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Abstract
The wavelength of microwave is longer than that of lightwave, causing the interferometric optical path difference induced by the measurand changes to be relatively smaller than that of microwave, which results in the lower sensitivity of sapphire fiber Fabry-Perot interferometer (FPI) sensor in microwave band. To improve sensitivity, a parallel FPI sensing system is constructed, in which a section of sapphire fiber connected to a single-mode transmission fiber is used as a sensing FPI, and a single-mode fiber (SMF) with a slightly different optical path from a sensing FPI is utilized as a reference FPI. By connecting two FPIs in parallel, Vernier effect is formed to improve sensitivity. The influence of relationship between the optical path difference of the reference FPI and the sensing FPI on the sensitivity amplification factor is analyzed based on the microwave interference spectrum of the parallel FPI. A section of sapphire fiber with the length of 8 cm is used as temperature sensor to construct high-temperature sensing system. The results demonstrate that the temperature sensitivity reaches about 2338.68kHz/°C, which is approximately 130 times higher than that of the sensing FPI alone. Furthermore, when the difference of optical path between the sensing FPI and the reference FPI is kept constant while the sensing FPI is unchanged, the amplification factor of the temperature sensitivity is approximately 2.64 times higher with longer length of the reference FPI compared to the situation with shorter length of the reference FPI.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Single-crystal sapphire fibers have attracted increasing attention due to their advantages such as high melting point (∼2040°C), high mechanical strength, and good chemical stability [1]. Furthermore, sapphire fiber made with high-concentration Al2O3 exhibits transparency in ultraviolet to infrared wavelength range, making it possible to fabricate sapphire fiber-based high-temperature sensor [2]. Therefore, there is significant potential for its application in the field of harsh environment testing under ultra-high temperatures [3].
The interferometric high temperature sensor based on the sapphire fiber uses multi-beam Fabry-Perot interference as sensing mechanism [4], and possesses advantages such as a compact structure [5], easy fabrication [6], and a broad temperature measurement range [7]. However, as a kind of large core diameter fiber, sapphire fiber has multiple internal modes [8], and interference between these modes resulting in mode interference effects, which have a significant impact on the quality of the FPI’s spectrum and consequently its sensing performance [9].
The fiber FPI sensing system based on microwave photonics uses lightwave as the carrier signal and microwave as the modulation signal [10], thereby shifting the modulation and demodulation frequency domain from the high-frequency, easily-interfered optical interference domain to the low-frequency, stable microwave-photonic interference domain [11]. By using lightwave as the carrier signal and microwave as the modulation signal, both signals are introduced into the sensor. When the sensor is affected by the measurand, the reflected interference signal of the sensor contains both lightwave and microwave [12]. By demodulating only the microwave signal with respect to the measurand changes in the detected signal [13], the problem of interference between internal modes of sapphire fiber can be avoided, thus reducing measuring error [14].
However, because of the longer wavelength of microwave compared to lightwave, the optical path difference caused by the measurand changes is relatively small in the microwave band, and leading to low sensitivity of the sensor. For example, a temperature sensor based on a Michelson interferometer made of two sapphire fibers with lengths of 0.7 m and 0.85 m had a sensitivity of only −64 kHz/°C, relative to the GHz-level microwave frequency, as reported by Clemson University [15]. To improve sensitivity, some studies have reported the amplification of the sensitivity based on the Vernier effect. Chen Zhu et al. [16] used a 7.568 m SMF as reference FPI, while another 7.854 m SMF was used as temperature sensing FPI. The two FPIs were cascaded to form the Vernier effect, which increased the temperature sensitivity of sensing FPI to −266.1kHz/°C. In the following year [17], they used SMFs to create a cascaded distributed strain sensor, where reference FPI was 2.174 m, and sensing FPIs were 2.081 m and 2.322 m, respectively. The Vernier effect was applied to increase the strain sensitivity of the two cascaded sensors from −1.04 kHz/µm and −0.685 kHz/µm to 22.59 kHz/µm and −11.21 kHz/µm, respectively. In the same year [18], they employed SMFs with FPI lengths of 2.076 m and 2.314 m, along with a virtual reference FPI with a slightly different optical path, to form a distributed strain sensing system based on the Vernier effect. Increasing the sensitivity of the sensor from −3.677kHz/µɛ and −3.321kHz/µɛ to −387.2kHz/µɛ and −343.7kHz/µɛ, respectively.
In the case where the thermal expansion coefficient, thermo-optic coefficient, and refractive index (RI) of fiber sensors are unchangeable, sensitivity can also be improved by increasing the length of the sensor. For example, Zuowei Xu et al. [19] utilized a 200m-long SMF as temperature sensing FPI and cascaded it with another slightly different length single-mode fiber as the reference FPI. The Vernier effect was used to increase the temperature sensitivity of the sensor from −19.068kHz/°C to −556.856kHz/°C. Yixin Zhang et al. [20] used two SMFs of lengths 210 m and 201 m respectively as a strain sensor, and by forming the Vernier effect, the strain sensitivity was increased by about 20 times, reaching −910.67 kHz/µɛ. However, large-sized temperature sensors with sensing lengths in meters have comparably poor adaptability in application. Thus, it is necessary to improve the sensitivity of the sensor while reducing its size.
In this study, a parallel FPI temperature sensing system is constructed, in which a section of sapphire fiber connected to a single-mode transmission fiber as a sensing FPI and a SMF with slightly different optical path as a reference FPI. By connecting the two FPIs in parallel, Vernier effect is formed to improve the sensitivity of the sensor. The impact of the relationship between the optical path of the reference FPI and the sensing FPI on the sensitivity amplification factor is analyzed. A section of 8 cm sapphire fiber is used as temperature sensor, the sensing system for high temperature experiments is constructed. The results demonstrate that the temperature sensitivity of the parallel FPI reaches about 2338.68 kHz/°C, which is about 130 times higher than that of sensing FPI alone. When the difference of optical path between the sensing FPI and the reference FPI is kept constant while the sensing FPI is unchanged, the amplification factor of the sensitivity of the sensor is increased by 2.64 times with longer length of the reference FPI compared to the situation with shorter length of the reference FPI.
2. Principle and simulation
Figure 1 illustrates the schematic of the paralleled FPI sapphire fiber temperature sensing system based on microwave photonics. The electro-optic modulator (EOM) simultaneously receives the optical signal generated by the ASE broadband light source and the microwave signal emitted by the vector network analyzer (VNA). And then the microwave-modulated optical signal is formed. The signal is amplified by the erbium-doped fiber amplifier (EDFA) before enters optical circulator and then divided into two parallel light paths via a 3 dB coupler. A SMF is used as a reference FPI, with the optical path from the coupling point of 3 dB coupler to the far end face of SMF. A section of sapphire fiber connected to the single-mode transmission fiber is used as a sensing FPI (only the sapphire fiber is used for temperature sensing), with the optical path from the coupling point of 3 dB coupler to the far end face of sapphire fiber. Vernier effect is then formed by the two paralleling FPIs. The reflected signals from the two paths are detected by photodetector (PD) after passing through by the optical circulator, and then enter VNA for synchronized detection within the microwave frequency range Ω. The reflected frequency spectrum (i.e., parameter S21) is analyzed.
Fig. 1. Schematic of the paralleled FPI sapphire fiber temperature sensing system based on microwave photonics.
If the reflected frequency interference spectra of the sensing FPI WSEN(f) and the reference FPI WREF(f) are detected separately, we can get [21]:
The resonance frequency of sensing FPI fSEN is given by:
where k is an integer and fSEN denotes the resonance frequency of the k-th order.The optical path of the sensing FPI changes with variations in the ambient temperature, leading to changes in the resonant frequency. As a result, the temperature sensitivity SSEN can be calculated as:
Connecting the reference FPI and the sensing FPI in parallel, the output spectrum of the parallel FPI Wpara(f) is obtained by sum-to-product-formulas of cosine functions:
Based on Eq. (1), Eq. (2), and Eq. (5), simulation of the paralleled FPI sapphire fiber sensing system based on microwave photonics is conducted, as shown in Fig. 2.
Fig. 2. Simulated interferometric spectra of paralleled FPI sapphire fiber system based on microwave photonics. (a) Reference FPI, (b) Sensing FPI, (c) Paralleled FPI. (nSMF = 1.468, nSF = 1.75, LREF = 2.72 m, LSMF = 2.7 m, LSF = 0.06 m, g = 1, R = 0.5, I = 1, M = 1, c = 3 × 108 m/s, Ω=8.5 GHz, LREF × nSMF = 4 m, LSMF × nSMF + LSF × nSF =4.065 m).
The free spectral range (FSR) difference between the reference FPI and the sensing FPI is relatively small, as shown in Fig. 2. The parallel FPI exhibits a distinct envelope (represented by the red dashed line in Fig. 2), which is the beat frequency signal formed by the Vernier effect.
It can be seen from Eq. (5) that the output spectrum of the parallel FPI contains both the sum-frequency component and the beat-frequency envelope signal. By extracting the beat-frequency envelope signal, the resonant frequency fENV can be obtained by:
When the ambient temperature changes, the resonant frequency of the parallel FPI also changes, and the change amount is larger than that of the sensing FPI. The temperature sensitivity of the measured resonant frequency of the parallel FPI SENV is given by:
To analyze the impact of the length relationship between the reference FPI and the sensing FPI on the sensitivity, the ratio of the optical path of the reference FPI and the sensing FPI during the temperature change is defined as N:
Then Eq. (7) is rewritten by:
The temperature sensitivity SENV of the paralleled FPI envelope signal is related to SSEN (which is the sensitivity of the sensing FPI) and the amplification factor A. If length of sensing FPI increases, the SSEN increases, also the SENV. To meet requirement of the practical application, length of the sensing FPI needs to be deceased.
To reduce the length and improve the sensitivity at the same time, we can try to increase the A in Eq. (9). It can be observed that the temperature sensitivity of the resonant frequency of the paralleled FPI is amplified by a factor of A compared to the temperature sensitivity of the resonant frequency of sensing FPI alone.
According to Eq. (9), the amplification factor of temperature sensitivity A is affected by the ratio N between the optical paths of the reference FPI and the sensing FPI during temperature change process. It can be seen from Eq. (8) and Eq. (9) that, if LSMF remains unchanged, LSF has little effect on N, because LSF is 2 orders of magnitude smaller than that of LSMF for system configuration in Fig. 1 and simulation parameters in Fig. 2. Furthermore, if LSF changes a lot, the value of N can still be fixed by altering the values of LREF and LSMF, thus obtaining a fixed amplification factor A.
To further investigate the impact of N on the amplification factor A, simulations based on Eq. (9) are conducted. Two cases are considered: N > 1 and N < 1, while the optical path of sensing FPI being kept fixed, as shown in Fig. 3(a).
Fig. 3. Two cases of paralleled FPI, N < 1 and N > 1. (a) Configuration of paralleled FPI, (b) The relation between the amplification factor and temperature. The optical path difference between reference FPI and sensing FPI is the same for N < 1 and N > 1, that is, ΔN < 1=ΔN > 1. LREF × nSMF = 4 m, LSMF × nSMF + LSF × nSF = 4.065 m when N < 1. LREF × nSMF = 4.13 m, LSMF × nSMFLSF × nSF = 4.065 m when N > 1. The initial amplification factor before temperature change is represented as a and set as 62.5.
According to Fig. 3(b), it can be observed that when the ratio of the reference FPI length to the sensing FPI length N is less than 1, the absolute value of the amplification factor A gradually decreases with increasing temperature. In contrast, when N > 1, the absolute value of A gradually increases with temperature. Additionally, A is positive when N < 1, and negative when N > 1. The sign of A affects the shift direction of the resonant frequency of the parallel FPI.
The resonance frequency fSEN of the sensing FPI decreases with increasing temperature, leading to a leftward shift of the interference spectrum. As a result, when N < 1, the amplification factor A > 0, fSEN and fENV move in the same direction. This implies that the envelope resonance frequency of the parallel FPI fENV shifts towards the low-frequency direction. In contrast, when N > 1, fENV shifts towards the high-frequency direction, as illustrated in Fig. 4.
Fig. 4. Envelope shifting of parallel FPI during heating. The parallel FPI with N < 1 is changed by −0.926 GHz. The parallel FPI with N > 1 is changed by 1.262 GHz.
Simulations of the sensing characteristics of the parallel FPI are conducted for two cases, N > 1 and N < 1, as shown in Fig. 5.
Fig. 5. Resonance frequency shifts of paralleled FPI with both N > 1 and N < 1 as a function of temperature. For N > 1, the temperature sensitivity of parallel FPI SN > 1 is observed to be 1262kHz/°C, which is approximately 74 times higher than that of sensing FPI alone. In the case of N < 1, the temperature sensitivity of parallel FPI SN < 1 is −926kHz/°C, with an amplification factor of approximately 54 times. The ratio of the sensitivity amplification factor K was found to be 1.36.
It can be observed from Fig. 5 that, the temperature sensitivity of the parallel FPI SN > 1 of N > 1 is higher than SN < 1 of N < 1, meaning a larger amplification factor A can be achieved. Combining with Eq. (6), the ratio of the sensitivity amplification factor K can be calculated as:
Based on the analysis above, it can be concluded that when the optical path difference between the reference FPI and the sensing FPI is the same, a larger amplification factor A can be obtained by setting the ratio of the reference FPI optical path length to the sensing FPI optical path length N > 1 (i.e., the reference FPI is longer than the sensing FPI), which can improve K times compared to that when N < 1. In addition, it can be observed that the amplification factor A is barely independent of the length of sensor, and only related to the ratio N of the optical path length between the reference FPI and the sensing FPI. This means that the size of sapphire fiber of the sensing FPI can be reduced while keeping the sensitivity amplification factor A unchanged.
3. Experimental results and discussion
To verify the theoretical analysis above, a high-temperature experimental system of the paralleled FPI based on microwave photonics was set up, as shown in Fig. 6. The first reflecting surfaces of both the sensing FPI and the reference FPI and are formed by the air gap between the fiber end-face of the 3 dB coupler output port and the end-face of a SMF. The sapphire fiber was 100µm in diameter, made by Shandong University with self-made Laser Heated Pedestal Growth (LHPG) furnace. The sapphire fiber was jointed to the single-mode transmission fiber by mechanical splice with customized ceramic ferrule. The sapphire fiber segment of the sensing FPI was placed in a high-temperature Muffle furnace while the transmission SMF (Corning SMF−28e+) was placed outside of the furnace at room temperature. Meanwhile, a standard type N (provided by the muffle furnace manufacturer CARBOLITE GERO) thermocouple was also placed to measure the real-time temperature. High-temperature experiments was carried out by gradually increasing the temperature from 100°C to 1100°C in steps of 100°C.
As shown in Fig. 7, the frequency interference spectra of the reference FPI, the sensing FPI, and the parallel FPI were obtained at room temperature. The envelope of the parallel FPI signal interference spectrum (red dashed line in Fig. 7(a)) was extracted, as shown in Fig. 7(b).
Fig. 7. Characteristic results of the paralleled FPI sapphire fiber system based on microwave photonics. (a) The frequency interference spectra of the reference FPI, the sensing FPI and the paralleled FPI, respectively. (b) The extracted spectrum of the envelope of the paralleled FPI. LREF × nSMF = 3.83 m, LSMF × nSMF + LSF × nSF = 3.78 m, N > 1.
The spectrum shifting of the sensing FPI was tracked during the heating process, as shown in Fig. 8.
The slight shift towards lower frequency as the temperature increases of the sensing FPI spectrum can be observed, as shown in Fig. 8, which indicates low temperature sensitivity of the sensing FPI.
In order to perform comparative analysis, two sets of experiments were conducted. In the first set of experiments, the reference FPI was longer than the sensing FPI (i.e., N > 1). In the second set of experiments, the reference FPI was shorter than the sensing FPI (i.e., N < 1), the detailed configuration was shown in Table 1 (considering the RI of SMF and SF are 1.468 and 1.75, respectively).
Table 1. Configuration of two comparative experiments.
The shifting of the paralleled FPI spectrum is observed during the heating process. when N > 1, the envelope spectrum gradually shifts towards the high frequency direction. When N < 1, the envelope spectrum gradually shifts towards the low frequency direction (as shown in Fig. 9(b)). Furthermore, the frequency shifts when N > 1 is greater than that when N < 1. This is consistent with the theoretical analysis which indicates there is a negative amplification factor AN > 1 when N > 1, and a positive amplification factor AN < 1 when N < 1, and |AN > 1|>|AN < 1|.
Fig. 9. Shifts of the paralleled FPI envelope spectrum during heating. (a) Envelope spectrum shifts towards high frequency direction when N > 1. (b) Envelope spectrum shifts towards low frequency direction when N < 1.
Two heating experiments were performed for each set, and the results were depicted in Fig. 10(a) and Fig. 10(b). It can be seen that in the case of N > 1, the average temperature sensitivity calculated from the first experiment is found to be 2338.68kHz/°C. However, the temperature sensitivity of the sensing FPI alone is merely −17.98kHz/°C, indicating an amplification factor AN > 1 of approximately 130. In the case of N < 1, the average temperature sensitivity calculated from the second experiment is −884.45kHz/°C, indicating an amplification factor AN < 1 of approximately 50.
Fig. 10. Temperature sensing results of the paralleled FPI. (a) The resonance frequency shifts of the sensing FPI alone and the paralleled FPI with N > 1 as a function of temperature. (b)The resonance frequency shifts of the paralleled FPI with N < 1 as a function of temperature.
By comparing the results of two experiments, it can be concluded that, with the same optical path difference between the sensing FPI and the reference FPI at 0.05 m, the temperature sensitivity of the parallel FPI with N > 1 is higher than that with N < 1, with an improvement of approximately 2.64 times.
Comparing our proposed method with the reported microwave photonics interference temperature sensing system based on the Vernier effect or sapphire fiber, as shown in Table 2, it is evident that the proposed sensing system achieves much higher sensitivity with a reduced sensor size.
Table 2. Comparison of microwave-photonic interferometric temperature sensor based on Vernier effect or sapphire fiber
However, due to the temperature limit of the furnace, we only carried out the experiment to 1100°C. We will test this sapphire fiber sensor performance in higher temperature in the future.
4. Conclusion
In this study, a high sensitivity microwave-photonic sapphire fiber Fabry-Perot interferometry based on the Vernier effect is proposed. By connecting the sensing FPI and the reference FPI with slightly different optical path in parallel, the Vernier effect is formed to improve sensitivity. The impact of the ratio N of the optical path between the reference FPI and the sensing FPI on the amplification factor of sensitivity is analyzed. High-temperature experiments demonstrate that the average temperature sensitivity of the microwave-photonic sapphire fiber Fabry-Perot interferometry temperature sensor can be increased to 2338.68kHz/°C when the sensor size is reduced to 8 cm, which is approximately 130 times higher than that of the sensing FPI alone. With the same difference of optical path between the sensing FPI and the reference FPI, the amplification factor of the sensitivity of the parallel FPI sensor with N > 1 is approximately 2.64 times higher than that with N < 1.
Funding
National Natural Science Foundation of China (51675068, 51975077, 52175530, 61875023).
Disclosures
The authors declare no conflicts of interest.
Data availability
The raw data reduced by the methods of this article to the results are not publicly available at this time but can be made available upon reasonable request.
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