光电工程

飞秒激光刻写并行FBG免包络游标高灵敏温度传感器

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杨文熙 , 庞清顺 , 张丽强 , 田振 , 王明红 , 姚一村 ^*^,^*

光电工程 | 科研论文 2026,53(7): 260079-1

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光电工程 |科研论文 2026 , 53 (7) : 260079 -1

飞秒激光刻写并行FBG免包络游标高灵敏温度传感器

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杨文熙 (2000-)，男，硕士研究生，主要从事飞秒激光微加工与光纤传感器的研究。E-mail：yangwx915@163.com yangwx915@163.com

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庞清顺 (2001-)，男，硕士研究生，主要从事飞秒激光微加工与光纤传感器的研究。E-mail：pqs20010221@163.com pqs20010221@163.com

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姚一村 (1987-)，男，博士，副教授，硕士研究生导师，主要从事波导光学、光纤传感和非线性光学方面的研究。E-mail：yaoyicun@lcu.edu.cn yaoyicun@lcu.edu.cn

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姚一村 (1987-)，男，博士，副教授，硕士研究生导师，主要从事波导光学、光纤传感和非线性光学方面的研究。E-mail：yaoyicun@lcu.edu.cn yaoyicun@lcu.edu.cn

杨文熙, 庞清顺, 张丽强, 田振, 王明红, 姚一村^*^,^*

作者信息

聊城大学物理科学与信息工程学院，山东聊城 252000

通讯作者:

姚一村，yaoyicun@lcu.edu.cn

作者简介:

作者贡献

杨文熙：实验开展及论文写作；庞清顺：实验开展及数据分析；张丽强：实验和论文指导；田振：实验设计，论文指导；王明红：选题和论文指导；姚一村：论文指导和修改。

杨文熙 (2000-)，男，硕士研究生，主要从事飞秒激光微加工与光纤传感器的研究。E-mail：yangwx915@163.com yangwx915@163.com

庞清顺 (2001-)，男，硕士研究生，主要从事飞秒激光微加工与光纤传感器的研究。E-mail：pqs20010221@163.com pqs20010221@163.com

姚一村 (1987-)，男，博士，副教授，硕士研究生导师，主要从事波导光学、光纤传感和非线性光学方面的研究。E-mail：yaoyicun@lcu.edu.cn yaoyicun@lcu.edu.cn

Femtosecond laser inscribed parallel FBG envelope-free vernier high-sensitivity temperature sensor

Wenxi Yang, Qingshun Pang, Liqiang Zhang, Zhen Tian, Minghong Wang, Yicun Yao

Affiliations

School of Physical Science and Information Engineering, Liaocheng University, Liaocheng, Shandong 252000, China

Corresponding Author:

yaoyicun@lcu.edu.cn

出版时间: 2026-07-25 doi: 10.12086/oee.2026.260079

文章导航

摘要

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针对传统光纤布拉格光栅 (FBG)温度传感器本征灵敏度低，且传统光学游标效应依赖包络拟合易引发光谱展宽、检测限劣化的问题，本文提出一种结合飞秒激光微加工技术与免包络游标方法的并行FBG高灵敏温度传感器。利用飞秒激光冷加工的高精度与三维加工优势，在单模光纤同一横截面内刻写并行FBG阵列。通过构建理论参考臂与截线追踪法，以FBG离散高Q值共振峰代替传统干涉仪，消除包络展宽误差。所制备的并行FBG传感器，其温度灵敏度达到244.48 pm/℃，相较于单一FBG实现了超19.5倍的提升，为FBG在高精度温度传感领域的应用提供了新方案。

关键词

光纤布拉格光栅 / 飞秒激光刻写 / 光学游标效应 / 温度传感器

Abstract

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Objective

High-precision temperature measurement is critical for aerospace, industrial process control, biomedical microenvironment monitoring and other applications. Conventional fiber Bragg grating (FBG) temperature sensors suffer from intrinsically low sensitivity (~10 pm/°C) restricted by the thermo-optic effect and thermal expansion coefficient of silica fiber. Existing sensitivity enhancement strategies, such as coating high-thermal-expansion polymers or packaging with metal substrates, usually introduce extra stress cross-sensitivity and poor long-term reliability, and cannot meet the demand for miniaturized all-fiber sensing devices. Meanwhile, traditional optical Vernier effect relies on envelope fitting of cascaded interferograms, which inevitably induces severe envelope broadening, deteriorated detection limit and narrowed dynamic range as the magnification factor increases. This inherent performance trade-off has become a critical technical limitation restricting the application of Vernier-enhanced fiber sensors in high-precision temperature measurement fields. To break through these inherent bottlenecks, this paper proposes and fabricates a parallel FBG high-sensitivity temperature sensor combining femtosecond laser micromachining and an envelope-free Vernier demodulation algorithm, aiming to achieve simultaneous optimization of sensitivity, detection limit and measurement range for high-precision temperature detection.

Methods

In this work, parallel FBG sensing arrays are fabricated via femtosecond laser point-by-point inscription within the same cross-section of standard single-mode fiber, leveraging the cold-processing property, nanoscale spatial resolution and three-dimensional fabrication flexibility of femtosecond laser. The spatially parallel configuration effectively eliminates axial stress crosstalk and internal temperature gradient errors commonly existing in cascaded or series grating structures, ensuring synchronous and proportional thermal drift of each FBG resonance peak under uniform temperature excitation. This one-step in-fiber fabrication avoids the alignment error and extra insertion loss caused by cascading discrete fiber devices, and fully maintains the structural integrity of the all-fiber sensing system. For signal demodulation, an envelope-free Vernier method based on a virtual theoretical reference arm and intercept tracking strategy is developed. Instead of building a physical reference interferometer, a set of reference resonance peaks is numerically generated with a designed free spectral range. The discrete high-Q resonance peaks of parallel FBGs are used to equivalently replace the continuous cosine spectrum of conventional interferometers. By tracking the wavelength drift of the intercept between the fitting curve and a fixed horizontal reference line, envelope extraction and fitting procedures are completely avoided. The virtual reference arm can flexibly adjust its free spectral range via algorithm parameters to match different magnification demands, without reprocessing or modifying the physical sensing structure. Both four-FBG and simplified two-FBG parallel structures are fabricated and tested, and the detection limit performance is quantitatively evaluated via Monte Carlo simulations with 200 independent noise-injection experiments.

Results and Discussions

Experimental results demonstrate that the parallel FBG sensors fabricated by femtosecond laser exhibit excellent spectral quality and stable thermal response. All FBG resonance peaks show good linear red-shift characteristics with temperature rise, without obvious crosstalk or peak distortion. Multiple repeated temperature cycling tests also verify that the sensor exhibits favorable repeatability and low hysteresis, with negligible wavelength deviation after multiple heating-cooling cycles. After envelope-free Vernier demodulation, the four-FBG sensor achieves temperature sensitivities of 110.18 pm/°C (M=10) and 208.51 pm/°C (M=20), corresponding to 11.2-fold and 21.3-fold enhancement compared with a single bare FBG, respectively. The optimized parallel two-FBG structure delivers a temperature sensitivity of 244.48 pm/°C at M=20, which is 19.5 times higher than that of a single FBG, with a linear correlation coefficient R² above 0.999 under all test conditions. The experimental sensitivity values under different magnification factors are in good agreement with the theoretical calculation results, which confirms the correctness of the proposed envelope-free Vernier amplification model. Benefiting from the noise averaging effect of multi-peak fitting, the temperature detection limit is reduced by 43.34% to 0.0931 °C at M=10, breaking the inherent trade-off between sensitivity and detection limit in traditional Vernier sensors. Unlike the conventional envelope-based Vernier effect, the proposed method preserves the narrow linewidth of FBG resonance peaks without spectral broadening, thus effectively expanding the effective dynamic measurement range while enhancing sensitivity. Compared with traditional envelope-based Vernier sensors with equal magnification, the proposed scheme avoids the sharp shrinkage of measurement range, and achieves a better balance between sensitivity and measurable range. The simplified two-FBG structure achieves comparable magnification performance with significantly reduced device footprint and fabrication cost.

Conclusions

This work proposes, fabricates and experimentally characterizes a parallel FBG high-sensitivity temperature sensor integrated with femtosecond laser inscription and envelope-free Vernier demodulation. By inscribing parallel FBG arrays in the same cross-section of single-mode fiber via femtosecond laser, axial crosstalk and temperature gradient errors are effectively suppressed. The envelope-free Vernier scheme with virtual reference arm and intercept tracking replaces traditional envelope fitting, fundamentally eliminating measurement errors induced by spectral broadening and envelope distortion. The sensor achieves over 19.5-fold sensitivity enhancement relative to a single FBG, and realizes simultaneous improvement in sensitivity, detection limit and measurement range. Furthermore, the proposed sensing structure and demodulation framework can be extended to multi-parameter monitoring such as micro-strain, refractive index and micro-pressure, showing broad prospects in industrial precision manufacturing and biomedical scenarios. With the advantages of compact structure, no physical reference arm required and good compatibility with existing femtosecond micromachining processes, this work provides a promising technical approach for high-precision temperature sensing scenarios and the development of miniaturized high-performance optical fiber sensors.

Key words

fiber bragg grating / femtosecond laser inscription / optical vernier effect / temperature sensor

引用本文

杨文熙, 庞清顺, 张丽强, 田振, 王明红, 姚一村. 飞秒激光刻写并行FBG免包络游标高灵敏温度传感器. 光电工程, 2026 , 53 (7) : 260079 -1 . DOI: 10.12086/oee.2026.260079

Wenxi Yang, Qingshun Pang, Liqiang Zhang, Zhen Tian, Minghong Wang, Yicun Yao. Femtosecond laser inscribed parallel FBG envelope-free vernier high-sensitivity temperature sensor[J]. Opto-Electronic Engineering, 2026 , 53 (7) : 260079 -1 . DOI: 10.12086/oee.2026.260079

正文

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1　引　言

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光纤传感器凭借抗电磁干扰、体积小巧及易于多路复用等优势，在航空航天、工业过程控制及结构健康监测等高精度测量领域展现出不可替代的价值^[1-3]。其中，光纤布拉格光栅 (fiber Bragg grating, FBG)因其高品质因数和优异的波分复用特性，成为目前最核心的传感元件之一^[4]。然而，受限于石英光纤固有的热光效应与热膨胀系数，传统裸FBG的温度灵敏度较低 (通常仅在~10 pm/℃量级)，这一本质局限严重制约了其在生物医学微环境监测、微纳加工工艺控温等需要捕捉微小温度波动的高精度场景中的应用^[5-6]。飞秒激光微加工技术作为微纳光子器件制备的核心手段，凭借超短脉冲带来的“冷加工”特性、纳米级空间分辨率及三维加工灵活性，为光纤传感结构的创新设计提供了关键支撑^[7-9]。与传统紫外光刻技术相比，飞秒激光可直接在光纤纤芯、包层甚至特种光纤内部实现高精度微纳结构刻写，并且不受光纤材料光敏性限制，能够灵活制备各类定制化FBG阵列。

另一方面，为突破灵敏度瓶颈，光学游标效应被广泛引入传感系统^[10-12]。传统光学游标传感器通常基于物理干涉仪级联构建，如级联法布里-珀罗干涉仪 (Fabry-Perot interferometer, FPI)，通过叠加两个自由光谱范围 (free spectral range, FSR)存在微小差异的干涉光谱，追踪其宽带拍频包络的漂移实现灵敏度放大^[13-15]。例如，北京信息科技大学刘福璐等人提出了一种将空心光纤熔接在两段单模光纤之间的级联温度传感器，温度灵敏度达706.9 pm/℃，较裸FBG提升76倍^[16]，此外另有研究在结构、算法等方面对传感器性能进行优化^[17-18]。但基于包络拟合的传统机制存在不可调和的物理矛盾：追求更高增敏倍数必然导致包络半峰全宽 (full-width at half maximum, FWHM)急剧展宽，不仅恶化光谱分辨率，还会引发寻峰误差与检测极限劣化，对其在高精度传感中的监测能力形成负面影响^[19-20]。

为解决以上问题，本课题组近年来提出免包络游标方法，并已成功应用于多类微纳传感器的信号解调^[21-23]。该方法摒弃了传统游标效应中的包络拟合过程，通过联合传感臂干涉器和虚拟参考臂干涉器的峰位信息，实现等效于游标效应的灵敏度放大效果^[24-26]。本论文进一步将该方法推广至FBG传感器，通过级联多个FBG，实现了灵敏度的大幅增强，并在温度传感实验中得到验证。更为重要的是，由于该方法联合了多个FBG共振峰的信息，达到了噪声平抑的效果，实现了超过43%的检测限降幅，从而显著提升了传感器的实际监测精度。

2　基于FBG传感器的免包络游标增敏原理

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传统游标效应需要将传感臂及参考臂干涉光谱进行组合以构成包络调制曲线，其过程如图1(a, b)示意，其中黑色和红色曲线分别代表两套FSR略有差别的干涉光谱。显然，图1(b)中包络调制曲线的峰值，恰好对应两套干涉谱共振峰发生最大重合的位置。因此，包络曲线本质上反映的是两套干涉谱的共振峰的峰位信息，而干涉光谱的具体线型并不重要。考虑到FBG的共振峰漂移规律与特定干涉器相近，即特定干涉峰的漂移量正比于共振峰波长，本研究利用一系列FBG的尖锐共振谱线 (图1(c))代替传感臂干涉光谱 (图1(a)中黑色曲线)，并通过理论计算，得到一组虚拟参考共振峰 (图1中红色竖直虚线)，用以代替实际参考臂干涉谱 (图1(a)中红色虚线)。通过追踪两套光谱的峰位信息，寻找其最佳理论重合位置，无需拟合包络曲线，即可实现等同于传统游标效应的灵敏度增强效果^[27]。其具体实施方式将在后文中进行详述。

3　实验测试与结果分析

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3.1　传感器制备

本研究中的并行FBG传感器采用飞秒激光逐点刻写技术在标准单模光纤 (single-mode fiber, SMF)中制备而成，制备示意图如图2(a)所示。实验加工平台所搭载的飞秒激光器初始工作波长为1040 nm，经倍频晶体处理后转换为520 nm的输出光束，其重复频率设置为200 kHz。为实现对折射率微区的精准调制，光路系统中引入了半波片 (half wave plate, HWP)、四分之一波片 (quarter wave plate, QWP)和格兰-泰勒棱镜 (Glan-Taylor prism, GTP)的组合器件，将作用于光纤的单脉冲能量调节至224 nJ，并将出射激光调制圆偏振以尽量降低双折射效应。

在刻写操作前，剥除了涂覆层的单模光纤被平直且无应力地固定于高精度的三维电控位移台上。随后，飞秒激光束通过数值孔径为0.75的40倍物镜精准聚焦于光纤纤芯区域。此外，为了有效消除光纤圆柱形包层与空气界面之间因折射率失配而产生的像差及光散射干扰，刻写区域的光纤被全程浸没于折射率匹配液中。通过计算机程序控制三维位移台沿预设轨迹匀速移动，利用逐点曝光的方式，本研究在单模光纤微小的纤芯内部依次加工出多组互相平行且互不重叠的FBG。光栅中心之间的横向刻写间隔d为2 μm，每个FBG的长度均为2 mm，其横截面示意如图2(b)所示。

并行FBG的各布拉格峰位严格对照某特定FPI相应的共振峰位进行设计。对于理想FPI，其m阶共振峰波长λ_m满足以下关系：

$ m\cdot {\lambda }_{m}=2{n}_{\text{eff}}L \ ,$

(1)

其中n_eff和L分别是FPI的有效折射率和腔长。为了在宽带光源有效波长范围 (1250~1650 nm)内尽可能合理分配各FBG的中心波长，实验对所参照FPI的有效折射率及腔长进行了合理选取。刻写完成后，在室温下提取了该四组并行FBG的反射光谱如图3所示，其中FBG1至FBG4的中心波长分别为1288.53 nm，1354.98 nm，1430.09 nm，1512.25 nm。

3.2　温度传感测试

如图4所示，为全面评估所制备的并行FBG传感器的温度响应特性，本研究搭建了高精度的温度传感与光谱解调测试系统。该测试系统主要由超辐射发光二极管 (superluminescent diode, SLD)、光纤环形器 (circulator)、高精度恒温实验箱，以及光谱分析仪 (optical spectrum analyzer, OSA)组成。

测试过程中，宽带光源发出的连续宽谱光经由光环形器并传输至放置于恒温箱内的并行FBG传感探头，其反射信号再次经过环形器并最终被引入光谱分析仪进行实时采集与记录。在温度响应测试环节，将传感器件置于高精度恒温箱的均温区内，并尽量消除环境气流扰动。测试过程中，温度范围被设定为30~100 ℃。为确保传感器与环境达到接近热平衡状态，在每一个设定的温度节点处，系统均保持恒温10 min后再进行光谱数据的采集。

实验结果表明，各组FBG的中心波长均随温度升高而向长波长方向漂移。以FBG 2为例，其光谱漂移规律展示如图5所示。可以清晰地观察到随着环境温度的逐渐升高，受石英光纤自身热光效应和热膨胀效应的综合影响，FBG共振峰呈现出规律地红移。经测试，FBG 1~4的温度灵敏度分别为9.3 pm/℃、9.8 pm/℃、10.3 pm/℃和10.6 pm/℃。

3.3　免包络游标增敏研究

本文所采用的免包络游标方法，采用多个FBG的组合作为传感臂，并根据预设灵敏度放大因子M，计算得到理想干涉器的一系列共振波长，以代替参考臂干涉器。其中虚拟参考臂的共振波长通过如下方法确定^[27]：游标效应中，灵敏度放大因子M可表示为

$ M=\frac{{L}_{\rm s}}{\left| {L}_{\rm s}-{L}_{\rm r}\right| }=\frac{{F_{\rm r}}}{\left| {F_{\rm s}}-{F_{\rm r}}\right| } \ ,$

(2)

其中：L_s，F_s分别为传感臂干涉器的长度和自由光谱范围，L_r，F_r分别为参考臂干涉器的长度和自由光谱范围。当选定放大因子M，即可由传感臂干涉器的长度或读取的自由光谱范围，计算得到参考臂的L_r或F_r，并最终计算得到参考臂干涉器的一系列共振峰值。如前所述，免包络游标方法的本质在于处理参考臂及传感臂的一系列干涉峰值信息，而具体的光谱线型则不十分重要。基于此理由，只需要得到虚拟参考臂的一系列峰值λ_m就可以获取这一系列干涉峰值信息，具体推导过程可参考文献[27]。虚拟参考臂的m阶共振峰λ_m最终可表示为

$ {\lambda }_{m}=\frac{1}{m}\cdot \frac{M{\lambda }^{2}}{ (M+1){F_{\rm s}}} \ .$

(3)

图6(a, c)分别给出了放大倍数M=10和M=20条件下并行FBG反射峰与理论参考峰之间的位置关系。其中红色实线为并行FBG反射谱，黑色虚线为计算出的理论参考峰位置。为进一步寻找两套光谱的最大重合位置，按如图所示方式将传感臂和参考臂的系列共振峰位重新编号为λ_s_,_n及λ_r_,_n，其中n取整数。当M=10时，参考峰 λ_r,−1至λ_r,3分别为1248.91 nm、1318.29 nm、1395.84 nm、1483.08 nm、1581.95 nm；当M=20时，参考峰 λ_r,−1至λ_r,3分别为1242.96 nm、1308.38 nm、1381.07 nm、1462.31 nm、1553.70 nm。

为量化两套干涉峰的重合度，本研究定义传感峰在相邻理论参考峰位构成的网格中的相对位置百分比Y。对于编号为n的传感峰，定义Y_n= (λ_s,n−λ_r,n)/ (λ_r,n+1−λ_r,n)。将实验测得的传感峰波长λ_s,n 作为横坐标X_n，计算得出的相对位置 Y_n作为纵坐标，则每个FBG峰对应一对 (X_n, Y_n)坐标点，并采用二次多项式对其进行拟合，可分别得到图6(b, d)所示的拟合曲线。显然，Y取0、±1、±2等整数时，两套光谱具有最大的重合度。考虑到环境变化时，光谱拟合曲线仅做整体漂移，因此，可以选取其他Y=C (C为常数)水平轴，并截取其与拟合曲线的交点作为传感参考峰^[27]。当环境变化时，通过读取该交点处传感参考峰的漂移量，即可实现等效于传统游标效应的放大效果。因此，相较于传统游标效应中对包络峰或谷的追踪，该方法可以实现高灵敏度下动态范围的扩展。即使包络峰/谷本身在环境变化中漂移出光谱仪检测范围，也可以通过改变Y=C水平轴的位置，实现漂移量的追踪。

图7展示了原始FBG (中心波长为1354.98 nm)及采用免包络游标效应放大后的灵敏度曲线对比情况。当M=10时，传感器温度灵敏度达到 110.18 pm/℃；当M=20时，温度灵敏度提高至 208.51 pm/℃，相比原始FBG约9.8 pm/℃的温度灵敏度，分别提高了约11.2倍和21.3倍，与理论设定的放大倍数较为接近。

3.4　检测限分析

除温度灵敏度外，最低检测限 (detection limit, DL)能够更准确地反映传感器的实际监测能力，DL=R/S。其中，R为光谱分辨率，S为传感器灵敏度。在实际传感过程中，考虑到光谱仪具有有限的分辨率 (本实验中设置为0.05 nm)，需对共振峰附近波长范围的光谱数据点进行高斯拟合，以准确读取其共振峰位置^[20]。另一方面，光谱仪的热噪声、散粒噪声，以及宽谱光源的相对强度噪声，相当于对原始光谱叠加一套随机噪声光谱，进而影响FBG峰位的读取精度。为模拟噪声干扰，本研究在实测反射光谱数据中加入标准差为5×10⁻⁴的高斯白噪声，随后采用蒙特卡洛方法进行200次独立模拟实验，统计随机噪声作用下的波长漂移结果。波长分辨率 R定义为波长漂移结果95%置信区间的宽度，即R=1.96×2σ^[20]。

图8(a)展示了采用免包络游标方法，并预设M=10时，传感参考峰在随机噪声影响下的分布情况，其中红色虚线和绿色虚线分别代表传感参考峰位的平均值及置信区间。与未采用游标放大的单一FBG相比，系统温度检测限降低了43.34%，达到0.0931℃。采用同样方法测得，当M=20时，检测限较原始FBG传感器降低了38.71%，达到0.1007 ℃。以上结果表明，与传统游标效应中灵敏度提升伴随检测限升高的结果不同，本文所采用的免包络游标方法，可以在灵敏度提升的同时，实现检测限的有效抑制，从而改善其实际传感精度。

为了进一步阐释其检测限降低的原因，图8(b)展示了以M=10为例，200组随机噪声叠加后的光谱拟合曲线。可以看到，该曲线呈现明显的抖动。由于曲线是由多个FBG共振峰拟合而来，当各共振峰存在随机噪声导致的峰位偏差时，该偏差在拟合曲线的中段得到一定程度的平均化，而在两侧偏差逐渐加大。这类似于“平衡木”效应，当平衡木上各点存在随机噪声影响时，其中段起到了稳定器作用，并实现了一定程度的噪声抑制效果。需要说明的是，为了更加清晰地展示这一效应，在图8(b)的绘制过程中，本文将随机噪声的幅度进行了适当扩大。

需要指出的是，在使用免包络游标方法时，灵敏度放大因子M虽然可以根据需求进行自由选择，但其具体数值并非越大越好。首先，进一步提升的M因子并不能显著改善最低检测限，如前所分析的那样，检测限的改善，主要在于将多个共振峰的信息进行关联，以实现噪声的平抑，M的单独提升并不能实现噪声抑制。其次，考虑到实际飞秒激光刻写过程中，FBG的中心波长及光谱线型相较于理论预期存在一定偏差，当M进一步增加时，随着光谱拟合曲线的斜率下降，这一误差的影响也将被放大，从而导致曲线的拟合精度下降，影响结果的稳定性^[27]。

3.5　基于并行2-FBG结构的器件优化与游标增强

考虑到并行4-FBG结构中，各FBG位于纤芯横截面的不同位置，因此与芯模之间的耦合效率存在差异，导致各FBG的反射率及3 dB带宽存在差异，从而导致系列峰位的识别精度一致性难以保证。然而，免包络算法的核心在于重构一条多项式曲线并追踪其整体平移，而确定一条拟合线在理论上仅需两个传感峰数据点及三个参考峰数据点。这意味着，只需要提取两个传感FBG的峰位，即可唯一确定该拟合曲线的理论峰位。因此本研究尝试在确保游标放大效果不打折扣的前提下，进一步剥离硬件冗余，仅采用并行双FBG结构完成高效的游标温度传感，以进一步降低光纤微纳传感器的空间占用与制备成本。两组并行FBG的结构示意图如图9(a)所示。

本研究采用与前述一致的飞秒激光逐点刻写方式，并对照某特定FPI的共振峰，将并行2-FBG的Bragg波长分别设置为1353.0 nm和1476.0 nm。实验中，同样分别选取M=10、20，引入免包络游标方法以实现灵敏度增强。以灵敏度增强因子M=20为例，扫描并行2-FBG的透射/反射光谱与采用的虚拟参考臂干涉峰波长展示如图9(b)所示。其中，蓝色虚线为并行2-FBG理论参考峰，当M=10时，理论参考峰λ_r,−1、λ_r,0、λ_r,1分别为1368.72 nm、1505.59 nm、1672.88 nm；当M=20时，理论参考峰λ_r,−1、λ_r,0、λ_r,1分别为1314.40 nm、1433.90 nm、1577.28 nm。

为直观展示精简双光栅结构在极限增敏条件下的解调过程与传感性能，本研究选取目标放大因子M=20时的实验数据，并将光谱拟合曲线展示如图10(a)。可见，当温度由30 ℃提高至100 ℃，理论重合峰拟合曲线发生显著红移。拟合曲线与Y=0.33水平轴的交点由1436.75 nm漂移至1419.58 nm。图10(b)则直观呈现了传感系统在算法增强前后的温度灵敏度的变化。未经游标放大的单一FBG，其本征温度响应斜率十分平缓，而在引入免包络游标算法后，系统的温度响应斜率变得显著陡峭，实际测试灵敏度与理论放大预期接近。放大后的测试数据点依然紧密贴合线性回归模型，其线性相关系数R²高达0.999以上。

实验结果表明，构成并行2-FBG的单一光栅本征温度灵敏度为12.52 pm/℃。当设定放大因子M=10时，经免包络解调后的实际温度灵敏度升至132.87 pm/℃，实际放大倍数为10.6倍；当设定放大因子M=20时，实际温度灵敏度进一步大幅提升至244.48 pm/℃，实际放大倍数达到19.5倍。在所有测试条件下，灵敏度拟合曲线的线性相关系数R²均不低于0.999。如图10(b)所示，两种结构具有相近的温度灵敏度。以灵敏度的理想放大倍数为基准，当M=10、20时，并行2-FBG与并行4-FBG的实际灵敏度误差分别为4.25%及9.15%。以上结果说明，可以采用结构更为简化的并行2-FBG传感器替代并行4-FBG传感器，结合免包络游标算法，实现显著的温度灵敏度提升，从而为紧凑型、高灵敏度点式温度传感器的开发提供了新的思路。

4　结　论

收起

本研究针对传统FBG温度传感器本征灵敏度低、传统光学游标效应包络拟合易引发光谱分辨率下降及检测限劣化问题，提出并实现了基于飞秒激光微加工的并行FBG高灵敏温度传感器，结合免包络游标方法实现了灵敏度与检测限的双重优化。

实验结果表明，在预设放大因子为10倍和20倍情况下，传感器温度灵敏度分别达到110.18 pm/℃及208.51 pm/℃，相比原始FBG，分别提高约11.2倍和21.3倍。与此同时，利用免包络游标方法，实现了温度检测限的优化 (下降约43.3%)，展现出优良的温度传感性能。另外，论文还提出了简化的双FBG结构，在实现免包络游标增敏的同时，进一步降低传感器的制作成本。总之，结合免包络游标方法，本文提供的光纤并行FBG传感器无需物理参考臂，结构紧凑且制备工艺与现有飞秒激光微加工技术兼容，为FBG传感器在高精度温度传感领域的应用提供了新方案。

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2026年第53卷第7期

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doi: 10.12086/oee.2026.260079

接收时间：2026-03-29
首发时间：2026-10-22
出版时间：2026-07-25

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收稿日期：2026-03-29
修回日期：2026-06-24
录用日期：2026-06-29

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聊城大学物理科学与信息工程学院，山东聊城 252000

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姚一村，yaoyicun@lcu.edu.cn

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2种不同金属材料的力学参数

科 Family	属数 Number of genus	种数 Number of species	占总种数比例 Percentage of total species (%)	属 Genus	种数 Number of species	占总种数比例 Percentage of total species (%)
鹅膏菌科Amanitaceae	2	11	5.26	鹅膏菌属 Amanita	10	4.78
小菇科 Mycenaceae	2	12	5.74	丝盖伞属 Inocybe	5	2.39
多孔菌科 Polyporaceae	8	14	6.70	蜡蘑属 Laccaria	5	2.39
红菇科 Russulaceae	3	23	11.00	小皮伞属 Marasmius	6	2.87
				小菇属 Mycena	11	5.26
				光柄菇属 Pluteus	5	2.39
				红菇属 Russula	17	8.13
				栓菌属 Trametes	5	2.39

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