折射率调制矩阵的Bragg光栅光谱分布特性研究  

Research on Bragg Spectral Distribution Based on Refractive Index Modulation Matrix

作　　者：刘智超 张丽娟[3] 杨进华[1] 王高 LIU Zhi-chao;ZHANG Li-juan;YANG Jin-hua;WANG Gao(Key Laboratory of Optoelectric Measurement and Optical Information Transmission Technology of Ministry of Education,School of Opto-Electronic Engineering,Changchun University of Science and Technology,Changchun 130000,China;National Demonstration Center for Experimental Opto-Electronic Engin eering Education,School of Opto-Electronic Engineering,Changchun University of Science and Technology,Changchun 130000,China;College of Computer Science and Engineering,Changchun University of Technology,Changchun 130012,China;National Key Laboratory for Electronic Measurement Technology,North University of China,Taiyuan 030051,China)

机构地区：[1]长春理工大学光电工程学院,光电测控与光信息传输技术教育部重点实验室,吉林长春130000 [2]长春理工大学光电工程学院,光电工程国家级实验教学示范中心,吉林长春130000 [3]长春工业大学计算机科学与工程学院,吉林长春130012 [4]中北大学,仪器科学与动态测试教育部重点实验室,山西太原030051

出　　处：《光谱学与光谱分析》2018年第12期3718-3723,共6页Spectroscopy and Spectral Analysis

基　　金：国家自然科学基金项目(61703056);高等学校学科创新引智计划(111计划);光电工程国家级实验教学示范中心资助。

摘　　要：为了实现对光纤光栅回波光谱分布的控制,利用传输矩阵法构建了分段调制折射率的数学模型。通过在各个分段中以不同形式的折射率调制组合实现对回波光谱分布的控制,研究了基于不同折射率分布条件下的谱形特性,为实现获取任意形态的Bragg光谱分布提供了理论支撑。系统结合耦合模理论与矩阵传输算法,当分段后子光纤光栅尺寸符合边界条件时,即仍可应用耦合模理论计算,同时又可以将多段的耦合方程以正、反向模式的形式通过矩阵函数进行表达。由此可知,虽然任意折射率调制组合构成的整个光纤光栅不具备通解形式,但分段后的子光纤光栅具有可解析的特性,同时再利用矩阵传输算法可以将m段子光纤光栅的正反向模式进行计算,就能将任意形式光纤光栅的折射率调制函数转化为传输矩阵组,再对其反射率分布场进行解析。最终,可以得到整个光纤光栅的等效正、反模式,即实现回波光谱分布的控制。由理论部分可知,回波光谱分布特性主要受正反向导模耦合系数、纤芯位置、分段数决定,可由^σ(z)和k(z)表示。通过MATLAB仿真分析可知,两参数在(0,1)范围内对反射率函数具有明显的调制作用。随着控制参数阶数的增大,反射率调制斜率也会增大;当k(0. 38,0. 48),^σ(0. 52,0. 58)时,反射率调制符合单调特性。从而得到了不同控制参数条件下反射率函数的分布变化,讨论了耦合系数对回波谱形控制的量化效果。实验利用AVESTA公司的Ti:Sapphire飞秒激光器完成了四种不同结构光纤光栅的制作,采用了四种折射率分段调制的FBG结构,分别是:(1)在m段中Λ1和Λ2交替均匀分布;(2)在m/2段中Λ1和Λ2交替均匀分布,其余段随机分布;(3)在m/2段中Λ1和Λ2随机分布,其余段也随机分布;(4)在整个光纤光栅段折射率随机分布。对以上四种FBG的回波光谱分布进行测试与比较,可知采�According to the form of its engraved grid,FBG sensor can be divided into uniform type,chirp type and so on.The spectrum dist ributions of FBG are different for different grid forms.At present,it has been reported that existing structural parameters were mainly analyzed by the litera ture.The functional model was studied for obtaining the spectral distribution,which can be from any kind of FBG,and its parameter design was realized.In ord er to realize the control of the echo spectrum distribution by FBG,a mathematic al model of the segmented modulation index was established by using transfer mat rix method.The spectrum distribution of the echo was controlled by the combinat ion of different refractive index modulations in each segment,and the spectral characteristics under different refractive index distributions were studied.It provided theoretical support for obtaining the Bragg spectrum distribution in an y form.In the system,coupled-mode theory and matrix transmission algorithms w ere used in combination.Compared with the traditional uniform FBG,σand k were no longer constants,but ratherσ(z)and k(z)as a function of form,so for any FBG structure did not have an analytic solution.However,if the F BG was divided into m sections,m sub-FBGs could be obtained from the con creteσ(z)and k(z)functions on each small section,so that the overa ll effects of the FBG could be obtained by the matrix transmission method.The F BG was divided into m small sections in the z-axis direction,and m su b-FBGs could be obtained from the specificσ(z)and k(z)functions in e ac h small section,so that the overall effects of the FBG can be obtained by the matrix transmission method.When the size of sub-FBG segmented meets the b oundary conditions,the coupling mode theory can still be applied.At the same time,it can express the multi-section coupled equations through the matrix f unction in the form of positive and negative modes.It can be seen from this th a t the entire FBG composed of arbitrary refractive index modulation does not h

关 键 词：光纤光栅 光谱分布 传输矩阵组 折射率调制 

分 类 号：TN253[电子电信—物理电子学]