Fiber optic sensors play an important role in the field of optoelectronics and have advantages such as small size, light weight, high sensitivity, anti-electromagnetic interference, and remote sensing. Temperature detection is one of the most basic applications of fiber optic sensors. Optical fiber temperature sensing is mainly based on the fiber optic grating and interferometer structures. Fiber optic gratings have a relatively low sensitivity to temperature, typically in the order of pm/℃, whereas the temperature sensitivity of fiber interferometers, such as Fabry-Perot (FPIs), Mach-Zehnder (MZIs), and fiber Sagnac interferometers (SIs), is relatively high, reaching the order of nm/℃. However, in some application areas, a temperature sensitivity of the order of nm/℃ still cannot meet the requirements. To further improve the sensitivity of optical fiber interferometers, researchers have recently proposed the ordinary vernier effect (OVE) and harmonic vernier effect (HVE). Both the OVE and HVE are based on two cascaded or parallel interferometers. However, unlike the OVE, the HVE breaks the restriction stating that the optical path differences of cascaded or parallel interferometers in the OVE must be approximately equal. The optical path difference of one interferometer in the HVE can be an integer multiple of that of the other interferometer. Therefore, compared to the OVE, the HVE increases the design freedom of the sensor, which can lower the preparation difficulty to some extent. However, to date, there has been no research reported on this issue. Therefore, this study conducts an in-depth investigation on this issue.

A fiber-optic temperature sensor based on the HVE generated by a cascaded SI and FPI is proposed, in which the free spectral range of the FPI is approximately a multiple of that of the SI. First, we derive the sensitivity and detuning of the proposed sensor when the HVE is generated and then verify them via experiments. To facilitate analysis and verification, the magnifications for different order HVEs are designed to have the same value. In the experiments, by fixing the length of the FPI and adjusting the panda fiber length in the SI, the sensor generates the 0th- (that is, the OVE), 1st-, and 2nd-order HVEs with approximately the same magnification.

Both the simulation and experimental results show that when the free spectral ranges of the FPI and SI satisfy RFSR,FPI=i+1RFSR,SI, the i-order HVE can be generated. If RFSR,FPI>i+1RFSR,SI, the interference spectrum envelope gradually blueshifts with increasing temperature, whereas if RFSR,FPI<i+1RFSR,SI, the interference spectrum envelope gradually redshifts with increasing temperature. For the 0th-, 1st-, and 2nd-order HVEs, the temperature sensitivities of the sensor are 18.88, 18.49, and 17.80 nm/℃, respectively. Compared with that of a single SI, their sensitivity is amplified by 10.12 times, 10.10 times, and 9.64 times, respectively, with corresponding panda fiber length detunings of 48, 90, and 150 mm, respectively. If the amplification is the same, the OVE and HVE have almost the same temperature sensitivity; however, the panda fiber length detuning of the HVE is significantly larger than that of the OVE, and the higher the order of the HVE, the larger the detuning.

A fiber-optic temperature sensor based on the HVE generated by a cascaded SI and FPI is proposed, in which the free spectral range of the FPI is approximately a multiple of that of the SI. By fixing the length of the FPI and adjusting the panda fiber length in the SI, 0th-, 1st-, and 2nd-order HVEs with approximately the same magnification are generated. Both the simulation and experimental results show that if the amplifications are the same, the OVE and HVE have almost the same temperature sensitivity; however, the panda fiber length detuning of the HVE is significantly larger than that of the OVE, and the higher the order of the HVE, the larger the detuning. Therefore, in terms of preparation difficulty, the HVE is evidently better than the OVE.