Research on Bragg Spectral Distribution Based on Refractive Index Modulation Matrix
LIU Zhi-chao1, 2, ZHANG Li-juan3, YANG Jin-hua1, WANG Gao4
1. 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
2. National Demonstration Center for Experimental Opto-Electronic Engineering Education, School of Opto-Electronic Engineering, Changchun University of Science and Technology, Changchun 130000, China
3. College of Computer Science and Engineering, Changchun University of Technology，Changchun 130012, China
4. National Key Laboratory for Electronic Measurement Technology, North University of China, Taiyuan 030051, China
Abstract：According to the form of its engraved grid, FBG sensor can be divided into uniform type, chirp type and so on. The spectrum distributions of FBG are different for different grid forms. At present, it has been reported that existing structural parameters were mainly analyzed by the literature. 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 order to realize the control of the echo spectrum distribution by FBG, a mathematical model of the segmented modulation index was established by using transfer matrix method. The spectrum distribution of the echo was controlled by the combination 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 any form. In the system, coupled-mode theory and matrix transmission algorithms were used in combination. Compared with the traditional uniform FBG, σ and k were no longer constants, but rather σ(z) and k(z) as a function of form, so for any FBG structure did not have an analytic solution. However, if the FBG was divided into m sections, m sub-FBGs could be obtained from the concrete σ(z) and k(z) functions on each small section, so that the overall effects of the FBG could be obtained by the matrix transmission method. The FBG was divided into m small sections in the z-axis direction, and m sub-FBGs could be obtained from the specific σ(z) and k(z) functions in each 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 boundary conditions, the coupling mode theory can still be applied. At the same time, it can express the multi-section coupled equations through the matrix function in the form of positive and negative modes. It can be seen from this that the entire FBG composed of arbitrary refractive index modulation does not have the generalized form, but it can be resolvable for the segmented sub-FBGs. And the matrix transmission algorithm can be used to calculate the positive and negative modes of the m-segment sub-FBGs. So the refractive index modulation function of any type of FBG can be transformed into a transmission matrix group. The reflectivity distribution field can also be analyzed. Finally, the equivalent positive and negative modes of the whole FBG can be obtained, so as to realize the control of the echo spectrum distribution. As can be seen from the theoretical part, the spectrum distribution characteristics of echo are mainly determined by the coupling coefficients of the forward and reverse guided modes, the position of the core and the number of segments. They can be represented by σ(z) and k(z). Through MATLAB simulation analysis showed that the two parameters have significant modulation effects on the reflectivity function in the range of (0,1). As the order of control parameters increases, the slope of reflectivity modulation will also increase. In case of k(0.38, 0.48), σ(0.52, 0.58), it is monotonically tuned for reflectivity modulation. The distribution of the reflectivity function under different control parameters was obtained. The quantitative effects of the coupling coefficient on the control of the echo spectrum were discussed. Taking two specific pitch Λ1 and Λ2 as an example, after splitting the whole FBG into m sub FBGs, Λ1 and Λ2 were placed on different sub-sections. The spectrum distribution patterns of FBG were analyzed according to different grid layouts. If the spectrum characteristics of FBG change by the parameters and distribution forms of Λ1 and Λ2, and they are resolvable, the Bragg spectral characteristics can be considered as controllability. Through the parameter control any spectrum distribution can be achieved. In the experiment, AVESTA’s Ti: Sapphire femtosecond laser (Its center wavelength 800 nm, frequency 1 kHz, peak pulse energy 800 nJ.) was used to fabricate four different structured fiber gratings. Four kinds of refractive index modulation FBG segment structure were employed. Respectively: (1) Λ1 and Λ2 were evenly distributed alternately in the m section; (2) Λ1 and Λ2 were evenly distributed alternately in the m/2 section, and the rest of section were randomly distributed; (3) Λ1 and Λ2 were randomly distributed in the m/2 section, and the rest of section were randomly distributed, too; (4) The refractive index of the entire fiber grating segment was randomly distributed. Echo spectrum distribution of the above four FBGs was tested and compared, so the spectrum properties of Bragg was studied by the segmented refractive index modulation. The experimental results showed that when the FBGs in the form of matrix group are distributed in the m section, they are consistent with the traditional series homogeneous FBG test and have two obvious Bragg characteristic peaks, and they are located at 1 551.485 and 1 563.572 nm, respectively, and have a high signal-to-noise ratio. It is consistent with the test results of two series-connected FBGs with fixed pitch and is also a special solution to the piecewise modulated function. In case 2, its characteristic peak positions are 1 551.499 and 1 563.551 nm, its absolute error is better than 0.030 nm. Its half-width is better than that of case 1, but its noise power increases greatly and the signal-to-noise ratio decreases. In case 3, the absolute error of the characteristic peak position is better than 0.050 nm, and the sharpness of the characteristic peak is further increased, and the noise power is further increased, and the signal-to-noise ratio is the worst. When the matrix group is distributed in the m/2 segment, the refractive index modulation characteristic information can still be obtained obviously in the test spectrum, that is, there are two Bragg characteristic peaks, but the peak-peak value decreases, and the noise spectrum increases, and the half-width narrows. At the same time, the trend of stochastic distribution is more obvious than that of alternation. Thus, the characteristic peak, half-width and power spectrum in the echo spectrum can be modulated by controlling the matrix group distribution. The method can accurately control the Bragg spectrum distribution under the pre-designed refractive index modulation matrix to obtain the target echo spectrum.
刘智超，张丽娟，杨进华，王 高. 折射率调制矩阵的Bragg光栅光谱分布特性研究[J]. 光谱学与光谱分析, 2018, 38(12): 3718-3723.
LIU Zhi-chao, ZHANG Li-juan, YANG Jin-hua, WANG Gao. Research on Bragg Spectral Distribution Based on Refractive Index Modulation Matrix. SPECTROSCOPY AND SPECTRAL ANALYSIS, 2018, 38(12): 3718-3723.
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