}\mathit{t}} \right){\rm{ = }}\sqrt {\mathit{f}\left( \mathit{\theta } \right)} \left[ {\sqrt {{\mathit{I}_\mathit{1}}} {\rm{exp(i}}{\mathit{\boldsymbol{K}}_{{\rm{1}}\mathit{, s}}}\mathit{s}} \right){\rm{exp(i}}{\mathit{\boldsymbol{K}}_{{\rm{1, }}\mathit{t}}}\mathit{t}{\rm{) + }}\\ \sqrt {{\mathit{I}_{{\rm{ - 1}}}}} {\rm{exp(i}}{\mathit{\boldsymbol{K}}_{{\rm{ - 1, }}\mathit{s}}}\mathit{s}{\rm{)exp(i}}{\mathit{\boldsymbol{K}}_{{\rm{ - 1, }}\mathit{t}}}\mathit{t}{\rm{)]d}}\mathit{\theta } \end{array} $
(9) 式中,I1和I-1分别为±1阶衍射光的直流光强,跟衍射效率有关,此处假设均为0.5;K1, s和K1, t分别为1阶衍射光波失在s方向和t方向上的分量;K-1, s和K-1, t分别为-1阶衍射光波失在s方向和t方向上的分量;f(θ)为紫外光束在Δθ内呈高斯分布的分布函数,即:
$ \mathit{f}\left( \mathit{\theta } \right){\rm{ = }}\frac{1}{{\sqrt {{\rm{2 \mathit{ π} }}} {\rm{\Delta }}\mathit{\theta }}}{\rm{exp}}\left[ {{\rm{ - }}\frac{{\rm{1}}}{{\rm{2}}}{{\left( {\frac{\mathit{\theta }}{{{\rm{\Delta }}\mathit{\theta }}}} \right)}^{\rm{2}}}} \right] $
(10) 则±1阶衍射光共同作用的干涉光强为:
$ \begin{array}{c} {\mathit{I}_{{\rm{ \pm 1}}}}{\rm{ = }}\frac{{\rm{1}}}{{\rm{2}}}\int_{ - \frac{{{\rm{\Delta }}\mathit{\theta }}}{{\rm{2}}}}^{\frac{{{\rm{\Delta }}\mathit{\theta }}}{{\rm{2}}}} {{\rm{[exp}}\left( {{\rm{i}}{\mathit{\boldsymbol{K}}_{{\rm{1,}}\mathit{s}}}\mathit{s}} \right){\rm{exp(i}}{\mathit{\boldsymbol{K}}_{{\rm{1,}}\mathit{t}}}\mathit{t}{\rm{) + }}} \\ {\rm{exp(i}}{\mathit{\boldsymbol{K}}_{{\rm{ - 1,}}\mathit{s}}}\mathit{s}{\rm{)exp(i}}{\mathit{\boldsymbol{K}}_{{\rm{ - 1,}}\mathit{t}}}\mathit{t}{\rm{)][exp(i}}{\mathit{\boldsymbol{K}}_{{\rm{1}}{\rm{.}}\mathit{s}}}\mathit{s}{\rm{)exp(i}}{\mathit{\boldsymbol{K}}_{{\rm{1,}}\mathit{t}}}\mathit{t}{\rm{) + }}\\ {\rm{exp(i}}{\mathit{\boldsymbol{K}}_{{\rm{ - 1,}}\mathit{s}}}\mathit{s}{\rm{)exp(i}}{\mathit{\boldsymbol{K}}_{{\rm{ - 1,}}\mathit{t}}}\mathit{t}{\rm{)}}{{\rm{]}}^{\rm{*}}}\mathit{f}{\rm{(}}\mathit{\theta }{\rm{)d}}\mathit{\theta } \end{array} $
(11) 将θ看作自变量,采用1阶泰勒函数展开的方法,由(8) 式~(11)式可得:
$ {\mathit{I}_{{\rm{ \pm 1}}}} \approx \frac{{\rm{1}}}{{{\rm{2}}\sqrt {{\rm{2 \mathit{ π} }}} }}\left\{ {\frac{{{\rm{11}}}}{{{\rm{12}}}}{\rm{[2 + cos}}\mathit{D}{\rm{] - cos}}\mathit{D}{\rm{ \times }}\frac{{{\rm{17\Delta }}{\mathit{\theta }^{\rm{2}}}}}{{{\rm{240}}}}} \right\} $
(12) 其中,
$ \begin{array}{c} \mathit{D}{\rm{ = 2}}\mathit{Gs}{\rm{cos}}{\mathit{\varphi }_{\rm{0}}}{\rm{ + 2}}\mathit{tG}{\rm{sin}}{\mathit{\varphi }_{\rm{0}}}{\rm{ - }}\\ \frac{{{\rm{2}}\mathit{Gs}{\mathit{K}_{{\rm{UV}}}}{\mathit{\theta }_{\rm{0}}}\mathit{sin}{\mathit{\varphi }_{\rm{0}}}}}{{\sqrt {{\mathit{K}_{{\rm{UV}}}}^{\rm{2}}{\rm{ - }}{\mathit{G}^{\rm{2}}}} }}{\rm{ + }}\frac{{{\rm{2}}\mathit{Gt}{\mathit{K}_{{\rm{UV}}}}{\mathit{\theta }_{\rm{0}}}{\rm{cos}}{\mathit{\varphi }_{\rm{0}}}}}{{\sqrt {{\mathit{K}_{{\rm{UV}}}}^{\rm{2}}{\rm{ - }}{\mathit{G}^{\rm{2}}}} }} \end{array} $
(13) 由(12)式可知,紫外准分子激光无论是发散或是会聚(Δθ取正值或负值),干涉光强均会减小。
将(13)式中s的系数记为ws,即:
$ {\mathit{w}_\mathit{s}}{\rm{ = 2}}\mathit{G}{\rm{cos}}{\mathit{\varphi }_{\rm{0}}}{\rm{ - }}\frac{{{\rm{2}}\mathit{Gs}{\mathit{K}_{{\rm{UV}}}}{\mathit{\theta }_{\rm{0}}}{\rm{sin}}{\mathit{\varphi }_{\rm{0}}}}}{{\sqrt {{\mathit{K}_{{\rm{UV}}}}^{\rm{2}}{\rm{ - }}{\mathit{G}^{\rm{2}}}} }} $
(14) WFBG的反射波长为:
$ {\mathit{\lambda }_\mathit{b}}{\rm{ = 2}}{\mathit{n}_{{\rm{eff}}}}{\mathit{\Lambda }_{{\rm{ \pm 1}}}}{\rm{ = 2}}{\mathit{n}_{{\rm{eff}}}}\frac{{{\rm{2 \mathit{ π} }}}}{{{\mathit{w}_\mathit{s}}}} $
(15) 式中,neff为纤芯的有效折射率;Λ±1为±1阶衍射光干涉条纹周期。
由(14) 式、(15)式可知,随着掩模板与光纤的夹角变大(φ0小角度变大),WFBG反射波长向长波长方向移动;随着紫外准分子激光与掩模板夹角变大(θ0小角度变大),WFBG反射波长同样往长波长方向移动。
将(13)式中t的系数记为wt,即:
$ {\mathit{w}_\mathit{t}}{\rm{ = 2}}\mathit{G}{\rm{sin}}{\mathit{\varphi }_{\rm{0}}}{\rm{ + }}\frac{{{\rm{2}}\mathit{G}{\mathit{K}_{{\rm{UV}}}}{\mathit{\theta }_{\rm{0}}}{\rm{cos}}{\mathit{\varphi }_{\rm{0}}}}}{{\sqrt {{\mathit{K}_{{\rm{UV}}}}^{\rm{2}}{\rm{ - }}{\mathit{G}^{\rm{2}}}} }} $
(16) 由(12) 式、(13) 式、(16) 式可知,当θ0小角度增大时,干涉光强减小;当φ0小角度增大时,干涉光强同样减小。
综上所述,紫外准分子激光会聚或发散都将引起±1级衍射光的干涉光强降低,从而引起FBG反射率减小。紫外光与掩模板相互垂直,干涉光强最大,发生斜入射后,干涉光强降低,波长向长波长方向移动。掩模板与光纤相互平行,干涉光强最大,发生倾斜后,干涉光强降低,波长向长波长方向移动。此外,把θ看作自变量,采用1阶泰勒函数展开,导致Δθ与中心波长的变化无关,实际上,紫外激光发散导致中心波长向长波长漂移;会聚导致中心波长向短波长方向漂移[20]。因此,为使刻栅系统效率最大,必须调节紫外准分子激光束平行,激光束与相位掩模板垂直,相位掩模板与待刻光纤平行。
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把栅长为L的FBG平均分为M段(Δz=L/M),第k个分段的传输矩阵为[21]:
$ \begin{array}{c} {\mathit{\boldsymbol{F}}_\mathit{k}}{\rm{ = }}\\ \left[ {\begin{array}{*{20}{c}} {{\rm{cosh(}}\mathit{\gamma }{\rm{\Delta }}\mathit{z}{\rm{) - i}}\frac{{\mathit{\hat \sigma }}}{\mathit{\gamma }}{\rm{sinh(}}\mathit{\gamma }{\rm{\Delta }}\mathit{z}{\rm{)}}}&{{\rm{ - i}}\frac{\mathit{\kappa }}{\mathit{\gamma }}{\rm{sinh(}}\mathit{\gamma }{\rm{\Delta }}\mathit{z}{\rm{)}}}\\ {{\rm{i}}\frac{\mathit{\kappa }}{\mathit{\gamma }}{\rm{sinh(}}\mathit{\gamma }{\rm{\Delta }}\mathit{z}{\rm{)}}}&{{\rm{cosh(}}\mathit{\gamma }{\rm{\Delta }}\mathit{z}{\rm{) + i}}\frac{{\mathit{\hat \sigma }}}{\mathit{\gamma }}{\rm{sinh(}}\mathit{\gamma }{\rm{\Delta }}\mathit{z}{\rm{)}}} \end{array}} \right] \end{array} $
(17) 式中,$\mathit{\gamma }{\rm{ = }}{\left( {{\mathit{\kappa }^{\rm{2}}}{\rm{ - }}\mathit{\hat \sigma }} \right)^{{\rm{1/2}}}}$,${\mathit{\hat \sigma }}$为直流自耦合系数:
$ \mathit{\hat \sigma }{\rm{ = }}\mathit{\delta }{\rm{ + }}\mathit{\sigma } $
(18) 式中,δ为归一化频率失谐量, δ=β-π/Λ=2πneff(1/λ-1/λB),λ为光源入射波长,λB为FBG的设计波长, σ和κ分别为直流和交流耦合系数:
$ \mathit{\sigma }{\rm{ = }}\frac{{{\rm{2 \mathit{ π} }}}}{\mathit{\lambda }}\overline {{\rm{\Delta }}\mathit{n}} $
(19) $ \mathit{\kappa }{\rm{ = }}\frac{{\rm{ \mathit{ π} }}}{\mathit{\lambda }}\mathit{v}\overline {{\rm{\Delta }}\mathit{n}} $
(20) 式中,v为折射率调制的条纹可见度,$\overline {{\rm{\Delta }}\mathit{n}} $为平均折射率变化。
整段FBG传输矩阵即为:
$ \mathit{\boldsymbol{F}}{\rm{ = }}\left[ {\begin{array}{*{20}{c}} {{\mathit{F}_{{\rm{11}}}}}&{{\mathit{F}_{{\rm{12}}}}}\\ {{\mathit{F}_{{\rm{21}}}}}&{{\mathit{F}_{{\rm{22}}}}} \end{array}} \right]{\rm{ = }}{\mathit{\boldsymbol{F}}_\mathit{M}}{\mathit{\boldsymbol{F}}_{\mathit{M}{\rm{ - 1}}}}{\rm{ \ldots }}{\mathit{\boldsymbol{F}}_\mathit{k}}{\rm{ \ldots }}{\mathit{\boldsymbol{F}}_{\rm{1}}} $
(21) 整段FBG功率反射率即为:
$ {\mathit{R}_{{\rm{FBG}}}}{\rm{ = }}{\left| {\frac{{{\mathit{F}_{{\rm{21}}}}}}{{{\mathit{F}_{{\rm{11}}}}}}} \right|^{\rm{2}}} $
(22) 对(22)式仿真,λ取为1548nm~1552nm;M取为50;$\overline {{\rm{\Delta }}\mathit{n}} $取为1×10-4;neff取为1.48;λB取为1550nm;v取为1。L分别取为1mm,2mm,5mm和10mm,不同栅长的FBG反射光谱如图 2a所示, 反射率分别为0.041,0.148,0.589,0.933;3dB带宽分别为0.219nm,0.090nm,0.052nm,0.036nm。L取为1mm,$\overline {{\rm{\Delta }}\mathit{n}} $分别取为1×10-4, 1.5×10-4和2×10-4时,FBG反射光谱如图 2b所示, 反射率分别为0.041,0.064,0.078;3dB带宽分别为0.219nm,0.265nm,0.315nm。由此,在反射率一定的情况下,若要刻制3dB带宽较窄的WFBG,需要采用较长的相位掩模板,控制较短的曝光时间,选用较低的光纤掺杂浓度,使平均折射率变化较小;若要刻制3dB带宽较宽的WFBG,需要选用较窄的相位掩模板,控制较长的曝光时间,选用较高的光纤掺杂浓度,使平均折射率变化较大。
由上述理论分析得出,采用相位掩模板法刻制WFBG,需要调节紫外准分子激光束平行,并与相位掩模板垂直,且相位掩模板与光纤平行。若刻制窄带宽FBG需要较长的相位掩模板,刻制宽带宽FBG需要较窄的相位掩模板。
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图 3显示为窄带宽WFBG刻栅与实时显示系统。刻栅系统中,激光器(型号:Coherent COMPexPro 110)出射248nm的紫外准分子激光;采用两个焦距分别为150mm和300mm的平凸柱透镜(L1,L2)实现横向2倍激光准直扩束,以及一个焦距为50mm的平凸柱镜(L3)压缩曝光光束纵向尺寸,从而聚焦纵向激光能量;相位掩模板的长度为10mm,周期为1058.74nm,零级衍射效率为1.1%;待刻写光纤采用长飞公司G652D单模阶跃光纤。在线监测系统中,宽带光由环形器端口1注入,经端口2所接WFBG反射后,由端口3输出至光谱仪。
为估算WFBG的反射率,采用一个与WFBG同波长的、已知反射率的FBG进行参考计算。分别将参考FBG和待测WFBG连接在环形器的端口2上,得到反射光谱(如图 4所示)。假设两次测量的光源光强无变化,则由两者的反射光强比值即可计算得WFBG的反射率,如下:
$ {\mathit{R}_{{\rm{WFBG}}}}{\rm{ = }}\frac{{{\mathit{I}_{{\rm{WFBG}}}}{\mathit{R}_{{\rm{FBG}}}}}}{{{\mathit{I}_{{\rm{FBG}}}}}} $
(23) 式中,IWFBG, RFBG, IFBG分别为WFBG的最大反射光强、FBG的反射率和FBG的最大反射光强,计算过程中需要把光强单位dBm转换为mW。另外,观察WFBG的反射光谱细节,谱型较为对称,边模抑制比较高。
固定紫外准分子激光的曝光频率为30Hz、脉冲能量为90mJ,曝光次数分别设置为100次、200次、300次、400次、500次、1000次和2000次,制备了7根WFBG(见图 5)。WFBG的反射率从0.00017递增至0.0033,确定系数为0.9806。分析斜率小的原因主要为所曝光的光纤为普通单模光纤,光敏性不及掺杂、载氢光纤。
曝光400次时,WFBG的反射率约为0.001。固定曝光频率30Hz、能量90mJ、曝光次数400次,刻写7根WFBG,反射光谱如图 6所示。
图 6中7根WFBG的相关参量如表 1所示。7根WFBG的中心波长范围为1531.973nm~1532.046nm,平均值为1532.027nm,标准差为0.023nm;反射率变化范围为0.0007~0.0021,平均值为0.0016,标准差为0.0004;3dB带宽变化范围为0.08nm~0.12nm,平均值为0.096nm,标准差为0.013nm。由此,7根WFBG的3dB带宽较窄,适合波长解调使用,且反射率较为一致,虽然中心波长差别较大,但对波长解调不会有影响。
Table 1. Related parameters of 7 WFBGs under exposure of 400 times
central wavelength/nm reflectivity 3dB bandwidth/nm 1 1532.034 0.0019 0.08 2 1532.042 0.0007 0.12 3 1532.023 0.0018 0.09 4 1532.046 0.0017 0.09 5 1531.973 0.0013 0.11 6 1532.041 0.0019 0.09 7 1532.029 0.0021 0.09 average value 1532.027 0.0016 0.096 root mean square 0.023 0.0004 0.013 -
由第1.2节可知,缩短FBG的长度,可以增大FBG的3dB带宽,但反射率会降低,可以通过增大光纤的平均折射率变化来提高反射率。基于此,在图 3刻栅系统中插入2mm长的光窗,使照射到相位掩模板上的紫外激光宽度为2mm,制备宽带宽WFBG,现场照片如图 7所示。
固定紫外准分子激光的曝光频率为30Hz、脉冲能量为90mJ,曝光次数设置为5000次, 刻写了6根WFBG,反射光谱如图 8所示。由图可知,反射光谱的谱型较为对称。
图 8中6根WFBG的相关参量如表 2所示。由表 2可知,6根WFBG中心波长变化范围为1538.77nm~1538.92nm,平均值为1538.8533nm,标准差为0.0534nm。反射率变化范围为0.000048~0.000079,平均值为0.000061,标准差为0.00001。3dB带宽变化范围为0.316nm~0.386nm,平均值为0.3433nm,标准差为0.0227nm。由此,6根WFBG的3dB带宽较宽,适合匹配干涉解调使用,且反射率较为一致。
Table 2. Related parameters of 6 WFBGs under exposure of 5000 times
central wavelength/nm reflectivity 3dB bandwidth/nm 1 1538.864 0.000079 0.332 2 1538.880 0.000058 0.316 3 1538.892 0.000066 0.386 4 1538.92 0.000052 0.344 5 1538.772 0.000048 0.327 6 1538.792 0.000063 0.355 average value 1538.8533 0.000061 0.3433 root mean square 0.0534 0.00001 0.0227 综上所述,基于相位掩模板法,采用曝光频率为30Hz、脉冲能量为90mJ的248nm紫外准分子激光器在CSMF上制备WFBG,其中采用10mm相位掩模板,曝光400次制备出窄带宽WFBG,平均中心波长为1532.0289nm,反射率为0.001629,3dB带宽为0.09517nm;采用2mm光窗遮挡相位掩模板,曝光5000次制备出宽带宽WFBG,平均中心波长为1538.8533nm,反射率为0.000061,3dB带宽为0.3433nm。
基于相位掩模板的常规光纤制备弱反射光栅
Fabrication of weak fiber Bragg grating with conventional fiber based on phase mask
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摘要: 为了探索采用常规单模光纤制备弱反射光纤光栅的可行性,以降低材料成本和传输损耗,基于相位掩模板法,在常规单模光纤上刻制弱反射光纤布喇格光栅(WFBG),并进行了实验验证。建立相位掩模板刻栅系统光场统一方程,分析光场分布对光纤布喇格光栅(FBG)中心波长和反射率的影响;采用传输矩阵法分析相位掩模板长度、平均折射率变化对FBG反射率和3dB带宽的影响,为WFBG刻制提供理论依据。采用248nm紫外准分子激光器在常规单模光纤上刻制WFBG,分析相位掩模板长度、曝光能量、曝光频率,曝光次数对WFBG中心波长、反射率和3dB带宽的影响,制备出反射率和3dB带宽分别约为0.0016,0.10nm和0.00006,0.34nm两种窄宽的WFBG。结果表明,基于相位掩模板法由紫外准分子激光对常规单模光纤多脉冲曝光,能够稳定刻制WFBG。该研究对WFBG制备的材料选型提供了参考。
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关键词:
- 光纤光学 /
- 弱反射光纤布喇格光栅 /
- 相位掩模板 /
- 单模光纤 /
- 衍射光场
Abstract: In order to explore the feasibility of using conventional fiber to fabricate weak fiber Bragg grating (WFBG) and reduce the material cost and transmission loss, a WFBG was fabricated on a conventional single-mode fiber (CSMF) based on phase mask method. The unified optical field equation of phase mask grating system was established, and the influence of optical field distribution on center wavelength and reflectivity of FBG was analyzed. The influence of phase mask length and average change of refractive index on reflectivity and 3dB bandwidth of FBG was analyzed by transfer matrix method, which provides theoretical basis for improving WFBG lithography. WFBGs were fabricated on CSMFs by 248nm UV excimer laser. The effects of phase mask length, exposure energy, exposure frequency, and exposure times on central wavelength, reflectivity, and 3dB bandwidth of WFBG were respectively analyzed. Two kinds of WFBGs with narrow and wide bandwidths were fabricated with reflectivity and 3dB bandwidth of 0.0016 and 0.10nm, 0.00006 and 0.34nm, respectively. Theoretical and experimental results show that WFBG can be fabricated on CSMF stably by the multi-pulse exposure of UV excimer laser based on the phase mask method, which provides a reference for the material selection of the weak reflection fiber grating.-
Key words:
- fiber optics /
- weak fiber Bragg grating /
- phase mask /
- single-mode fiber /
- diffraction field
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Table 1. Related parameters of 7 WFBGs under exposure of 400 times
central wavelength/nm reflectivity 3dB bandwidth/nm 1 1532.034 0.0019 0.08 2 1532.042 0.0007 0.12 3 1532.023 0.0018 0.09 4 1532.046 0.0017 0.09 5 1531.973 0.0013 0.11 6 1532.041 0.0019 0.09 7 1532.029 0.0021 0.09 average value 1532.027 0.0016 0.096 root mean square 0.023 0.0004 0.013 Table 2. Related parameters of 6 WFBGs under exposure of 5000 times
central wavelength/nm reflectivity 3dB bandwidth/nm 1 1538.864 0.000079 0.332 2 1538.880 0.000058 0.316 3 1538.892 0.000066 0.386 4 1538.92 0.000052 0.344 5 1538.772 0.000048 0.327 6 1538.792 0.000063 0.355 average value 1538.8533 0.000061 0.3433 root mean square 0.0534 0.00001 0.0227 -
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