Objective High-sensitivity temperature detection is important for precision temperature control, industrial process monitoring and optical sensing systems. Interferometric fiber sensors, including Mach-Zehnder interferometer (MZI), Sagnac interferometer (SI), Fabry-Perot interferometer (FPI), and Michelson interferometers, have attracted wide attention because of their compact structures, strong immunity to electromagnetic interference, and compatibility with all-fiber systems. However, the temperature sensitivity of a single interferometric sensing structure is usually limited by its optical path difference, material thermo-optic coefficient, and effective sensing length. The Vernier effect can enhance sensitivity by cascading two interferometers with similar but unequal free spectral range (FSR), but physical cascading often increases insertion loss, fabrication difficulty, system size, and environmental crosstalk. To address these limitations, this work proposes a fiber-optic temperature sensor based on an SMF-NCF-FMF-NCF-SMF (SNFNS) sensing structure and the virtual Vernier effect. The SNFNS structure acts as a compact MZI-like modal sensing interferometer, while an ideal SI reference spectrum is digitally generated. By combining FFT-IFFT reconstruction with a virtual reference interferometer, the proposed method enables flexible sensitivity enhancement and avoids the instability associated with physical reference interferometers.

Methods The proposed SNFNS structure consists of single-mode fiber (SMF), no-core fiber (NCF), few-mode fiber (FMF), NCF, and SMF. When light from the input SMF enters the first NCF, the abrupt mode-field mismatch excites higher-order modes in addition to the fundamental core mode. These modes propagate through the FMF section, where part of the optical energy is guided in the core and another part is distributed in the cladding region. The core and cladding modes accumulate different phases and are recombined by the second NCF before coupling into the output SMF, producing a periodic modal interference spectrum. BeamPROP simulations based on the beam propagation method were used to optimize the structure. The results show that an NCF length of 1 cm effectively excites cladding modes while maintaining sufficient core-mode intensity, and an FMF length of 5 cm provides adequate modal interaction with low propagation loss. Therefore, the NCF and FMF lengths were selected as 1 cm and 5 cm, respectively. In the experiment, the output spectrum of the SNFNS sensing interferometer was measured and processed in MATLAB. Fast Fourier transform (FFT) was used to convert the measured spectrum into the spatial-frequency domain. A dominant characteristic peak at 0.13317 nm⁻¹ was observed, indicating that the interference was mainly governed by the fundamental mode and a specific cladding mode. According to the reciprocal relation FSR = 1/f, where f is the spatial frequency, the estimated FSR of the sensing interferometer was 7.509 nm, agreeing well with the measured value of approximately 7.5 nm. The characteristic component was extracted by band-pass filtering, and inverse FFT (IFFT) was used to reconstruct a cleaner sensing spectrum. An ideal SI reference spectrum was then generated in MATLAB by setting the birefringence coefficient of polarization-maintaining fiber and the virtual reference length. Finally, the reconstructed SNFNS spectrum was superimposed with the virtual SI spectrum to obtain the virtual Vernier envelope.

Results and Discussions The temperature response of the standalone SNFNS sensing interferometer was investigated from 30 ℃ to 60 ℃ with a step of 5 ℃ during both heating and cooling. At each temperature point, the sensor was allowed to stabilize before spectral data were recorded. The interference dip shifted toward longer wavelengths as temperature increased and shifted back toward shorter wavelengths as temperature decreased. Linear fitting gave temperature sensitivities of 63.16 pm/℃ during heating and 63.72 pm/℃ during cooling, with fitting coefficients of 0.9989 and 0.9949, respectively, confirming good linearity and repeatability. After the virtual SI reference spectrum was introduced, the sensitivity was greatly enhanced through the virtual Vernier effect. When the virtual SI length was set to 0.6 m, the calculated FSR_SI was 7.7003 nm, slightly larger than the FSR_MZI of the SNFNS sensing interferometer. In this case, the Vernier envelope shifted in the same direction as the SNFNS interference spectrum, namely red-shifting during heating and blue-shifting during cooling. The envelope sensitivity reached 2.4755 nm/℃ during heating and 2.6276 nm/℃ during cooling; the heating-process magnification factor was 39.19, which agrees well with the theoretical value of 39.25 calculated from the FSR relationship. When the virtual SI length was adjusted to 0.63 m, the calculated FSR_SI became 7.334 nm, smaller than FSR_MZI. The Vernier envelope then exhibited the opposite response direction, blue-shifting with increasing temperature and red-shifting with decreasing temperature. The sensitivities were −2.7384 nm/℃ during heating and −2.8868 nm/℃ during cooling, with fitting coefficients of 0.9998 and 0.9978, respectively. The maximum experimental magnification factor was about 43.4, close to the theoretical value of 42.82. These results show that both the magnitude and direction of the temperature response can be adjusted by controlling the relative FSR relationship between the sensing interferometer and the virtual reference interferometer. Stability tests at 30 ℃ and 60 ℃ further verified the reliability of the sensor, with wavelength fluctuation standard deviations of 0.01489 nm and 0.05449 nm, respectively.

Conclusions A high-sensitivity fiber-optic temperature sensor based on an SNFNS sensing structure and the virtual Vernier effect has been designed, fabricated, and experimentally investigated. The NCF sections excite and recombine multiple modes, while the FMF section provides the modal interference region. FFT-IFFT processing extracts and reconstructs the dominant interference component, reducing noise and suppressing unwanted multimode interference. The virtual SI reference spectrum then produces a Vernier envelope without adding physical devices. The standalone SNFNS sensor exhibits a temperature sensitivity of 63.16 pm/℃ in the range of 30-60 ℃. After applying the virtual Vernier effect, the sensitivity is enhanced to 2.4755 nm/℃ with a 0.6 m virtual SI and to −2.7384 nm/℃ with a 0.63 m virtual SI, corresponding to heating-process magnification factors of 39.19 and about 43.4, respectively. The experimental results agree well with theoretical predictions and confirm that the proposed virtual SI approach can flexibly control the Vernier response direction and amplification factor. Owing to its simple fabrication, low insertion-loss requirement, reduced environmental crosstalk, and high linearity, the proposed sensor is promising for high-precision temperature measurement in optical sensing, industrial monitoring, and complex environmental detection.