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Abstract
A new approach to conquer the thermal phase drift of an optical fiber Fabry-Perot interferometer (FPI) sensor is proposed and experimentally demonstrated. By employing a hollow-core anti-resonant fiber (HC-ARF) and optimizing the fusion splicing (includes mode field adaptation) between the lead-in single-mode fiber (SMF) and the HC-ARF, a high spectral resolution (λ/Δλ ≈ 3.8 × 104) optical fiber air-cavity FPI sensor with a fringe visibility higher than 7 dB is constructed. To eliminate the thermal phase drift (i.e. temperature crosstalk) of the sensor that originates from the intrinsic thermal expansion effect of the silica material of the HC-ARF, the FPI air cavity is connected to the external environments, by which the effect of air expelling from the cavity with temperature increasing can well compensate the temperature-induced cavity elongation. As a result, the thermal phase drift of the FPI is reduced to zero at a temperature range of ∼ 80–110 °C and within the temperature range of 40–80 °C, the thermal phase drift is still halved compared with the sealed FPI cavity. The nearly zero thermal phase drift of a FPI at such a temperature range has never been achieved before, to our best knowledge. As a proof of concept, a temperature-immune fiber-optic strain sensor is demonstrated. This work offers a new and efficient approach to eliminate the thermal phase drift (i.e. temperature crosstalk) of a fiber-optic device, which may significantly improve the measurement accuracy and detection limit of fiber-optic FPI sensors. Furthermore, the principle and schema can be generalized to a wide variety of fiber-optic devices.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
As one of the vital fiber-optic devices, optical fiber Fabry-Perot interferometer (FPI) has been demonstrated for widespread applications such as optical fiber communication [1,2], fiber laser [3,4] and precise metrology [5,6]. For instance, the optical switches and add-drop multiplexers (ADMs) in optical communication systems use FPIs as filters. The fiber lasers employ FPIs as resonant cavities or wavelength tuning elements. For precise metrology applications, FPIs can be employed not only for signal demodulations of the in-fiber grating sensors [7] but for directly measurements of temperature [8,9], tension [10,11], pressure [12–14], gas [15,16] and acoustic wave [17,18] by appropriate structure or material designs of the FPIs.
For these applications mentioned above, except for temperature sensing, thermal induced optical phase drift (i.e. temperature crosstalk) is highly problematic. For optical fiber communication devices using FPI, the thermal phase drift shifts the working wavelength. The thermal-induced phase change of a FPI also makes the output wavelength skew of fiber laser that using a fiber FPI as a cavity or filter. For sensing applications, the thermal phase drift results in crosstalk to the target parameters, limiting the measurement accuracy and detection limit.
The temperature crosstalk of a fiber FPI mainly results from two aspects, i.e. thermal-optic and thermal expansion effects of the cavity medium. It has been recently demonstrated that hollow-core fiber (HCF) based air cavity shows a thermal phase drift ∼20 times smaller than the silica cavity due to the negligible thermal-optic coefficient of air within a sealed cavity [19]. However, the thermal expansion effect which is intrinsic for silica material become dominant for the thermal phase drift. Fortunately, the thermal expansion of silica material is nearly zero at ∼-71 °C [20]. Benefits from this attribute of silica material, Zhu et al. demonstrated a temperature insensitive fiber interferometry in 2019 using a HCF at a special cryogenic temperature of -71 °C [21]. Ding et al. demonstrated the reduction of temperature sensitivity of a HCF interferometer by winding the HCF on a thermally-insensitive coil in 2021 [22]. However, all the schemas mentioned above need a special working condition [a very low temperature (such as -71 °C)] which is not available in a realistic circumstance. Alternatively, in 2019, Slavik et al. found that the air within an opened HCF shows a negative thermal-optic coefficient which may be employed to compensate the fiber elongation with temperature increasing [23]. This work enlightens us a new thinking and approach to conquer the temperature crosstalk of a fiber FPI device, which has never been studied or reported before.
Herein, a new way to eliminate the temperature crosstalk of an optical fiber FPI sensor is proposed and experimentally demonstrated. By designing an opened hollow-core anti-resonant fiber (HC-ARF) cavity and compensating the elongation of HC-ARF cavity by the air expelling effect with temperature increasing, the thermal phase drift is reduced to zero in a temperature range of ∼ 80–110 °C and halved in 40–80 °C range. As a proof of concept, a temperature-immune, high spectral resolution ($\lambda /\Delta \lambda \approx 3.8 \times {10^4}$) optical fiber FPI strain sensor is demonstrated.
2. Principle
A conventional fiber-optic FPI with a HC-ARF cavity is sketched in Fig. 1(a), where the air is sealed in the cavity. When the external temperature is raised from ${T_0}$ to ${T_0} + \Delta T$, the cavity length will increase from ${L_0}$ to ${L_0} + \Delta L$, while the gas refractive index (RI) has little change since the density and species of gas hardly change if neglecting the little volume variation of the cavity. Assuming the intensity of incident light is ${I_0}(\lambda )$ and the high-order reflection of light can be neglected since the reflectivity of the silica/air interface is far less than 1 (${R_1} \approx {R_2} < < 1$). The reflection spectrum can be denoted by:
Fig. 1. Schematic diagrams and working principles of (a) a conventional HC-ARF FPI with a sealed end, and (b) the proposed HC-ARF FPI with an opened end.
For a conventional sealed FPI, as shown in Fig. 1(a), $d{n_{air}}/dT$ is approximate to zero, and the thermal induced phase drift is attributed to the cavity elongation: $dL/dT$. While for an opened cavity that connected to the external environment, the $d{n_{air}}/dT$ is negative due to the expelling of air from the cavity, as shown in Fig. 1(b). The decrease of gas RI and the fiber elongation with temperature increasing can be used to balance each other. The gas RI in a sealed (black curve) and opened cavity (red curve) versus temperature is calculated and plotted in Fig. 2(a), respectively, and the relative cavity length change ($\Delta L/{L_0}$) versus temperature is calculated and shown in Fig. 2(b). Here, the original cavity length at ∼40 °C is denoted as ${L_0}$ and a thermal expansion coefficient of ∼0.55 ppm/°C is employed, which is reasonable at a considered temperature range of 40 °C–140 °C [25]. Calculations indicate that when the temperature is around 103 °C, the effect of gas expelling can ideally compensate the HC-ARF elongation, rendering a zero thermal phase drift (i.e. $d{\lambda _{dip}}/dT = 0$). This is amazing since it means that a total temperature-insensitive fiber FPI can be achieved within a more accessible or convenient condition such as a boiling water bath. Even at a temperature of 40 °C, the thermal phase sensitivity is still halved in comparation with a sealed HC-ARF FPI. It is worth noting that the thermal-optic coefficient of air within an opened FPI $d{n_{air}}/dT$ is proportional to the gas pressure P according to ${n_{\textrm{air}}} = 1 + \frac{{2.8793 \times {{10}^{ - 9}}}}{{1 + 0.00367 \times T}}P$. As such, it may be possible to shift the temperature of zero thermal phase drift to a lower or a higher temperature range. Theoretical calculation indicates that when the applied pressures are 55940, 59970, 64141, 68452, 72903, 77495, 82226, 87098, 92111, 97263, and 102555 Pa, the corresponding temperatures of zero thermal phase drift are 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, and 110 °C, respectively. This is amazing since it make the device possible to work at a room temperature condition. However, tuning the working pressure of the device may be technically complex, which needs further studies and explorations in future works.
Fig. 2. (a) The calculated RI of air within a HC-ARF cavity versus temperature: the black and red curves denote the sealed and opened cavities, as shown in Fig. 1(a) and 1(b), respectively; (b) the calculated relative cavity length change within a temperature range of 40-140 °C.
3. Method and fabrication
3.1 High spectral resolution FPI design
The thermal phase drift caused by thermal expansion of HC-ARF cavity is small (∼1 pm/°C by calculation), which cannot be identified accurately if the full width at half maximum (FWHM) (denoted as $\Delta \lambda$) of the peak (or dip) in the interference spectra is too large [26]. As such, a long cavity FPI is designed to narrow the FWHM of the peak (or dip) in the interference spectrum. Here, we define the spectral resolution of the FPI as $r = {{{\lambda _0}} / {\Delta \lambda }}$, where ${\lambda _0}$ is the center wavelength and $\Delta \lambda$ is the FWHM. Assuming the the reflectivity of the two silica/air interfaces is 0.04, the RI of air is 1 and the cavity has no loss, i.e. the transmission coefficient $\eta$ of the cavity is 1 (it is reasonable when using a low-loss HC-ARF as the cavity medium), the reflection spectra and the corresponding spectral resolutions of four FPIs that with cavity length L of 0.1 mm, 1 mm, 10 mm, and 100 mm are calculated and plotted in Fig. 3(a) and (b), respectively. The calculation results indicate that by increasing the cavity length L of the FPI from 0.1 mm to 100 mm, the FWHM ($\Delta \lambda$) of the interference spectrum is decreased linearly from ∼6.4 nm to ∼0.006 nm, corresponding to the spectral resolution r of the FPI increases from ∼240 to $2.58 \times {10^5}$. As such, long cavity FPIs (i.e. high spectral resolution FPI) will dramatically improve the detection limit of small signals such as the thermal induced phase changes (in this study).
Fig. 3. (a) The simulated reflection spectra and (b) the corresponding spectral resolutions of four FPIs with cavity length L of 0.1 mm, 1 mm, 10 mm, and 100 mm, respectively.
3.2 FPI fabrication
Experimentally, a single-ring HC-ARF with core diameter of ∼31 µm and transmission loss of ∼0.1 dB/m is employed to construct the long cavity FPI. The scanning electron microscopy (SEM) image of the cross section of the HC-ARF is shown in Fig. 4(a). It is worth noting that, low-loss fusion spicing between the lead-in SMF and the HC-ARF is imperative for a high fringe visibility of the interference spectrum. As such, a mode-field diameter matching technique that has been developed and detailed in our previous literature [27] is employed, which is sketched in Fig. 4(b). Together with an optimized arc discharge procedure, a fusion splicing loss estimated to be ∼0.5 dB is achieved. The morphology of the fusion splicing point under an optical microscope is shown in Fig. 4(c). Finally, a matched hollow-core tube (HCT) that has an air core diameter of ∼2 µm is fusion spliced to the other end of the HC-ARF, providing a second reflection interface and a gas channel to the external environment, simultaneously, as sketched in Fig. 1(b).
Fig. 4. (a) Scanning Electron Microscopy (SEM) image of the cross section of the employed HC-ARF; (b) sketch of the mode field diameter matching between the lead-in SMF and the HC-ARF using a gradient-index fiber (GIF) [27]; (c) optical microscope image of the fusion splicing point.
All the aforementioned designs and optimizations together, an opened, long-cavity fiber FPI is prepared and the measured reflection spectrum is shown in Fig. 5(b). For comparation purpose, a sealed long-cavity fiber FPI with similar cavity length is prepared by fusion splicing a conventional SMF to the other end of the HC-ARF, as sketched in Fig. 1(a). The reflection spectrum of the sealed FPI is shown in Fig. 5(a). According to the reflection spectra, the cavity length L (i.e. HC-ARF length) is calculated to be ∼10.45 mm and 9.25 mm for the sealed and opened FPI, respectively. The FWHM $\Delta \lambda$ of the interference dips near 1555 nm is measured to be 0.04 nm and 0.05 nm, corresponding to a high spectral resolution (r) of 38750 and 31000, respectively. Benefits from the low fusion splicing loss as well as the low transmission loss of the HC-ARF, the fringe visibilities in the interference spectra are measured to be ∼7.35 dB and ∼5.49 dB for the sealed and opened FPIs, respectively. The high spectral resolution together with the high fringe visibility of the interference spectra make the FPI capable of distinguishing tiny phase change. It is worth noting that the fringe visibility of ∼7.35 dB is not quite high, which is limited by the reflectivity of the silica/air interfaces. If reflection coatings are applied to the interfaces, the fringe visibility can be improved significantly. While for sensing applications, the fringe visibilities are high enough.
Fig. 5. Reflection spectra of the prepared (a) sealed cavity and (b) opened cavity FPIs. The cavity lengths are measured to be ∼10.45 mm and 9.25 mm, and the FWHMs are ∼0.04 nm and ∼0.05 nm, and the fringe contrasts are 7.35 dB and 5.49 dB, respectively.
4. Results
4.1 Thermal phase drift comparations
Firstly, the thermal phase drift of the sealed and the opened FPIs are charactered by placing the devices into a high-precision digital temperature oven, which has a precision of ∼0.5 °C. For the sealed FPI, the temperature is increased from 40 °C to 140 °C with a step of 20 °C. At each step, the temperature is kept for ∼5 mins to make the temperature within the oven stable. Figure 6(a) shows the tracked dip wavelength at around 1550 nm versus the applied temperature. A “red shift” of the dip wavelength is clearly observed, and the sensitivity is ∼1.14 × 10−3 nm/ °C which agrees well with the thermal expansion of the silica cavity. Meanwhile, in the measured temperature range of 40–140 °C, a linear wavelength shift (R2 = 0.9985) is identified. Then, the opened FPI is tested using the same equipment and procedure. The only difference is the reduced measurement step length (10 °C) to observe a more detailed phase change at a much smaller temperature scale. In the temperature range of 40–80 °C, the tracked wavelength shows an opposite shift (i.e. “blue shift”) with temperature rising and the rate of phase change (∼-0.64 × 10−3 nm/ °C) is significantly lower than the sealed FPI. While in the temperature range of ∼80–110 °C, the wavelength drift almost remains unchanged, which indicates that in such a temperature range, the effect of gas expelling perfectly compensates the HC-ARF elongation, as shown in Fig. 6(b). As a result, a nearly zero thermal phase drift can be achieved in such a temperature range. This result agrees well with the calculations that the temperature of zero thermal phase drift is around 103 °C. As the demonstrated temperature (80–110 °C) of zero wavelength drift locates in the water temperature range, the sensing schema may find vital applications in the sensing of strain within mechanical structures that equipped with water cooling setups. In addition, to make the sensor totally immune to the temperature, one could seal the sensor in a miniature water bath that has a temperature range from 80 to 110 °C. In a higher temperature range, the opened FPI shows a similar thermal phase drift (∼0.83 × 10−3 nm/ °C) to the sealed FPI.
Fig. 6. (a) The measured wavelength drift versus temperature for the sealed FPI: the wavelength sensitivity is ∼1.14 × 10−3 nm/°C with a linearity of ∼0.9985; (b) The measured wavelength drift versus temperature for the opened FPI: in the temperature range of 40-80 °C, the temperature sensitivity is ∼-0.64 × 10 -3 nm/ °C; in the temperature range of 80-110 °C, the wavelength drift is nearly zero, and in the temperature range of 110-140 °C, the sensitivity is 0.83 × 10 -3 nm/ °C.
4.2 Strain response of the FPI sensor
The sealed and opened FPIs are further employed for temperature-immune strain sensing. The experiment is conducted in a clean room that with a constant temperature of ∼25 °C. Thanks to the high spectral resolution together with the high fringe visibility, the FPI sensors can distinguish much smaller strain changes. As show in Fig. 7, the applied strain is increased from 100 µɛ to 900 µɛ in a step of 100 µɛ. The strain sensitivities are 3.425 × 10−4 and 3.495× 10−4 nm/µɛ for the sealed and opened FPIs, respectively. The little difference in the sensitivity may be attributed to the different mechanical properties between the SMF and the HCT pigtails, as shown in Fig. 1. Benefiting from the reduced thermal phase drift and the high spectral resolution as well as high fringe contrast of the proposed FPI, the strain detection limit and accuracy can be improved significantly.
Fig. 7. The wavelength shifts versus applied strain for the sealed (black diamonds) and opened (red dots) FPIs, respectively.
5. Conclusion
A new, effective approach to conquer the temperature crosstalk of fiber FPI sensors is proposed and a near zero thermal phase drift within a temperature range of ∼80–110 °C is demonstrated for the first time to our best knowledge. As a proof of concept, a fiber FPI strain sensor with high spectral resolution and nearly zero temperature crosstalk is demonstrated. The reduced thermal phase drift, together with the high spectral resolution and fringe contrast make the FPI sensor capable of detecting a lot of tiny phase (signal) changes, which is promising in precision metrologies. Moreover, the principle and schema can be generalized and used to other fiber-optic devices such as the Mach-Zehnder Interferometers (MZIs), Sagnac Interferometer (SIs), as well as Lyot interferometers (LI).
Funding
National Natural Science Foundation of China (62075170); Basic and Applied Basic Research Foundation of Guangdong Province (32221295); Department of Education of Guangdong Province (2020KCXTD029); Science and Technology Innovation Commission of Shenzhen (JCYJ20200109144003948).
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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