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.