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利用光纤布拉格光栅方程和光纤基模有效折射率随纤芯半径和环境折射率的函数关系, 建立了微纳光纤布拉格光栅(MNFBG)反射波长随环境折射率变化的数学模型, 给出了波长灵敏度函数, 并指出MNFBG反射波长的变化规律决定于有效折射率随纤芯半径和环境折射率变化的关系. 详细探究了有效折射率及其灵敏度的变化规律, 结果表明: 有效折射率随纤芯半径和环境折射率的减小而非线性减小, 其对环境折射率变化的灵敏度随环境折射率的增大而非线性增加, 而且随纤芯半径减小, 有效折射率的灵敏度、线性度以及线性响应范围均呈递增规律. 通过对纤芯半径为0.5 μm的MNFBG在1.20–1.30和1.33–1.43 环境折射率范围内的波长响应关系拟合, 分别获得了477.33 nm/RIU和856.30 nm/RIU的波长灵敏度以及99.58 %和99.7%的高线性度, 论证了分析结论以及折射率区间划分测量方案的正确性, 为MNFBG折射率传感器的设计、优化以及应用提供了参考依据.Using the fiber Bragg grating equation and the functional relation of the fundamental effective mode refractive index (RI), the mathematical model of the wavelength shift and the relational function of wavelength sensitivity are established, when the reflected wavelength of the micro/nanofiber Bragg grating (MNFBG) changes with ambient RI and the fiber radius. The theoretical relationship demonstrates that the variation of MNFBG reflected wavelengths is dependent on the change of effective RI with fiber radius and ambient RI. Meanwhile, we also study the variation of effective RI and its sensitivity in detail. The results show that the effective RI nonlinearly decreases with fiber-core radius and ambient refractive index decreasing, and its sensitivity increases as the ambient refractive index increases, and the sensitivity, linearity and the linear response range increase with the decrease of the fiber radius. For a fiber radius of 0.5 μm, by simulating the curves of the effective index versus ambient RI in the index ranges of 1.20-1.30 and 1.33-1.43 respectively, the values of wavelength sensitivity of 477.33 nm/RIU and 856.30 nm/RIU and the values of high linearity of 99.2% and 99.7% are obtained, which not only verifies the analysis conclusions and the measurement program for RI sensing with MNFBG, but also supplies references for the RI sensor design, optimization and the application.
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[1] Sun W F, Wang X K, Zhang Y 2009 Chin. Phys. Lett. 26 114210
[2] Tong L M, Pan X Y 2007 Physics 36 626 (in Chinese) [童利民, 潘欣云 2007物理 36 626]
[3] Liang R B, Sun Q Z, Wo J H, Liu D M 2011 Acta Phys. Sin. 60 104221 (in Chinese) [梁瑞冰, 孙琪真, 沃江海, 刘德明 2011 60 104221]
[4] Tong L M, Gattass R R, Ashcom J B, He S L, Lou J Y, Shen M Y, Maxwell I, Mazur E 2003 Nature 426 816
[5] Tong L M, Lou J Y, Mazur E 2004 Opt. Express 12 1025
[6] Liang W, Huang Y Y, Xu Y, Lee R K, Yariv A 2005 Appl. Phys. Lett. 86 151122
[7] Fang X, Liao C R, Wang D N 2010 Opt. Lett. 35 1007
[8] Iadicicco A, Campopiano S, Cutolo A, Giordano M, Cusano A 2005 IEEE Photon. Technol. Lett. 17 1250
[9] Zhang Y, Lin B, Tjin S C, Zhang H, Wang G H, Shum P, Zhang X L 2010 Opt. Express 18 26345
[10] Chiang K S, Liu Y Q, Ng M N, Dong X Y 2000 Electron Lett. 36 966
[11] Ran Y, Jin L, Sun L P, Li J, Guan B O 2012 Opt. Lett. 37 2649
[12] Lee S M, Jeong M Y, Saini S S 2012 J. Lightwave Technol. 30 1025
[13] Ran Y, Tan Y N, Sun L P, Gao S, Li J, Jin L, Guan B O 2011 Opt. Express 19 18577
[14] Li B, Jiang L, Wang S M, Tsai H L, Xiao H 2011 Opt. Laser Technol. 43 1420
[15] Dan G, Stephen J M, Huimin D, Christopher W S 2006 IEEE Photon. Technol. Lett. 18 160
[16] Xu B, Li Y, Dong X Y, Jin S Z, Zhang Z X 2012 Chin. Phys. Lett. 29 094203
[17] Liao Y B 2000 Fiber Optics (Beijing: Tsinghua University Press) p200 (in Chinese) [廖延彪 2000 光纤光学(北京: 清华大学出版社) 第200页]
[18] Zhou H Q, Sui C H 2011 J. Zhejiang Univ. Technol. 39 228 (in Chinese) [周寒青, 隋成华 2011 浙江工业大学学报 39 228]
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