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Abstract
We report a high-resolution and wide-range thermometer using a fiber Bragg grating Fabry–Perot cavity (FBG-FP) combined with beat frequency interrogation. Two distributed feedback (DFB) lasers are locked to the FBG-FP sensing head and a hydrogen cyanide H13C14N (HCN) gas cell, respectively, both using the Pound-Drever-Hall (PDH) technique. The light beams from two lasers are brought together to interfere on a photodetector producing a beat frequency signal which provides a measure of the temperature change. Our sensor exhibits a dynamic range of ∼109 °C, a high resolution of 2×10−4 °C with an averaging time of 1 s. By introducing the reference frequency, the sensor has demonstrated good long-term stability. This sensor provides a useful tool for those fields where resolving slight temperature changes is crucial, such as deep ocean temperature measurement.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
For the past few decades, fiber-optic thermometers based on optical resonators have been extensively studied for broad applications [1–4]. Especially, precise temperature measurement is important for monitoring the slight temperature changes in oceanographic applications [5,6]. However, the performance of sensors, including fiber-optic sensors, is commonly limited by the paradox between a large dynamic range and a high resolution. Liu et al. developed a fiber-optic thermometer based on dual-cascaded silicon cavities, one thin and one thick, to tackle this problem [1]. The thin cavity defines the large dynamic range, and the thick cavity provides the ability for high-resolution measurement. This sensor exhibits a temperature range of -50 °C to 130 °C and a resolution of 6.8×10−3 °C. But the fabrication of the cavities in the micron dimension is complex. Recently, we developed a fiber-optic temperature sensor by using the laser-frequency dither locking scheme with a fiber Bragg grating based Fabry-Perot cavity (FBG-FP) as the sensing head and the feedback voltage as the sensor signal [2]. This sensor exhibits a dynamic range of ∼46 °C and a resolution of 7×10−4 °C. Because the laser tracks one resonance of the FBG-FP, the temperature dynamic range is limited by the laser frequency tuning range. However, the sensor exhibits some drift due to the instability of the laser frequency [7], including fluctuations in the laser current and thermal and mechanical coupling into the laser diode, or any instability of the electronic equipment, such as in the lock-in amplifier or the PID controller. These factors affect the resolution and the long-term stability. In contrast, the laser frequency always tracks the frequency of the FBG-FP after frequency locking [8]. So with optical heterodyne detection scheme [9] that relies on frequency measurements, the addition of a steady reference frequency will ensure good long-term stability and thus accuracy without sacrificing the resolution.
Here, we propose and demonstrate a fiber-optic thermometer using the beat frequency variation between two distributed feedback (DFB) lasers. One laser is locked to a FBG-FP sensing head and the other is stabilized against a hydrogen cyanide H13C14N (HCN) gas absorption line, both using the Pound-Drever-Hall (PDH) technique [8]. The HCN gas absorption line is not sensitive to temperature variation, so it could be used as a frequency reference to ensure good long-term stability. To extend the temperature dynamic range, we use the method of locking one laser to the resonances of the FBG-FP sensing head one by one [3]. As a result of the combination of deploying the above techniques, the new sensor has achieved a larger dynamic range, higher resolution, and better long-term stability than our previous work [2].
2. Temperature sensing principle and experimental setup
2.1 Operating principle
A FBG-FP consists of two identical 98% reflective Bragg gratings inscribed in an acrylate-coated fiber. The length of each FBG is ∼1 mm, and the spacing between them is 27 mm. The fiber cladding and coating diameters are 125 µm and 250 µm, respectively. The reflection spectrum of the FBG-FP was measured with an optical spectrum analyzer (YOKOGAWA, AQ6374), as shown in Fig. 1(a). Its 3 dB bandwidth is 1.6 nm. However, the optical spectrum analyzer’s resolution (50 pm) is not sufficient to distinguish the resonances. More details were then obtained by laser frequency scanning [2]. For example, the reflected signal of the FBG-FP from 1550.25 to 1550.56 nm is shown in Fig. 1(b), where many narrow transmission resonances appear at the high-reflection band with constant frequency interval. The free spectral range (FSR) and the full width at half maximum (FWHM) were measured to be about 3.84 GHz and 56 MHz, respectively.
Fig. 1. (a) The reflection spectrum of the FBG-FP measured with an optical spectrum analyzer. (b) The reflected signal measured by laser frequency scanning.
In the FBG-FP, the resonance frequencies are calculated by v = mc/(2nL), where m is the mode number, c the speed of light, n the refractive index of the cavity medium, and L the cavity length. The resonance frequency shift δν as a function of a temperature change δT at constant strain can be expressed as [10]:
The typical values for numerical estimation are as follows [11–13]: αn = 6.3 × 10−6 /°C, αf = 5.5 × 10−7 /°C, αp = 8 × 10−5 /°C, Ep = 0.5 GPa, Ef = 72 GPa, Pe = 0.213. From this, the temperature sensitivity of the acrylate-coated FBG-FP is estimated to be 12.57 pm/°C.
2.2 Experimental implementation
The experimental setup is illustrated in Fig. 2(a). Two DFB lasers with ∼2 MHz linewidth were used. The laser 1 was locked to one resonance of the FBG-FP using the PDH technique. Here we used the PDH technique instead of the laser-frequency dither locking scheme [2] to avoid the wavelength chirping in DFB lasers [14]. The laser 2 was locked to one absorption line of a fiber-coupled HCN gas cell (Wavelength references, HCN-13-H(16.5)-25) as a frequency reference. The long-term stability of the HCN-stabilized laser is determined by the absorption line, which has a nominal temperature drift of <0.01 pm/°C [15,16]. The absorption wavelength at 1550.51546 nm was chosen because it was close to the resonances of the FBG-FP.
Fig. 2. (a) A schematic of the experimental setup. (b) Conceptual basis for temperature measurement. The laser 1 (orange solid line) is locked to one resonance vi of the FBG-FP (blue line) at initial temperature. The laser 2 frequency (black solid line) is locked to one absorption line vr of a fiber-coupled HCN gas cell as an absolute frequency reference. Detected beat frequency is fi = |vi - vr|. When the temperature changes, the resonances shift (green dashed line). Once the resonance under locking shifts so that the beat frequency exceeds 6 GHz, the laser 1 (orange dashed line) is no longer locked to the mth resonance dip and relocked to the dip number (m-1), then Δm = 1. At current temperature, the laser 1 (orange dotted line) tracks the new resonance frequency vc. Detected new beat signal is fc = |vc - vr|. Then the beat trace fB is obtained.
The output of each laser was split into two branches using a 90/10 coupler. 90% of the laser output power was coupled into the corresponding FBG-FP or HCN gas cell. 10% of the laser power was picked off from each optical chain and the two beams were brought together using a 50/50 coupler to interfere on a high-speed photodetector (Keyang photonics, 10 GHz) producing a beat frequency signal in the radio-frequency (RF) range. The beat frequency signal was measured by an oscilloscope with 2-GHz bandwidth (Tektronix, MSO54) and a frequency counter with 6-GHz bandwidth (Keysight, 53230A).
2.3 Extension of measurement range
The beat-frequency dynamic range is limited by the photodetector's bandwidth, the frequency counter's range, and the laser tuning range [9]. In this experiment, the photodetector's bandwidth is 10 GHz, the frequency counter's range is 6 GHz, and the laser continuous range without mode hopping is 60 GHz, so the resulting continuous beat-frequency dynamic range in this setup is 12 GHz or ± 6 GHz around the reference frequency from the HCN gas cell, which is determined by the frequency counter's range.
To extend the dynamic range, the laser 1 was locked to the successive resonances of the FBG-FP [3]. This technique offers a significant cost saving than using electronics with larger bandwidth or a frequency comb. In this detection scheme, the beat-frequency range is larger than the FSR of the FBG-FP, so the laser 1 can always find a nearest resonance to lock. As shown in Fig. 2(b), once the resonance under locking moves so that the beat frequency exceeds 6 GHz, the laser 1 is no longer locked to the mth resonance dip and relocked to the dip number (m-1), then Δm = 1. With this procedure, the beat trace fB can be expressed as:
where Δm is the change in mode number going from initial temperature to current temperature, fc is the beat frequency at current temperature. The beat trace fB is the final sensor output.When the temperature varies, the laser 1 is locked to the resonances one by one and the change in mode number is counted. So the dynamic range of the proposed sensor is determined by how many resonances the FBG-FP can provide. Since the FBG-FP can provide resonances covering the 1.6-nm high-reflection band, the dynamic range is ∼200 GHz.
3. Results and analysis
To calibrate the temperature response, a calibrated platinum resistance thermometer with an uncertainty of 2×10−3 °C was mounted along with the FBG-FP on top of a thermoelectric cooler (TEC) controlled with a TEC controller. Then they were put in a temperature-controlled chamber which was used to provide an adjacent ambient temperature. To minimize the photothermal effect [17], the laser power was attenuated so that the optical power launched into the FBG-FP was ∼8.5 µW.
During the experiment, the initial temperature of the TEC was set to 21.39 °C. The heterodyne spectrum at different temperatures is shown in Fig. 3. When the TEC temperature varies, the central frequency of the heterodyne spectrum shifts to the higher frequencies, which indicates that the resonance of the FBG-FP is moving away from the reference line constantly. Limited by the oscilloscope’s bandwidth of 2 GHz, the displayable temperature range is from 20.86 °C to 22.80 °C.
To demonstrate the sensor's ability to measure temperature over a wide range, measurements were carried out in a temperature range of -14.82 °C to 94.12 °C. The obtained beat trace versus the temperature is shown in Fig. 4. As can be seen from Fig. 4(a), the linear fit on the data yields a sensitivity of 1769.5 MHz/°C when the temperature falls, while a sensitivity of 1370.5 MHz/°C is obtained when the temperature rises. This indicates that there is a nonlinear relationship between the beat trace and the temperature, which is verified in Fig. 4(b). The positive/negative beat trace in Fig. 4(b) indicates that the measured temperature is either higher or lower than the initial temperature. Because the laser 1 frequency only moves back and forth within ±6 GHz, the nonlinear relationship between the beat trace and the temperature mainly comes from the nonlinear temperature response of the FBG-FP over this wide temperature range [10]. The linear fit on the data yields a sensitivity of 1514.6 MHz/°C, close to the theoretical value. It is worth mentioning that we can adjust the temperature range for different applications by matching the laser frequency, the resonance frequencies of the FBG-FP, and the absorption lines of the HCN.
Fig. 4. The beat trace versus the temperature. (a) Different sensitivity as the temperature rises and falls. (b) The nonlinear relationship.
The temperature resolution of the sensor is not only related to the beat-frequency linewidth, but also to the beat-frequency stability. Figure 5 shows the measured heterodyne spectrum via the spectrum view tool on the oscilloscope. The resolution bandwidth was set to 10 kHz. Assuming that both lasers have similar linewidths and that the beat signal has a Lorentzian lineshape, the FWHM linewidth is ∼370 kHz.
To quantify the beat-frequency stability, the Allan deviation (AD) was calculated. The FBG-FP was put into a gallium-melting-point (GaMP) cell stabilized at 29.7646 °C [2]. The beat frequency was recorded for 10 minutes with a frequency counter gate time of 100 ms. Figure 6 shows the calculated beat-frequency AD after removal of the linear drift. The decreasing green dashed line τ-1/2 identifies a region of predominantly white noise. The beat-frequency AD shows a beat-frequency resolution of 264 kHz with an averaging time τ of 1 s, corresponding to a temperature resolution of 2×10−4 °C according to the sensitivity of 1370.5 MHz/°C.
Fig. 6. The beat-frequency Allan deviation. The green dashed line with a slope of -1/2 indicates a dominant white-noise character.
To compare the long-term stability of beat frequency and feedback voltage, each laser was locked to an HCN. Each HCN was kept in an incubator with a temperature fluctuation of ±0.5 °C. One set of laser-frequency locking system was placed in a testing chamber to change the temperature, and the other was placed at room temperature. It can be seen from Fig. 7, with the change of ambient temperature of the laser-frequency locking system, the fluctuation range of the beat frequency is ∼20 MHz, while the feedback voltage varies almost linearly, corresponding to the frequency change of ∼928 MHz according to the laser voltage tuning of 36 MHz/mV. This shows that the optical heterodyne detection scheme has good long-term stability.
Fig. 7. The long-term stability of (a) beat frequency and (b) feedback voltage with the change of (c) ambient temperature of the laser-frequency locking system.
Table 1 presents the performance comparison of different fiber-optic temperature sensors based on optical heterodyne configuration. Compared to other sensors, the temperature resolution and dynamic range of this proposed sensor are among the best. Besides, the HCN-stabilized laser enables this sensor to have better long-term stability. Furthermore, the temperature resolution of this sensor can be further improved by using narrower linewidth lasers, such as single-frequency fiber laser (SFFL).
Table 1. Performance comparison of temperature sensors
4. Discussion and conclusion
A high-resolution and wide-range fiber-optic thermometer based on a wide-band FBG-FP and optical heterodyne detection scheme is proposed and demonstrated. Through the method of locking one laser to the successive resonances of the FBG-FP, the dynamic range of ∼109 °C is achieved, which is limited by how many resonances the FBG-FP can provide. The beat-frequency resolution of 264 kHz with an averaging time of 1 s is achieved, which is not only related to the beat-frequency linewidth, but also to the beat-frequency stability. By introducing the HCN-stabilized laser, the optical heterodyne detection scheme significantly reduces the sensitivity to the environmental fluctuations which is a key advantage to ensure the long-term stability. The sensor can be useful for many applications within this temperature range, such as deep ocean temperature measurement.
Note that the optical heterodyne detection scheme is not limited to temperature sensing and can be adopted for other types of optical resonator-based sensors, such as whispering-gallery-mode (WGM) resonators [4] and optical microfiber based resonators [23] in numerous sensing applications, including humidity sensors, magnetometers and nanoparticle/biomolecule detection.
A photonic integrated circuit (PIC) [24–26] is a solution to reduce the footprint and cost of our sensor to be used for real-time, in-situ measurements in the future.
Funding
Southern Marine Science and Engineering Guangdong Laboratory (Guangzhou) (GML2021GD0808); Key Technology Research and Development Program of Shandong (2019JZZY020711, 2021-GJ-11); National Key Research and Development Program of China (2019YFC1408600).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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