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Abstract
A novel fiber Michelson interferometer (FMI) based on parallel dual polarization maintaining fiber Sagnac interferometers (PMF-SIs) is proposed and experimentally demonstrated for temperature sensing. The free spectral range (FSR) difference of dual PMF-SIs determines the FSR of envelope and sensitivity of the sensor. The temperature sensitivity of parallel dual PMF-SIs is greatly enhanced by the Vernier effect. Experimental results show that the temperature sensitivity of the proposed sensor is improved from −1.646 nm/°C (single PMF-SI) to 78.984 nm/°C (parallel dual PMF-SIs), with a magnification factor of 47.99, and the temperature resolution is improved from ±0.03037°C to ±0.00063°C by optimizing the FSR difference between the two PMF-SIs. Our proposed ultrasensitive temperature sensor is with easy fabrication, low cost and simple configuration which can be implemented for various real applications that need high precision temperature measurement.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Optical fiber temperature sensors have attracted increasing research interest due to their inherent advantages of fast response, high sensitivity, remote sensing capability and electromagnetic immunity [1–3]. Various optical fiber based temperature sensors have been proposed in recent years. In this line, fiber gratings have been implemented in remote and distributed temperature monitoring nevertheless with complex fabrication and relatively lower sensitivity [4]. Furthermore, the interferometers such as fiber Michelson interferometer (FMI) [5,6], fiber Sagnac interferometer (FSI) [7,8], Mach-Zehnder interferometer (MZIs) [9], Fabry-Perot interferometer (FPI) [10,11] have been introduced for temperature monitoring [12]. However, the sensitivity and response of single interferometer is limited by the intrinsic properties of the optical fiber.
To improve the performance of temperature sensing the Vernier effect has been introduced to fiber temperature sensors with enhanced sensitivity in recent years. Most of the Vernier effect based sensors are realized in cascaded interferometer structures, such as two cascaded MZIs [13,14], hybrid interferometers with FMI and FSI [15], two cascaded FSIs with high birefringence fiber [16–18], two cascaded FPIs with polydimethylsiloxane (PDMS) [19], and an FPI cascaded with an FSI [20]. The sensors above consist of two cascaded interferometers, one acts as the reference arm and the other acts as the sensing arm. The dual cascaded interferometers with slightly different free spectrum ranges (FSRs) work as a Vernier calipers, which can amplify the spectra of interferometers and then increase the sensitivity [21]. However, the transmission spectra of cascade configuration only have the upper envelope and wide full width at half maximum (FWHM). For further improvement, some parallel configurations based on Vernier effect have been proposed, such as parallel FMIs for bending sensor [22], parallel dual different structure fiber-optic FPI for strain sensor [23] and parallel FPI for transverse load sensor [24]. However, the fabrication of the above parallel configurations such as FMI constructed by dual-core fiber (DCF) spliced with a short section of dual-side-hole fiber (DSHF) [22] and structured fiber-optic FPI [23,24] is complicated and the repeatability of these devices is low.
In this work, an FMI constructed by parallel dual polarization maintaining fiber Sagnac interferometers (PMF-SIs) with small difference of FSR is proposed for ultrasensitive temperature sensing. The PMF can simplify the fabrication and enhance sensor stability and response. The spectra amplification of the Vernier effect can be enhanced and the clear upper and lower envelop can be obtained by parallel configuration. Compared to single PMF-SI or cascaded PMF-Sis, the temperature sensitivity of parallel dual PMF-SIs is greatly enhanced by the Vernier effect. By optimizing the PMF length difference of the two arms from 0.1 m to 0.03 m, the sensor can achieve an ultrahigh sensitivity increased from 24.285 nm/°C to 78.984 nm/°C. The proposed device has advantages such as ultrahigh temperature sensitivity, and easy fabrication, which shows the potential to be practically applied in applications that need precise temperature control and online temperature monitoring, such as precision processing, medical treatment, biochemical engineering.
2. Theory and simulations
The schematic diagram of the proposed temperature sensor based on FMI consisting of parallel dual PMF-SIs is illustrated in Fig. 1. The FMI temperature sensor is constructed by a 2×2 3dB coupler and parallel dual PMF-SIs. The PMF-SI consists of a section of polarization maintaining fiber (PMF) and a 1×2 3dB coupler. Dual PMF-SIs with slightly different PMF length provide different FSRs to obtain the Vernier effect and work as the sensing arm and reference arm, respectively. The 1×2 3dB coupler in the PMF-SI further splits the light from the 2×2 3dB coupler into two counter-propagating waves and the two waves interfere with each other when they encounter at the 1×2 3dB coupler. We insert a polarization controller (PC) into the PMF-SI reference arm to adjust the polarization state.
For a single PMF-SI, the transmission intensity at a specific wavelength is determined by the phase shift between two counter-propagating waves and it can be calculated as [16]
where B = nslow - nfast is birefringence of PMF; L and λ are the PMF length and the incident light wavelength respectively; θ=2πBL/λ is the phase difference between the two counter-propagating waves [20]. When the phase difference satisfies the equation θ=2mπ (m is an integer), the two waves interfere with each other, resonance dip occurs. The wavelength dips of the interference spectrum are defined at the wavelength And the FSR of single PMF-SI can be derived as When the temperature T changes, the spectral shift of single PMF-SI can be expressed as Here, we have neglected the thermal expansion effect since the wavelength shift induced by the thermal expansion effect is two orders smaller than that of the thermo-optic effect [25]. Then we use a 2×2 3dB coupler to connect dual PMF-SIs in series to construct an FMI at the same time as it is shown in Fig. 1. The dual parallel PMF-SIs are denoted as sensing arm and reference arm, respectively. The transmission spectra are like a ruler which the FSR remains as wide as the range of this ruler. Thus we can enhance the temperature sensitivity by constructing a “Vernier ruler” with parallel dual PMF-SIs. The total transmission spectrum, IP of parallel dual PMF-SIs configuration can be deduced from the transmission spectrum of FMI [23] that can be expressed asMeanwhile, we also make a comparison with the cascaded dual PMF-SIs configuration as it has been shown in Fig. 2, the total transmission spectra IC of cascade PMF-SIs can be derived as,
The envelope FSR of total FMI with parallel dual PMF-SIs is the same as that of cascaded configuration as it can be expressed as where FSRP and FSRC are the FSR of parallel dual PMF-SIs configuration and cascaded dual PMF-SIs configuration, respectively. The FSR of sensing arm can be enlarged with a magnification coefficient, Similarly, the envelope shift of Vernier configuration is magnified M times compared to individual one that can be given asTherefore, when the sensing arm experiences a dip shift Δλ with temperature variation ΔT, the Vernier configuration will undergo an envelope shift MΔλ, which can profoundly enhance the temperature sensitivity.
According to the theory analysis, we simulate the transmission spectrum of single PMF-SI sensing arm and single PMF-SI reference arm according to the Eq. (1). It is obvious from the simulation results shown in Fig. 3(a) and Fig. 3(b), the FSR of single PMF-SI with PMF length of 2.10 m and 1.99 m are 2.54 nm and 2.68 nm, respectively, which are in good agreement with the calculation results according to the Eq. (2) near 1550 nm. After that, we further simulate the transmission envelope spectrum of parallel dual PMF-SIs and cascaded dual PMF-SIs with PMF length difference of 0.11 m. The simulated envelope spectra are shown in Fig. 3(c) and Fig. 3(d). The FSR of parallel dual PMF-SIs and cascaded dual PMF-SIs are both 48.62 nm that is consistent with Eq. (5). It is obvious that the FSR of two Vernier configurations is much larger than single PMF-SI configuration. The magnification coefficients of the two Vernier configurations are both 18 compared to the single sensing arm with PMF length of 1.99 m. Even though the magnification coefficient of two Vernier configuration has the same, the spectra of parallel dual PMF-SIs has much clearer upper and lower envelope compared to that of cascaded dual PMF-SIs and narrower FWHM, as shown in Fig. 3(c) and Fig. 3(d). It responds to the advantages of improving sensing accuracy by tracking the wavelength shift more precision. Thus, we employ the parallel dual PMF-SIs configuration to realize the sensitivity enhancement of temperature sensing.
Fig. 3. The simulation transmission spectra for (a) the single reference arm PMF-SI with PMF length of 2.10 m; (b) the single sensing arm PMF-SI with PMF length of 1.99 m; (c) the cascaded dual PMF-SIs; (d) the parallel dual PMF-SIs.
We simulate the transmission spectra shift of single sensing arm PMF-SIs and parallel dual PMF-SIs with temperature variation by changing the B value as shown in Fig. 4. When we change B from 4.5×10-4 to 4.498×10−4, the resonance dip of single PMF-SI sensing arm shifts 0.68 nm to the shorter wavelength. The blue shift is caused by the negative thermo-optic coefficient of PMF. The envelope spectrum of parallel dual PMF-SIs shifts 12.68 nm to the longer wavelength. The redshift of the envelope is caused by the positive value of ΔFSR [19]. The spectra clearly show that the spectral shift of Vernier configuration is higher than the single PMF-SI when the two configuration experience the same temperature variation. The magnification coefficient is 18.64 which is consistent with the theoretical value calculated by Eq. (8). The simulation results indicate that the temperature sensitivity can be greatly improved by the Vernier effect.
Fig. 4. (a) Simulation dip wavelength shift of PMF-SI with different birefringence; (b) Simulation envelope spectrum shift of parallel dual PMF-SIs with different birefringence.
3. Experiment and results
In the experiment, a broadband light source (ASE, Fiberlake) with 400 nm wavelength range from 1250 nm to 1650 nm is utilized as an input light source. An optical spectrum analyzer (OSA, YOKOGAWA, AQ6370D) with a wavelength resolution of 0.05 nm is used to measure the transmission spectra. Two pieces of PMF with different length inserted into the sensing arm PMF-SI and reference arm PMF-SI are the same (PM1550-XP, Nufern). Two 1×2 3 dB coupler and one 2×2 3 dB coupler are the ordinary single mode type.
We have measured the transmission spectra of single PMF-SI reference arm with 2.10 m PMF, single PMF-SI sensing arm with 1.99 m PMF, cascaded dual PMF-SIs and parallel dual PMF-SIs configuration at room temperature. The measured results are shown in Fig. 5(a)-(d). The FSR of the reference arm and sensing arm are 2.54 nm and 2.68 nm respectively, while the envelope FSR of two Vernier configurations both are about 48 nm. The magnification coefficients of FSR remain around 18 which is in accordance with the theoretical result. In addition, the measured spectrum of parallel dual PMF-SIs has more clear and obvious envelope than the cascaded configuration as is shown in Fig. 5(c)-(d) which is consistent to the theoretical analysis.
Fig. 5. The measured transmission spectrum of (a) the single reference arm PMF-SI with PMF length of 2.10 m; (b) the single sensing arm PMF-SI with PMF length of 1.99 m; (c) the cascaded dual PMF-SIs; (d) the parallel dual PMF-SIs.
To investigate the performance of the proposed sensor, the temperature characteristics of the individual PMF-SI and parallel dual PMF-SIs are tested by placing the sensing arm in a temperature controlled furnace (SNR-030H, Schneier) with the resolution of 0.1 °C. Here, the PMF length of PMF-SI sensing arm and reference arm are 1.98 m and 2.10 m, respectively. Figure 6(a)-(b) shows the transmission spectra of the individual PMF-SI and the FMI configuration constructed by parallel dual PMF-SIs with the temperature range from 31-35 °C with a step of 1 °C. The spectrum of the individual PMF-SI sensor has a blue shift with the increase of temperature due to the negative thermos-optic coefficient of PMF. The FMI sensor has a redshift with the increase of temperature due to the positive FSR difference between the sensing arm and reference arm which is consistent with the previous theoretic analysis. The temperature sensitivity of the individual PMF-SI and the parallel dual PMF-SIs are shown in Fig. 6(c), which are −1.646 nm/°C and 24.285 nm/°C, respectively. The temperature sensitivity of the FMI configuration is 14.75 times of that for individual PMF-SI sensor. The little difference between the experiment magnification coefficient and theoretical analysis may result from the finite resolution of the OSA and thermostat. The resolution of the OSA used in this experiment is 0.05 nm. Therefore, the temperature resolution of the individual PMF-SI and parallel dual PMF-SIs can be calculated to be ±0.03037 °C and ±0.00206 °C, respectively.
Fig. 6. The measured spectra response of single PMF-SIs configuration (a) and parallel dual PMF-SIs configuration (b) as the temperature rises from 31°C to 35°C at a step of 1°C. (c) Linear fitting curves of temperature sensitivities of single PMF-SIs and the parallel dual PMF-SIs configuration.
To improve the sensor’s performance, we have shortened the PMF length of reference arm from 2.10 m to 2.08 m, 2.06 m, 2.03 m and 2.01 m, respectively. Furthermore, the PMF length difference of two arms has been shortened from 0.12 m to 0.1 m, 0.08 m, 0.05 m, 0.03 m, respectively. The relevant experimental results are shown in Fig. 7(a)-(d). The FMI sensor constructed by parallel dual PMF-SIs with different PMF length both have a redshift with the increase of temperature, the reason is that the FSRs of reference arm with five different PMF lengths are all smaller than the sensing arm with 1.98 m PMF length that induces the positive $\Delta FSR$. The envelope FSR of FMI sensor with 2.08, 2.06 m, 2.03 m and 2.01 m PMF length of reference arm are 48.16 nm, 56.82 nm, 95.12 nm, 160.47 nm near 1550 nm at 31°C, respectively, as shown in Fig. 6. The envelope FSR decrease a little with the temperature increasing. The reason can be expressed as follows:
Fig. 7. Measured envelope spectra shifts from 31-35°C with the 4 different length PMF-SIs reference arms of (a) 2.08 m, (b) 2.06 m, (c) 2.03 m, (d) 2.01 m, respectively.
The temperature characteristic of the FMI sensor with different PMF length of reference arm are shown in Fig. 7. The temperature sensitivity of FMI configuration with 2.10 m, 2.08 m, 2.06 m, 2.03 m and 2.01 m PMF length of the reference arm are 24.285 nm/°C, 29.073 nm/°C, 33.808 nm/°C, 45.244 nm/°C and 78.984 nm/°C, respectively. The linear coefficients of five temperature response curves are 0.999, 0.999, 0.995, 0.997 and 0.999, respectively, that show good linearity. The magnification coefficients are 14.75, 17.66, 20.54, 27.49 and 47.99, respectively. According to the resolution of OSA, the temperature resolutions of FMI configuration with 2.10 m, 2.08, 2.06 m, 2.03 m and 2.01 m PMF length of reference arm are ±0.00206°C, ±0.00172°C, ±0.00149°C, ±0.00111°C, ±0.00063°C, respectively. According to the wavelength range limit of the light source, the linear temperature detection ranges of the above 5 FMI sensors in order are 33 ± 8.24°C, 33 ± 6.88°C, 33 ± 5.91°C, 33 ± 4.42°C, 33 ± 2.53°C, respectively. The results indicate that higher temperature sensitivity of parallel dual PMF-SIs sensor will induce the narrower linear detection range and lower temperature sensitivity of the parallel dual PMF-SIs sensor results in the wider linear detection range. Different application scenarios need different sensitivity and temperature range. It can meet various application by changing the value of ΔFSR. For the biomedicine and precision processing, the proposed sensor with the sensitivity of 78.984 nm/°C could be an efficient candidate due to high temperature sensitivity and high resolution. For the occasions need large temperature detection, the proposed sensor with 24.285 nm/°C or 29.073 nm/°C, 33.808 nm/°C of sensitivity can be chosen owing to the wider linear detection range. In summary, we improve the temperature sensitivity of proposed sensor from 24.285 nm/°C to 78.984 nm/°C by optimizing ΔLPMF. the magnification coefficient is enhanced from 14.75 to 47.99 times of single PMF-SI sensor, the resolution is improved from ±0.00206°C to ±0.00063°C. The linear temperature detection range is narrow from 33 ± 8.24°C to 33 ± 2.53°C. However, the comprehensive performance of the FMI sensor can be greatly enhanced by optimizing the ΔLPMF value. The ultra-high sensitivity and resolution, fast response and simple configuration of proposed FMI sensor can be applied in many applications.
As we demonstrate in Fig. 8(a), the temperature sensitivity and the magnification coefficient increases with the decrease of the PMF length of the reference arm. Meanwhile, the temperature sensitivity and magnification coefficient increases slowly at first and then increase fast in the process of ΔLPMF reducing. The relationship between ΔLPMF and temperature sensitivity conforms to the change of hyperbola trend as shown in Fig. 8(b). That means when ΔFSR approaches to an infinitesimal so that the FSRenvelope and the temperature sensitivity will approach to infinity. Meanwhile, the linear detection range will become very narrow. In our work, the temperature detection range and the temperature sensitivity has been limited by the light source, when we increase the temperature sensitivity by reducing ΔFSR between dual PMF-SIs, the envelope spectra will shift beyond the efficient bandwidth of the light source. And the ΔFSR between dual PMF-SIs will increase as the temperature increases and the linear temperature detection range will be limited by the inherent negative thermos-optic coefficient of PMF even if we use a broader light source according to our previous analysis.
Fig. 8. (a) Linear fitting curves of temperature sensitivities of the sensor with five PMF-SIs reference arms. (b) The relationships between the temperature sensitivity and ΔLPMF.
The temperature sensitivity, resolution and magnification coefficient of our proposed sensor are 78.984 nm/°C, ±0.00063°C and 47.99, respectively, which indicates the highest compared with reported work as is listed in Table 1. Reference [26] parallel high birefringence fiber and cleaved single-mode fiber (SMF) to construct an FMI, the temperature sensitivity is −1.057 nm/°C. Reference [16] cascade two SIs to improve the sensor’s performance and the temperature sensitivity is enhanced from −1.46 nm/°C to −13.36 nm/°C with a magnification factor of 9.15. Reference [27] uses single SI by cascading two-section PMFs with a simple configuration to realize temperature sensing and the sensitivity is −2.147 nm/°C. Reference [20] cascade one FPI and one FSI to construct a hybrid sensor and realize 29.0 nm/°C temperature sensitivity with an enhancement factor of 20.7. Reference [19] parallel dual PDMS-filled FPIs exhibits a temperature sensitivity of 17.758 nm/°C. However, the PDMS-filled FPI is not easy to fabricate. Reference [17] uses two high birefringence fiber loop mirrors (HiBi-FLMs) with cost-effective cascade configuration and improve temperature sensitivity of 43 nm/°C. The parallel Vernier configuration with a clear upper and lower envelope which can track the wavelength shift more precision. Our proposed sensor using parallel dual PMF-SIs with FMI configuration has shown several advantages such as ultra-high sensitivity, ultrahigh resolution. In summary, the comprehensive performance of our proposed sensor is the best which makes it a simple and cost-effective alternative to other temperature sensors.
Table 1. Comparison of the proposed sensor with reported sensor for temperature sensing.
4. Conclusions
In conclusion, we have proposed and demonstrated an ultrahigh temperature-sensitive sensor based on parallel dual PMF-SIs with the Vernier effect. The Vernier effect is realized by FMI constructed by parallel dual PMF-SIs with slightly different FSRs. One PMF-SI is for the sensing arm, while the other PMF-SI acts as a reference arm. The principle of parallel Vernier configuration has been theoretically investigated and the temperature characteristic of the proposed sensor has been experimentally demonstrated. The envelope spectra of parallel Vernier configuration have a clear and neat upper and lower envelope so that we can accurately trace the dip wavelength shift. The experiment results show the temperature sensitivity of the proposed sensor can be enhanced from −1.646 nm/°C (single PMF-SI) to 78.984 nm/°C (FMI configuration), which is 47.99 times more sensitive than single PMF-SI by optimizing the PMF length difference from 0.1 m to 0.03 m. The temperature resolution can be improved from ±0.03037°C (single PMF-SI) to ±0.00063°C (FMI configuration). The proposed ultrasensitive temperature sensor is with high resolution, simple configuration, low cost and easy fabrication, which make it promising for high precision temperature measurement applications.
Funding
Shenzhen Science and Technology Innovation Commission (JCYJ20180507183815699); Tsinghua-Berkeley Shenzhen institute (Faculty Start-up Fund).
Disclosures
The authors declare no conflict of interest.
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