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Abstract
A compact fiber-optic temperature sensor with hybrid interferometers enhanced by the harmonic Vernier effect was proposed, which realized 36.9 times sensitization of the sensing Fabry-Perot interferometer (FPI). The hybrid interferometers configuration of the sensor consists of a FPI and a Michelson interferometer. The proposed sensor is fabricated by splicing the hole-assisted suspended-core fiber (HASCF) to the multi-mode fiber fused with the single-mode fiber, and filling polydimethylsiloxane (PDMS) into the air hole of HASCF. The high thermal expansion coefficient of PDMS improves the temperature sensitivity of the FPI. The harmonic Vernier effect eliminates the limitation of the free spectral range on the magnification factor by detecting the intersection response of internal envelopes, and realizes the secondary sensitization of the traditional Vernier effect. Combing the characteristics of HASCF, PDMS, and first-order harmonic Vernier effect, the sensor exhibits a high detection sensitivity of −19.22 nm/°C. The proposed sensor provides not only a design scheme for compact fiber-optic sensors, but also a new strategy to enhance the optical Vernier effect.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
As a fundamental physical quantity, accurate measurement of temperature is critical in biomedical diagnostics, industrial production, and environmental monitoring. Owing to its excellent properties, such as miniaturization, anti-electromagnetic interference, and corrosion resistance, the fiber-optic sensor has been applied widely to temperature detection in recent years [1–5]. However, the temperature sensitivities of the fiber-optic sensors are limited by the thermal expansion coefficient (TEC, 5.5 × 10−7/°C) and thermo-optic coefficient (TOC, 6.7 × 10−6/°C) of silica [5].
In past decades, various researches have been conducted to enhance the sensitivity of the fiber-optic temperature sensor [6–11]. There are primarily three approaches for fiber-optic sensors to enhance temperature sensitivity. The first approach involves the introduction of special fiber into the sensor, such as photonic crystal fiber [6,7], polarization maintaining fiber [8,9], hollow core fiber [10,11], and so on. Combining the microstructure or sensing mechanism of the special fiber, the sensitivity of the temperature sensor can be improved. Among the special fibers, the hole-assisted suspended-core fiber (HASCF) has drawn extensive attention due to its unique microstructure, which can realize the design of the sensor with high integration, high sensitivity, and composite structure. The second approach is combined with the thermo-sensitive materials, which exhibit a more sensitive response to external temperature variation than silica. As an excellent thermo-sensitive material, polydimethylsiloxane (PDMS) has been introduced into the fiber-optic sensor in recent years [12–16]. The third approach is combined with the optical Vernier effect, which can improve the sensitivity of the temperature sensor by detecting the response of the spectral envelope. Recently, various sensors based on Vernier effect have been provided for temperature measurement [17–21]. However, due to the limitation of the free spectral range (FSR) on the magnification factor, the sensors based on Vernier effect are challenging to achieve several hundred times magnification factor. To enhance the sensitivity of temperature sensors based on Vernier effect, the harmonic theory is introduced into the optical Vernier effect. By detecting the intersection response of internal envelopes, the fiber-optic temperature sensor based on harmonic Vernier effect can reduce the impact of peak intensity fluctuations and increase the temperature sensitivity by i + 1 times (i is the harmonic order) [22].
In this work, we proposed a fiber-optic temperature sensor based on the compact hybrid Fabry-Perot interferometer-Michelson interferometer (FPI-MI) configuration, and introduced the PDMS and first-order harmonic Vernier effect into the sensor for sensitization. The hybrid configuration of the sensor is fabricated by splicing the HASCF to the multi-mode fiber (MMF) fused with the single-mode fiber (SMF), and filling PDMS into the air hole of HASCF. Compared with the above sensors based on PDMS and Vernier effect, the proposed sensor combines the unique microstructure of HASCF, the high TEC of PDMS, and the first-order harmonic of optical Vernier effect, which can achieve compact structure and high sensitivity for temperature detection. This paper analyzes the theories of the harmonic Vernier effect, describes the principle and fabrication of the sensor, and investigates the temperature performance of the sensor.
2. Principle and fabrication
2.1 Principle of the harmonic Vernier effect
The fiber-optic sensor utilizes the slight difference in the optical path lengths (OPLs) of two fiber interferometers to achieve Vernier effect sensitization. The magnification factor can be adjusted by controlling the OPLs of two fiber interferometers. In the following, we analyze the principle of the harmonic Vernier effect based on the parallel configuration of fiber FPI and fiber MI. As shown in Fig. 1(a), the fiber FPI consists of an air cavity and the fiber MI consists of two silica arms. The reflective spectra of two fiber interferometers can be expressed as
Fig. 1. (a) Schematic diagrams and spectra of two fiber interferometers. Inset: the above is FPI and the below is MI. (b) Simulated temperature responses of two fiber interferometers.
The reflective spectra and temperature responses of two fiber interferometers have been simulated and analyzed, as shown in Fig. 1, where Fig. 1(a) corresponds to reflective spectra and Fig. 1(b) corresponds to temperature responses. The simulation parameters were set as follows: E0 = 1, σ1 = 0.4, σ2 = 0.2, n1 = nair = 1.0, n2 = nSMF = 1.46, L1 = L2 = 300.0 µm. The TOC and TEC of SMF are 6.7 × 10−6/°C and 5.5 × 10−7/°C, respectively, and temperature changes from 25 °C to 75 °C. It can be found that the FSRs of the fiber FPI (FSRFPI) and fiber MI (FSRMI) are 4.0 nm and 2.7 nm, respectively. The reflective spectra of fiber FPI and fiber MI experiences blue shift with increasing temperature, corresponding temperature sensitivities are 0.8 pm/°C and 11.3 pm/°C, respectively.
Due to the dual filtering of fiber FPI and fiber MI, the reflective spectrum of the sensor produces periodic interference fringes, resulting in a periodic spectral envelope. The reflective spectrum of the spectral envelope can be described as [23]
where a is the amplitude; b is a constant.The FSR of the spectral envelope (FSREnvelope) and the magnification factor of the sensor (M) can be described as [23]
Due to the limitation of the FSR on the magnification factor, the sensors based on Vernier effect are challenging to achieve several hundred times magnification factor. To improve the sensitivity of the sensor based on Vernier effect, the harmonic theory is introduced into the optical Vernier effect. To explore the influence of harmonic theory on the optical Vernier effect, the OPL of the fiber FPI is added with i-times the OPL of the fiber MI, OPLFPI = n1L1 + in2L2, where i is the harmonic order. When i = 0, the corresponding basic Vernier effect. The FSR of the fiber FPI with i-order harmonic is now described as [22]
The spectral envelope FSR of the sensor based on i-order harmonic ($FSR_{Envelope}^{i}$) can be described as
It can be found from Eq. (6) that the sensors based on different harmonic orders have the same FSR of the spectral envelope.
The influence of harmonic theory on the optical Vernier effect has been studied by simulating the fiber-optic sensors with Vernier effect sensitization based on different harmonic orders. The OPL of fiber FPI can be adjusted by changing the cavity length to achieve different harmonic orders. The cavity lengths of fiber FPI in the following simulations are set to 365.1 µm, 199.2 µm, 137.0 µm, and 104.4 µm, corresponding to zero-order harmonic to third-order harmonic, respectively. The length of the fiber MI is set as 300.0 µm. The simulated reflective spectra of the sensors based on different harmonic orders are illustrated in Fig. 2. The black lines and the color lines are the spectral envelopes and the internal envelopes, respectively. Figure 2(a)-(d) correspond to the basic Vernier effect, first-order harmonic, second-order harmonic, and third-order harmonic, respectively. The spectral envelopes in Fig. 2(b)-(d) shift slightly downward to distinguish them from the internal envelopes.
Fig. 2. Simulated reflective spectra (a) Basic Vernier effect, (b) First-order harmonic, (c) Second-order harmonic, and (d) Third-order harmonic.
It can be found that the sensors based on different harmonic orders have the same FSR of the spectral envelope, which is consistent with Eq. (6). The introduction of i-order harmonic does not change the FSR of the spectral envelope, while produces high-frequency interference fringes in the reflective spectra. The FSR of the internal envelope is i + 1 times that of the spectral envelope, and the spectral envelopes of the sensors based on odd-order harmonics present a π-shift. Thus, the FSR of the internal envelope ($FSR_{Internal \; Envelope}^{i}$) and the magnification factor (Mi) of the sensor based on the i-order harmonic can be defined as [22]
As seen in Eq. (7) and Eq. (8), the sensor based on harmonic Vernier effect can achieve i + 1 times sensitivity improvement by detecting the internal envelope response.
The temperature responses of the sensors based on different harmonic orders have been simulated and analyzed, and temperature changes from 25 °C to 75 °C. Figure 3(a) and (b) illustrate the temperature responses of the sensors with different harmonic orders and the internal envelope shift versus temperature, respectively. It shows that the reflective spectra of the sensors based on different harmonic orders all exhibit red shift with temperature increasing, corresponding the temperature sensitivity are 63.3 pm/°C, 120.7 pm/°C, 168.9 pm/°C, and 230.1 pm/°C, respectively. The temperature sensitivity of the sensor based on high-order harmonic Vernier effect is about i + 1 times that of the sensor based on basic Vernier effect, which is consistent with the above theories. The harmonic Vernier effect achieves i + 1 times sensitivity improvement of the traditional Vernier effect.
Fig. 3. (a) Simulated temperature responses of the sensors based on different harmonic orders, b) Internal envelope shift of the sensors versus temperature.
2.2 Principle and fabrication of the sensor
The schematic diagram of the sensor is illustrated in Fig. 4(a). The sensor with a hybrid configuration consists of a FPI and a MI, which is fabricated by splicing the HASCF to the MMF (60/125 µm) fused with the SMF (8.2/125 µm), and filling PDMS into the air hole of the HASCF. Figure 4(b) displays the three-beam interference model of the sensor. There exist primarily three reflected beams (I1, I2, and I3) and three reflectors (M1, M2, and M3) in the sensor. The optical paths of three reflected beams are as follows: The input beams entered MMF through SMF, distributed into multiple beams, and then transmitted to the HASCF. The I1 is reflected at the M1. The I2 and I3 entered the air hole and core of the HASCF, respectively, and reflected at the M2 and M3. The interference signal of the proposed sensor is composed of three reflected beams, which can be considered the superposition of the FPI and MI. I1 and I2 formed the FPI. I1 and I3 formed the MI.
Therefore, the reflective spectrum of the sensor can be described as
For the proposed sensor, the fiber FPI and the fiber MI are sensitive to temperature variation. For the fiber FPI, the L1 changes owing to the thermal expansion effect (TEE) of SMF and PDMS, and the n1 changes caused by the thermo-optic effect (TOE) of air can be ignored. The L1 changes caused by the TEE of PDMS is the half of the L3 changes; for fiber MI, the L2 and n2 change owing to the TEE and TOE of SMF. Therefore, the wavelength shift of fiber FPI (Δλ1) and fiber MI (Δλ2) can be expressed as
The proposed sensor achieves the first-order harmonic Vernier effect by controlling the lengths of two fiber interferometers and the filled PDMS, realizing two times sensitivity improvement of the traditional Vernier effect. The wavelength shift of the internal envelope ($\Delta \lambda _{Internal\;envelope}^{i}$) can be written as
Therefore, the temperature sensitivity of the sensor (SSensor) can be described as
For the fiber-optic sensors, the resolution (RSensor) and detection limit (DLSensor) are important indicators. The RSensor can be determined by three standard deviation models of systematic noises [24]. The RSensor can be described as
The proposed sensor with a low Q-factor (Qsensor=λ/ΔλFWHM = 28.2) is limited by the spectral resolution and spectral fluctuation noise [25]. The ΔλFWHM is the full-width at half-maximum. The σspectral-resolution can be modeled as a quantitative error. For the optical spectrum analyzer (OSA) with a determinate error of 0.5 pm and a spectral resolution of 1 pm, the σspectral-resolution is 0.29 pm [24]. Thus, the σspectral-resolution of the proposed sensor is 5.8pm. The σamplitude -noise can be determined by ΔλFWHM and signal-noise ratio (SNR) [24]
The DLSensor can be calculated by the ratio of RSensor to SSensor. Therefore, the DLSensor can be described as
The reflective spectrum and temperature response of the sensor have been simulated, and the parameters were set as follows: E0 = 1, L1 = 187.6 µm, L2 = 266.0 µm, L3 = 78.4 µm, α1 = 0.4, α2 = 0.2, n1 = nair = 1.0, n2 = nSMF = 1.46, nPDMS = 1.41, respectively. The TEC of the SMF and PDMS are 5.5 × 10−7/°C and 9.6 × 10−4/°C, respectively. The TOC of the SMF is 6.7 × 10−6/°C. The temperature changes from 42 °C to 43 °C. Figure 5(a) illustrates the simulated reflective spectrum, in which the spectral envelopes shift slightly downward to distinguish them from the internal envelopes. There are a periodic envelope and two periodic internal envelopes in the reflective spectrum, and the FSR of the internal envelope is two times that of the spectral envelope. The simulated temperature response is illustrated in Fig. 5(b). The internal envelope had a blue shift of 19.51 nm as the temperature increased from 42 °C to 43 °C. The simulated temperature sensitivity was 19.5 nm/°C.
Figure 6(a) displays the cross-sectional microscope image of the HASCF, which has an air hole (40 µm) in the middle of the cladding (125 µm) and a core (9.1 µm) suspended in the air hole. The fabrication processes are illustrated in Fig. 6(b)-(e). The PDMS precursor was synthesized by mixing elastomer and curing agent in a ratio of 10:1. Firstly, the MMF was spliced to the SMF and cleaved to a designed length like Fig. 6(b). Secondly, the HASCF was spliced to the cleaved MMF and cleaved to a designed length like Fig. 6(c). Thirdly, as shown in Fig. 6(d), the prepared structure was immersed in the PDMS precursor. Due to the capillary effect, the PDMS precursor gradually filled into the air hole of HASCF. The filling length of the PDMS precursor can be adjusted by controlling the time of capillary effect and the concentration of the PDMS precursor. Finally, the sensor was baked in the temperature-controlled furnace at 80 °C for 2 hours, as shown in Fig. 6(e).
Figure 7(a) illustrates the microscope image of the proposed sensor. The sensor is composed of a hybrid configuration of fiber FPI and fiber MI, which realizes the first-order harmonic Vernier effect by controlling the lengths of two fiber interferometers and the filled PDMS. The lengths of the MMF, the fiber FPI cavity (L1), the fiber MI (L2), and the filled PDMS (L3) are 157.0 µm, 187.6 µm, 266.0 µm, and 78.4 µm, respectively. The spectrum of the proposed sensor is illustrated in Fig. 7(b). There are a periodic envelope and two periodic internal envelopes in the reflective spectrum. The intersection of two internal envelopes is located at the maximum value of the periodic envelope, which is consistent with the simulation results.
3. Experiments and discussion
Figure 8 shows the temperature sensing system. The broadband light source (YSL SC-5) emits broadband light with a spectral range of 1400-1600 nm, which is transmitted to the sensor through the optical circulator. The light reflected by the sensor is detected by the OSA (YOKOGAWA AQ6370C) with a resolution of 0.02 nm. The temperature-controlled furnace displays and controls the ambient temperature of the sensor in the range of 10-110 °C.
The temperature performances of the sensor have been investigated through temperature sensing experiments, repeatability experiments, and stability experiments. In the temperature sensing experiment, the temperature response of the sensor is explored by detecting the intersection of internal envelopes in the reflective spectrum. The sensor is sealed in a temperature-controlled furnace to measure temperature variation, and the temperature variation is 41-44 °C in a step of 0.2 °C.
Figure 9(a) illustrates the spectra of the sensor at 41 °C, 42 °C, 43 °C, and 44 °C. It is obvious that the intersection of internal envelopes exhibited a blue shift as the temperature increased from 41 °C to 44 °C. Figure 9(a) displays the intersection shift of internal envelopes versus temperature. The detection sensitivity of the sensor is −19.22 nm/°C (R2 = 0.9968). The error bar has been introduced into the experimental results to investigate the uncertainty and potential error of the sensor.
Fig. 9. (a) Spectra of the sensor at 41 °C, 42 °C, 43 °C, and 44 °C, (b) Intersection shift of internal envelopes versus temperature.
In the repeatability experiment, the temperature in the temperature-controlled furnace gradually increased from room temperature (25 °C) to 44 °C, and then progressively reduced to 41 °C. The temperature repeatability of the sensor is shown in Fig. 10(a). It can be found that the intersection of internal envelopes shifted linearly with temperature, and the temperature sensitivities were approximately the same during the temperature increasing and decreasing (R2 > 0.9960). In the stability experiment, the sensor was continuously measured at 42.6 °C for 60 minutes. The temperature stability of the sensor was investigated by measuring the movement of the peak/valley near 1550 nm and the internal envelope intersection. The temperature repeatability of the sensor is illustrated in Fig. 10(b). It shows that the reflection spectrum of the sensor had barely shifted over 60 minutes.
Experimental results illustrate that the sensor realizes two times sensitivity improvement of the traditional Vernier effect through detecting the intersection response of internal envelopes, which is consistent with theoretical analyses. The sensor exhibits excellent repeatability and stability for temperature measurement, and provides a detection sensitivity of −19.22 nm/°C. According to Eqs. (12)–(15), the temperature detection limit of the sensor can reach 2.5 × 10−2 °C. The temperature performance of the sensor can be further improved by adjusting the order of harmonic and the parameters of two fiber interferometers.
Table 1 illustrates the temperature performance indicators of two fiber interferometers and the sensor. Compared with two fiber interferometers, the temperature sensor with hybrid interferometers enhanced by harmonic Vernier effect exhibits more excellent temperature performance. The sensor has significantly improved the temperature sensitivity of fiber interferometers, and its sensitivity can reach −19.22 nm/°C, which is 36.9 times that of the fiber FPI.
Table 1. Temperature performance indicators of two fiber interferometers and the sensor
The comparison of temperature sensing performance between our sensor and recently reported temperature sensors is illustrated in Table 2. Compared with the temperature sensors reported in recent years, the proposed sensor exhibits higher sensitivity for temperature sensing and obtains a larger magnification factor. By adjusting the parameters of two fiber interferometers and the order of harmonic, the temperature performance of the proposed sensor can be further improved. Therefore, the proposed sensor is suitable for high sensitivity and accuracy temperature measurement.
Table 2. Comparison of temperature sensing performance between our sensor and recently reported temperature sensors
4. Conclusion
In conclusion, we have proposed a compact hybrid interferometers temperature sensor based on PDMS-filled HASCF and harmonic Vernier effect, and investigated its temperature performances through theoretical analyses and characteristic experiments. The sensor exhibits excellent repeatability, high sensitivity, and stability for temperature measurement. Combing the characteristics of HASCF, PDMS, and first-order harmonic Vernier effect, the detection sensitivity of the sensor can reach −19.22 nm/°C. The sensor eliminates the limitation of the FSR on the magnification factor by detecting the intersection response of internal envelopes, and achieves two times sensitivity improvement of the traditional Vernier effect. Owing to its excellent properties, the sensor exhibits potential applications in temperature detection. Besides, the proposed sensor provides a new strategy for the design of compact fiber-optic sensors and the improvement of the optical Vernier effect.
Funding
National Natural Science Foundation of China (51777046); Natural Science Foundation for Post-doctoral Scientists of Heilongjiang Province (LBH-Z19070, LBH-Z22193).
Disclosures
The authors declare no conflicts of interest.
Data availability
No data were generated or analyzed in the presented research.
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