Abstract

A sapphire derived fiber (SDF) based Fabry-Perot interferometer (FPI) with an etched micro air cavity for strain measurement at high temperatures is proposed. The FPI is formed by splicing a section of SDF between an etched single mode fiber (ESMF) and a capillary. The SDF’s core containing 51.3mol.% aluminum provides the intrinsic Fabry-Perot interferometer cavity with an enhanced fringe contrast through the narrow etched air cavity reflector. Because the different Poisson effects of the cladding and the core have different deformations under axial stress, the transverse strain imposed from the cladding to the core was introduced to the additive model. The strain sensitivity of the FPI was theoretically analyzed and experimentally demonstrated at room temperature. A thermal annealing process was performed to study the stability in high temperatures and to release the residual stress during the sensor’s fabrication. The strain calibration was carried out subsequently from 20℃ to 1000℃. Benefiting from the doping in the core and diffusion in the cladding of the high temperature resistant material $\textrm{A}{\textrm{l}_\textrm{2}}{\textrm{O}_\textrm{3}}$, the proposed sensor was proved to operate well in 950℃ and was also characteristized by a sensitivity of 1.19 pm/µɛ and 1.06 pm/µɛ in the process of loading and unloading strain separately.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Strain measurement has been a reliable method for structural integrity monitoring since the principal failure mechanism in high-temperature components is creep damage that can be indicated by creep strain accumulation. The strain sensors based on fiber Fabry-Perot interferometer (FPI) play an active role in strain measurement at high temperatures due to competitive advantages of their compact size, easy fabrication, a high temperature resistance and immunity to electromagnetic interference.

A wide range of techniques have been developed in pursuit of FPI strain sensors. In order to obtain FPI strain sensors with a high sensitivity, the cavities are usually formed by spherical air cavities or cantilever-taper. The spherical air cavity structure can be created by the femtosecond laser micromachining [1,2], by wet chemical etching [35], by special fusion techniques [6,7], or by splicing the single mode fiber (SMF) with special fibers, such as a hollow core fiber [8] or a photonic crystal fiber (PCF) [9]. The cantilever-taper cavities [1012] provide a simple and cost-effective method for strain measurement with a high sensitivity. These methods, however, achieved a high strain sensitivity at the cost of extremely expensive fabrication equipment or complicated process. Meanwhile, many efforts based on FPI sensors are being made to realize the strain measurement at high temperatures. A PCF based FPI sensor [13] fabricated by 157nm laser micromachining was carried out at a high temperature up to 800℃ in a strain range of 0 µɛ to 600 µɛ. A multimode PCF-based FPI sensor [14] was used for strain measurement up to 1850 µɛ in a temperature range of 100 °C to 750 °C. A FPI cavity based on a silica tube with internal rods [15] performed well at a high temperature up to 900℃ in the strain range of 0 µɛ to 1000 µɛ.

On the other hand, the sapphire derived fiber (SDF) with specially high alumina dopant concentration to silica [16], was proposed for the first time in 2012, which has the distinct advantages of a lower Brillouin gain coefficient and a high temperature stability [17,18]. Bragg gratings made with infrared femtosecond radiation in the SDF [19] showed thermal stability at the temperature up to 900℃. Meanwhile, the mechanical strength is enhanced due to the high alumina dopant concentration, which offers the potential for the strain measurement at a high temperature.

In this paper, a FPI based on SDF with an etched micro air cavity was proposed and demonstrated for strain measurement at high temperatures. In order to improve the fringe contrast of the spectrum, a micro air cavity was fabricated at the tip of the SMF by wet chemical corrosion before splicing the SMF and SDF together through arc discharging. The other end of the SDF was spliced with a capillary. The measurement of strain at high temperatures can be realized by recording the interferometer fringe dips shift. After annealing treatment, the proposed structure achieved the sensitivities of 1.19 pm/µɛ and 1.06 pm/µɛ in the loading and unloading strain process separately with the strain range of 0-1000µɛ at a high temperature up to 950℃.

2. Basic principles

The scheme diagram of the FPI is indicated in Fig. 1. A section of SDF is sandwiched between the etched SMF and the capillary by splicing fusion. A micro air cavity with just several micrometers width is introduced by wet etching at the end of the SMF. The incident light from the light source into the SMF was reflected by two interfaces on the micro air cavity and the interface between the SDF and air due to Fresnel effect resulting from the refractive index differences among air and the cores of SMF and SDF. According to [4], the spherical surface of the air cavity can be assumed to be a single plane reflector when $d \ll D$ and $d \ll L$, where d and D are the width and height of the micro air bubble separately, L is the length of the SDF. Assuming the FPI sensor as a paraxial optical system, the model of the proposed FPI sensor is shown in Fig. 2, where the $\pi /2$ phase shift can be neglected in the reflector. Thus the total intensity of the reflection electric field ${E_{out}}$ can be expressed as:

$${E_{out}} = {E_0}\left( {\sqrt {{R_1}} + ({1 - {\eta_1}} )({1 - {R_1}} )\sqrt {{R_2}} {e^{ - j2\beta L}}} \right),$$
where ${E_0}$ is the intensity of input electric field; $\beta $ is the propagating constant of the incident light in propagating medium; ${\eta _1}$ is the transmission loss induced by the air reflector; ${R_1},{R_2}$ are the reflectance coefficients of the micro air cavity [4] and the interface between the SDF and air, and ${R_2} = {({{n_{\textrm{SDF}}} - {n_{\textrm{air}}}} )^2}/{({{n_{\textrm{SDF}}} + {n_{\textrm{air}}}} )^2}$, where ${n_{\textrm{SDF}}}$ and ${n_{\textrm{air}}}$ represent the effective refractive indexes (RIs) of SDF and air.

 figure: Fig. 1.

Fig. 1. The scheme diagram of the FPI.

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 figure: Fig. 2.

Fig. 2. The model of the proposed FPI sensor.

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Thus the normalized reflection spectrum is given by

$${I_\lambda } = {R_1} + {({1 - {\eta_1}} )^2}{({1 - {R_1}} )^2}{R_2} + 2({1 - {\eta_1}} )({1 - {R_1}} )\sqrt {{R_1}{R_2}} \cos ({4\pi {n_{\textrm{SDF}}}L/\lambda + {\varphi_0}} ),$$
where $\lambda $ represents the wavelength of incident light; ${\varphi _{0}}$ is the initial phase. At the fringe dips, the phase difference of the interference spectrum satisfies the condition
$$\frac{{4\pi {n_{\textrm{SDF}}}L}}{{{\lambda _m}}} = ({2m + 1} )\pi ,$$
where m is the interference order; ${\lambda _m}$ is the wavelength of the ${m^{th}}$ order interference dip. Thus the spectrum dip ${\lambda _{dip}}$ appears at the wavelength
$${\lambda _{dip}} = \frac{{4{n_{\textrm{SDF}}}L}}{{2m + 1}}.$$
When the strain is applied along the fiber axis, the spectrum dip shift is given as
$$\Delta {\lambda _{dip}} = \frac{4}{{2m + 1}}({n_{\textrm{SDF}}} \cdot \Delta L + L \cdot \Delta {n_{\textrm{SDF}}}),$$
where $\Delta {n_{\textrm{SDF}}}$ is the variation of the RI of the SDF core induced by the elasto-optical effect resulting from the applied strain and $\Delta L$ is the axial elongation, which can be expressed as
$$\Delta L = L{\varepsilon _z},$$
where ${\varepsilon _z}$ is the strain applied along the fiber axis.

Substituting Eq. (6) into Eq. (5), yields:

$$\Delta {\lambda _{dip}} = \frac{4}{{2m + 1}}({n_{\textrm{SDF}}} \cdot L{\varepsilon _z} + L \cdot \Delta {n_{\textrm{SDF}}}) = \frac{{4{n_{\textrm{SDF}}}L}}{{2m + 1}}({\varepsilon _z} + \frac{1}{{{n_{\textrm{SDF}}}}}\Delta {n_{\textrm{SDF}}}).$$
Thus, substituting Eq. (4) into Eq. (7), the strain sensitivity at ${\lambda _{dip}}$ can be given as
$$\frac{{\Delta {\lambda _{dip}}}}{{{\varepsilon _z}}} = {\lambda _{dip}}(1 + \frac{1}{{{n_{\textrm{SDF}}}}}\frac{{\Delta {n_{\textrm{SDF}}}}}{{{\varepsilon _z}}}).$$
Only the axis strain was considered in the conventional theoretical treatments of the sensitivity to strain, which is reasonable because the conventional fibers are mainly composed of silica. Such silica approximation, however, breaks down in the fiber with the multicomponent glass, each component of which has a different individual physical characteristic. As for the aluminosilicate optical fiber, the aluminosilicate core is rigidly clad in pure silica whose Poisson ratio is much lower than that of the aluminosilicate core [19]. When the axis stress was applied on the fiber, besides the axial strain, the core suffers from a transverse strain imposed from the cladding because of the different deformations resulting from the Poisson effects. For simplicity, such assumption can be usually made, that is the fiber core freely compresses with the strain, but a correction will be adopted in the form of a positive strain to compensate for the lower Poisson ratio of the cladding.

In order to analyze the total RI change, a classic binary glass system can be used to model the physical characteristics of the SDF’s core material consisting silica with highly-doped aluminosilicate. Thus the refractive index of the core can be found by [20]

$${n_{\textrm{SDF}}} = m{n_{\textrm{A}{\textrm{l}_\textrm{2}}{\textrm{O}_\textrm{3}}}} + (1 - m){n_{\textrm{Si}{\textrm{O}_\textrm{2}}}},$$
where ${n_{\textrm{A}{\textrm{l}_\textrm{2}}{\textrm{O}_\textrm{3}}}}$ and ${n_{\textrm{Si}{\textrm{O}_\textrm{2}}}}$ represent the refractive indexes of alumina and silica, respectively; m refers to the molar mass of alumina. The Poisson ratios of the core and the cladding can be assumed as
$${\nu _{core}} = m{\nu _{\textrm{A}{\textrm{l}_\textrm{2}}{\textrm{O}_\textrm{3}}}} + ({1 - m} ){\nu _{\textrm{Si}{\textrm{O}_\textrm{2}}}},$$
and
$${\nu _{cladding}} = {\nu _{\textrm{Si}{\textrm{O}_\textrm{2}}}}.$$
The strain-optic constant $\varepsilon \textrm{OC}$ and the stress-optic constant $\sigma \textrm{OC}$ of the SDF core are assumed to be obtained through the additive model via refractive index of each component and can be expressed as [21]
$$({\varepsilon \textrm{OC,}\sigma \textrm{OC}} ) = \frac{1}{{n_{\textrm{SDF}}^3}}({n_{\textrm{A}{\textrm{l}_\textrm{2}}{\textrm{O}_\textrm{3}}}^3m({\varepsilon \textrm{O}{\textrm{C}_{\textrm{A}{\textrm{l}_\textrm{2}}{\textrm{O}_\textrm{3}}}}\textrm{,}\sigma \textrm{O}{\textrm{C}_{\textrm{A}{\textrm{l}_\textrm{2}}{\textrm{O}_\textrm{3}}}}} )+ n_{\textrm{Si}{\textrm{O}_2}}^3(1 - m)({\varepsilon \textrm{O}{\textrm{C}_{\textrm{Si}{\textrm{O}_2}}}\textrm{,}\sigma \textrm{O}{\textrm{C}_{\textrm{Si}{\textrm{O}_2}}}} )} ),$$
where $\varepsilon \textrm{O}{\textrm{C}_{\textrm{A}{\textrm{l}_\textrm{2}}{\textrm{O}_\textrm{3}}}}$, $\sigma \textrm{O}{\textrm{C}_{\textrm{A}{\textrm{l}_\textrm{2}}{\textrm{O}_\textrm{3}}}}$, $\varepsilon \textrm{O}{\textrm{C}_{\textrm{Si}{\textrm{O}_2}}}$ and, $\sigma \textrm{O}{\textrm{C}_{\textrm{Si}{\textrm{O}_2}}}$ are the strain-optic and stress-optic constants of alumina and silica at zero strain separately. The Pockels’s coefficients are defined as
$${p_{11}} = \frac{{\varepsilon \textrm{OC} + 2\sigma \textrm{OC}}}{{1 + 2\nu }},$$
and
$${p_{12}} = \frac{{\varepsilon \textrm{OC} + 2\nu \sigma \textrm{OC}}}{{1 - 2\nu }}.$$
Furthermore, to study the axial and transversal strains, a simple unit volume of core material with the geometry can be assumed and shown in Fig. 3.

 figure: Fig. 3.

Fig. 3. Block diagram of a unit volume of the SDF core in the force mechanical system.

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An electromagnetic wave is assumed to propagate in the z direction and to polarize along the x direction. The hypothetic uniform compressions of the core and the cladding in the transverse directions are governed by the individual Poisson ratios with

$${\varepsilon _{core,x}} = {\varepsilon _{core,y}} = - {\nu _{core}}{\varepsilon _z},$$
and
$${\varepsilon _{cladding,x}} = {\varepsilon _{cladding,y}} = - {\nu _{cladding}}{\varepsilon _z},$$
where ${\nu _{core}}$ and ${\nu _{cladding}}$ are the Poisson ratios of the core and the cladding, ${\varepsilon _z}$ is the fractional elongation,${\varepsilon _{core,x}}$, ${\varepsilon _{cladding,x}}$, ${\varepsilon _{core,y}}$ and ${\varepsilon _{cladding,y}}$ are the transverse compressions of the core and the cladding in x and y directions, separately.

Next, considering hypothetically that strain only occurs in the z direction, the change in RI as a strain can be expressed as [22]

$$\Delta {n_z} = - \frac{1}{2}n_{\textrm{SDF}}^3({{p_{12}} - {\nu_{core}}({{p_{11}} + {p_{12}}} )} ){\varepsilon _z}.$$
Then, strains in the remaining two directions is considered. As the Poisson ratio of the pure silica (0.16) is smaller than that of Aluminium oxide (0.25) [23], the cladding experiences a smaller deformation than the core when the strain in the z direction is applied, resulting in a tension applied from the cladding to the core. Thus positive strains along x and y directions on the core are necessary to be considered, which are proportional to the Poisson ratios’ difference and follow the forms
$$\begin{aligned}\Delta {n_x} &= - \frac{1}{2}n_{\textrm{SDF}}^3({{p_{12}} - {\nu_{core}}({{p_{11}} + {p_{12}}} )} )({{\varepsilon_{cladding,x}} - {\varepsilon_{core,x}}} )\\ &= - \frac{1}{2}n_{\textrm{SDF}}^3({{p_{12}} - {\nu_{core}}({{p_{11}} + {p_{12}}} )} )({{\nu_{core}} - {\nu_{cladding}}} ){\varepsilon _z}, \end{aligned}$$
$$\begin{aligned}\Delta {n_y} &= - \frac{1}{2}n_{\textrm{SDF}}^3({{p_{11}} - 2{\nu_{core}}{p_{12}}} )({{\varepsilon_{cladding,x}} - {\varepsilon_{core,x}}} )\\ &= - \frac{1}{2}n_{\textrm{SDF}}^3({{p_{11}} - 2{\nu_{core}}{p_{12}}} )({{\nu_{core}} - {\nu_{cladding}}} ){\varepsilon _z}. \end{aligned}$$
The total RI change induced by the elasto-optical effect can be calculated as
$$\Delta {n_{\textrm{SDF}}} = \Delta {n_x} + \Delta {n_y} + \Delta {n_z}.$$
Finally, the strain sensitivity can be expressed as
$$\begin{aligned}\frac{{\Delta {\lambda _{dip}}}}{\varepsilon } &= {\lambda _{dip}}{\{1 - \frac{1}{2}n_{\textrm{SDF}}^2({p_{12}} - {\nu _{core}}({p_{11}} + {p_{12}})}\\ &+ {\frac{1}{2}n_{\textrm{SDF}}^2({p_{12}} - {\nu _{core}}({{p_{11}} + {p_{12}}} )+ {p_{11}} - 2{\nu _{core}}{p_{12}})({\nu _{\textrm{core}}} - {\nu _{cladding}})\}} . \end{aligned}$$
Utilizing the materials values listed in Table 1 [21], the strain sensitivity as a function of alumina content is calculated and shown in Fig. 4. An increasing strain sensitivity is obtained with the higher alumina content.

 figure: Fig. 4.

Fig. 4. Calculated strain sensitivity of the SDF based FPI as a function of alumina content.

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Tables Icon

Table 1. Parameters used to calculate the strain sensitivity

3. Experiments and discussions

The buffered hydrofluoric acid, containing 50% per weight hydrofluoric acid (HF), 40% per weight ammonium fluoride (NH4F) and 10% per weight deionized (DI) water (H2O) was used to etch the conventional Coring SMF-28. The ESMF with a micro pit was fabricated because the core is etched faster than the cladding due to the Ge-doped core in SMF [24]. A section of well cleaved SDF was then sandwiched between the ESMF and the capillary, and was spliced subsequently by using the commercial optical fiber splicer (FITEL-s178) with the standard SMF fusion parameters. The SDF is made through the molten-core method with doping of alumina to silica in the core. The diameters of the SDF’s core and cladding are 9µm and 130µm respectively and the RI of the core was measured to be 1.551 corresponding to 51.3 mol.% aluminum content. The capillary deserves the 200µm outer diameter and 50µm thick wall. The fabricated FPI with $L = \sim $ 279.8µm, $d = \sim 13.0$µm and $D = \sim 27.1$µm was indicated in Fig. 5 and the corresponding reflection spectrum was shown in Fig. 6 (with the blue curve). The fringe contrast (∼16.65dB) of FPI with an etched air cavity was effectively enhanced, comparing with that (∼3.54dB) of the directly fusion FPI without an etched air cavity but with the similar cavity length, as can be seen in Fig. 6 (with the red curve).

 figure: Fig. 5.

Fig. 5. The microscopic image of the sensor.

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 figure: Fig. 6.

Fig. 6. The reflection spectrum with and without an etched air cavity.

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Figure 7. indicates the experimental setup of the FPI for strain measurement at high temperatures. The sensor was located in the center of the high temperature furnace with a temperature resolution of 0.1℃. The leading-in and leading-out fibers were mounted on a translation stage with a resolution of 0.01mm and fixed stage separately by a distance of ${L_t}$ (∼80.1cm). The reflection spectrum was collected by Micron Optics Si720 with a spectral resolution 0.25pm.

 figure: Fig. 7.

Fig. 7. The experimental setup of the FPI for strain measurement at a high temperature.

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Firstly, strain measurements were carried out at the room temperature. As shown in Fig. 8, a linear behavior of the wavelength shift was obtained with first increasing and then decreasing applied strain in the range of 0µɛ to 1000µɛ with a step of 100µɛ. The strain sensitivities in both strain up and down are the same 1.25 pm/µɛ, which agree well with the theoretical prediction (1.25pm/µɛ) according to Eq. (21).

 figure: Fig. 8.

Fig. 8. The FPI sensor responses to the applied strain.

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To study the temperature sensitivity of the FPI sensor, the temperature was increased from 20℃ to 900℃ with a step of 100℃, and 900℃ to 1000℃ with a step of 50℃. The experimental data were indicated in Fig. 9, showing the temperature sensitivity of the proposed sensor was 15.41pm/℃. Furthermore, the annealing experiment was performed to study the stability in a high temperature and to release the residual stress during the sensor fabrication, as shown in Fig. 10. Over the 100min annealing time, the total wavelength shifts at 700℃, 800℃, 900℃ and 950℃ were 0.01nm, 0.02nm, 0.06nm and 0.16nm, separately. After the fast wavelength shift in the first 30min, the dip wavelength shift became slow from 60min to 100min. During the annealing experiments, a slight intensity fluctuation within 5% occurred, mostly resulting from the light source power instability. On the other hand, heating the FPI up to 1000℃ leads to a faster shift rate and more durable shift time, indicating a chemically instability at 1000℃ because of a large diffusion affinity between the aluminum and silicon ions [17].

 figure: Fig. 9.

Fig. 9. The FPI sensor responses to the temperature.

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 figure: Fig. 10.

Fig. 10. Wavelength shifts of the FPI sensor for different annealing temperature.

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Since the dip wavelength of the FPI sensor presents a good temperature stability below 950℃, it’s worthwhile to study the performance when strain is applied at extremely high temperatures. The temperature was increased from 20℃ to 900℃ with a step of 100℃, and 900℃ to 1000℃ with a step of 50℃. At each temperature step, the fiber was kept straight with a slight tension and the setup was kept stable for 30min at the initial stage in order to obtain the relative stable dip wavelength. By controlling the position of the translation stage, the tension in the fiber was increased from 0µɛ up to 1000µɛ by a step of 100µɛ and then decreased to 0µɛ by the same step. The responses of the FPI sensor to the applied strain at 700℃, 800℃, 900℃, 950 ℃ and 1000℃ were shown in Figs. 11 (a), (b) and (c). The sensitivity at each experimental temperature was obtained by the linear fitting of the wavelength shifts response to the applied strain. Until 700℃, when loading the strain, the sensitivity is nearly the same when unloading the strain. However, from 800℃ to 950℃, sensitivities obtained when the strain was loaded were higher than those when the strain was unloaded. The conspicuous red shifts of the interferometer fringes were observed when the strain was back to zero, which expanded with the temperature increasing. The reason is that the aluminosilicate core seems to phase-separate above 700℃ [19], resulting in a certain level of transformation induced plastic whose level increases with the temperature. When the temperature increased to an extremely high 1000℃, a nonlinear behavior was observed in the process of strain loading and unloading, which could resulted from the decrease of viscosity [25]. The piecewise linear fits at relatively small ranges are made in the process of strain loading and unloading, with ranging from 0µɛ to 500µɛ, from 500µɛ to 1000µɛ when loading the strain and from 0µɛ to 500µɛ, from 500µɛ to 1000µɛ when unloading the strain respectively.

 figure: Fig. 11.

Fig. 11. The responses of the FPI sensor to the applied strain at (a)700℃, 800℃, (b)900℃, 950, (c)1000℃.

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The sensitivities of loading and unloading strain at tested temperatures were shown in Fig. 12. The sensitivities fluctuated around 1.29pm/µɛ from 20℃ to 950℃ and the fluctuation range increased with the temperature increasing. Specifically, the maximum fluctuation ranges from 20℃ to 700℃, from 700℃ to 950℃ and from 950℃ to 1000℃ are 0.21pm/µɛ, 0.44 pm/µɛ and 1.07 pm/µɛ, separately. The temperature’s dependent characters of sensitivities are apparently different between our SDF based FPI strain sensor and the pure silica based sensors [15,26] at high temperatures, because the photoelastic effect of the pure silica at high temperatures are different from the aluminosilicate whose photoelastic effect is modified by mix influences of two components. It’s still worth noting that, benefiting from the doping in the core and diffusion in the cladding of the high temperature resistant material $\textrm{A}{\textrm{l}_\textrm{2}}{\textrm{O}_\textrm{3}}$, the proposed sensor operated well at 950℃ and was characteristiced by a sensitivity of 1.19pm/µɛ and 1.06pm/µɛ in the process of loading and unloading strain separately. The highest well operation temperature and the corresponding range of tested strain were compared among our proposed SDF based sensor and the other existing strain sensors in Table 2.

 figure: Fig. 12.

Fig. 12. The sensitivities of loading and unloading strain at each tested temperature.

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Tables Icon

Table 2. The comparison of the highest operation temperature and the strain range

4. Conclusions

A SDF based FPI with an etched micro air cavity for strain measurement at high temperatures is proposed in this paper. A section of SDF was spliced with an etched SMF and a capillary to fabricate the FPI. The core containing 51.3mol.% aluminum was chosen to act as the intrinsic Fabry-Perot interferometer cavity with the cavity length of ∼279.8µm, whose fringe contrast was enhanced through the ∼13.0µm wide etched-air-cavity reflector. The strain sensitivity 1.25 pm/µɛ was demonstrated experimentally, which accords with the theoretical prediction through the additive model at room temperature. A thermal annealing process was performed from 700℃ to 1000℃ to study the stability in a high temperature and to release the residual stress during the sensor fabrication process, indicating the proposed sensor could keep stable at 950℃ after 100min. The strain calibration was carried out subsequently from 20℃ to 950℃. The sensor operated well in 950℃ benefiting from the doping in the core and diffusion in the cladding of the high temperature resistant material $\textrm{A}{\textrm{l}_\textrm{2}}{\textrm{O}_\textrm{3}}$. The sensitivities of 1.19 pm/µɛ and 1.06 pm/µɛ were obtained in the process of loading and unloading strain separately. The results indicate that the proposed sensor has a potential application in aerospace engine, high-temperature power plants, oil and gas industries, etc.

Funding

Ministry of Industry and Information Technology of the People's Republic of China (KMA81801590); National Natural Science Foundation of China (51575032); Natural Science Foundation of Beijing Municipality (3172020).

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22. M. Huang, “Stress effects on the performance of optical waveguides,” Int. J. Solids Struct. 40(7), 1615–1632 (2003). [CrossRef]  

23. P. D. Dragic, C. Kucera, J. Ballato, D. Litzkendorf, J. Dellith, and K. Schuster, “Brillouin scattering properties of lanthano-aluminosilicate optical fiber,” Appl. Opt. 53(25), 5660–5671 (2014). [CrossRef]  

24. A. Klini, T. David, and E. Bourillot, “Reproducible Optical Fiber Tips for Photon Scanning Tunneling Microscopy with Very Small (<5°) Cone Angle,” J. Lightwave Technol. 16(7), 1220–1227 (1998). [CrossRef]  

25. R. Bruckner, “Properties and structure ofvitreous silica. II,” J. Non-Cryst. Solids 5(3), 177–216 (1971). [CrossRef]  

26. H. Z. Yang, X. G. Qiao, Y. P. Wang, M. M. Ali, M. H. Lai, K. S. Lim, and H. Ahmad, “In-Fiber Gratings for Simultaneous Monitoring Temperature and Strain in Ultrahigh Temperature,” IEEE Photonics Technol. Lett. 27(1), 58–61 (2015). [CrossRef]  

27. P. Zhang, H. Yang, Y. Wang, H. Liu, K. S. Lim, D. S. Gunawardena, and H. Ahmad, “Strain measurement at temperatures up to 800 degrees C using regenerated gratings produced in the highGe-doped and B/Ge co-doped fibers,” Appl. Opt. 56(22), 6073–6078 (2017). [CrossRef]  

References

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  1. Y. Liu, S. L. Qu, W. G. Qu, and R. Y. Que, “A Fabry–Perot cuboid cavity across the fibre for high-sensitivity strain force sensing,” J. Opt. 16(10), 105401 (2014).
    [Crossref]
  2. H. F. Chen, D. N. Wang, and Y. Wang, “Simultaneous strain and temperature sensing using a slightly tapered optical fiber with an inner cavity,” Analyst 140(6), 1859–1862 (2015).
    [Crossref]
  3. P. A. R. Tafulo, P. A. S. Jorge, J. L. Santos, and O. Frazão, “Fabry–Pérot cavities based on chemical etching for high temperature and strain measurement,” Opt. Commun. 285(6), 1159–1162 (2012).
    [Crossref]
  4. X. P. Chen, F. B. Shen, Z. Wang, Z. Huang, and A. B. Wang, “Micro-air-gap based intrinsic Fabry–Perot interferometric fiber-optic sensor,” Appl. Opt. 45(30), 7760–7766 (2006).
    [Crossref]
  5. Y. Liu, D. N. Wang, and W. P. Chen, “Crescent shaped Fabry-Perot fiber cavity for ultra-sensitive strain measurement,” Sci. Rep. 6(1), 38390 (2016).
    [Crossref]
  6. K. Tian, G. Farrell, X. Wang, W. Yang, Y. Xin, H. Liang, E. Lewis, and P. Wang, “Strain sensor based on gourd-shaped single-mode-multimode-single-mode hybrid optical fibre structure,” Opt. Express 25(16), 18885–18896 (2017).
    [Crossref]
  7. S. Liu, Y. Wang, C. Liao, G. Wang, Z. Li, Q. Wang, J. Zhou, K. Yang, X. Zhong, J. Zhao, and J. Tang, “High-sensitivity strain sensor based on in-fiber improved Fabry-Perot interferometer,” Opt. Lett. 39(7), 2121–2124 (2014).
    [Crossref]
  8. Y. Wu, Y. Zhang, J. Wu, and P. Yuan, “Temperature-insensitive fiber optic Fabry-Perot interferometer based on special air cavity for transverse load and strain measurements,” Opt. Express 25(8), 9443–9448 (2017).
    [Crossref]
  9. F. C. Favero, L. Araujo, G. Bouwmans, V. Finazzi, J. Villatoro, and V. Pruneri, “Spheroidal Fabry-Perot microcavities in optical fibers for high-sensitivity sensing,” Opt. Express 20(7), 7112 (2012).
    [Crossref]
  10. Y. Liu, C. Lang, X. Wei, and S. Qu, “Strain force sensor with ultra-high sensitivity based on fiber inline Fabry-Perot micro-cavity plugged by cantilever taper,” Opt. Express 25(7), 7797–7806 (2017).
    [Crossref]
  11. C. Lang, Y. Liu, K. Cao, and S. Qu, “Temperature-insensitive optical fiber strain sensor with ultra-low detection limit based on capillary-taper temperature compensation structure,” Opt. Express 26(1), 477–487 (2018).
    [Crossref]
  12. S. Pevec and D. Donlagic, “All-fiber, long-active-length Fabry-Perot strain sensor,” Opt. Express 19(16), 15641–15651 (2011).
    [Crossref]
  13. Z. L. Ran, Y. J. Rao, H. Y. Deng, and X. Liao, “Miniature in-line photonic crystal fiber etalon fabricated by 157 nm laser micromachining,” Opt. Lett. 32(21), 3071–3073 (2007).
    [Crossref]
  14. M. Deng, C. P. Tang, T. Zhu, and Y. J. Rao, “PCF-Based Fabry–Pérot Interferometric Sensor for Strain Measurement at High Temperatures,” IEEE Photonics Technol. Lett. 23(11), 700–702 (2011).
    [Crossref]
  15. M. S. Ferreira, P. Roriz, J. Bierlich, J. Kobelke, K. Wondraczek, C. Aichele, K. Schuster, J. L. Santos, and O. Frazao, “Fabry-Perot cavity based on silica tube for strain sensing at high temperatures,” Opt. Express 23(12), 16063–16070 (2015).
    [Crossref]
  16. P. Dragic, T. Hawkins, P. Foy, S. Morris, and J. Ballato, “Sapphire-Derived All-Glass Optical Fibers,” Nat. Photonics 6(9), 627–633 (2012).
    [Crossref]
  17. T. Elsmann, A. Lorenz, N. S. Yazd, T. Habisreuther, J. Dellith, A. Schwuchow, J. Bierlich, K. Schuster, M. Rothhardt, L. Kido, and H. Bartelt, “High temperature sensing with fiber Bragg gratings in sapphire-derived all-glass optical fibers,” Opt. Express 22(22), 26825–26833 (2014).
    [Crossref]
  18. P. H. Zhang, L. Zhang, Z. P. Mourelatos, and Z. Y. Wang, “Crystallization-sapphire-derived-fiber-based Fabry-Perot interferometer for refractive index and high-temperature measurement,” Appl. Opt. 57(30), 9016–9021 (2018).
    [Crossref]
  19. G. Dan, S. J. Mihailov, J. Ballato, and P. D. Dragic, “Type I and II Bragg gratings made with infrared femtosecond radiation in high and low alumina content aluminosilicate optical fibers,” Optica 2(4), 313 (2015).
    [Crossref]
  20. P. Dragic, J. Ballato, A. Ballato, S. Morris, T. Hawkins, P.-C. Law, S. Ghosh, and M. C. Paul, “Mass density and the Brillouin spectroscopy of aluminosilicate optical fibers,” Opt. Mater. Express 2(11), 1641–1654 (2012).
    [Crossref]
  21. P. D. Dragic, J. Ballato, S. Morris, and T. Hawkins, “Pockels’ coefficients of alumina in aluminosilicate optical fiber,” J. Opt. Soc. Am. B 30(2), 244–250 (2013).
    [Crossref]
  22. M. Huang, “Stress effects on the performance of optical waveguides,” Int. J. Solids Struct. 40(7), 1615–1632 (2003).
    [Crossref]
  23. P. D. Dragic, C. Kucera, J. Ballato, D. Litzkendorf, J. Dellith, and K. Schuster, “Brillouin scattering properties of lanthano-aluminosilicate optical fiber,” Appl. Opt. 53(25), 5660–5671 (2014).
    [Crossref]
  24. A. Klini, T. David, and E. Bourillot, “Reproducible Optical Fiber Tips for Photon Scanning Tunneling Microscopy with Very Small (<5°) Cone Angle,” J. Lightwave Technol. 16(7), 1220–1227 (1998).
    [Crossref]
  25. R. Bruckner, “Properties and structure ofvitreous silica. II,” J. Non-Cryst. Solids 5(3), 177–216 (1971).
    [Crossref]
  26. H. Z. Yang, X. G. Qiao, Y. P. Wang, M. M. Ali, M. H. Lai, K. S. Lim, and H. Ahmad, “In-Fiber Gratings for Simultaneous Monitoring Temperature and Strain in Ultrahigh Temperature,” IEEE Photonics Technol. Lett. 27(1), 58–61 (2015).
    [Crossref]
  27. P. Zhang, H. Yang, Y. Wang, H. Liu, K. S. Lim, D. S. Gunawardena, and H. Ahmad, “Strain measurement at temperatures up to 800 degrees C using regenerated gratings produced in the highGe-doped and B/Ge co-doped fibers,” Appl. Opt. 56(22), 6073–6078 (2017).
    [Crossref]

2018 (2)

2017 (4)

2016 (1)

Y. Liu, D. N. Wang, and W. P. Chen, “Crescent shaped Fabry-Perot fiber cavity for ultra-sensitive strain measurement,” Sci. Rep. 6(1), 38390 (2016).
[Crossref]

2015 (4)

H. F. Chen, D. N. Wang, and Y. Wang, “Simultaneous strain and temperature sensing using a slightly tapered optical fiber with an inner cavity,” Analyst 140(6), 1859–1862 (2015).
[Crossref]

G. Dan, S. J. Mihailov, J. Ballato, and P. D. Dragic, “Type I and II Bragg gratings made with infrared femtosecond radiation in high and low alumina content aluminosilicate optical fibers,” Optica 2(4), 313 (2015).
[Crossref]

M. S. Ferreira, P. Roriz, J. Bierlich, J. Kobelke, K. Wondraczek, C. Aichele, K. Schuster, J. L. Santos, and O. Frazao, “Fabry-Perot cavity based on silica tube for strain sensing at high temperatures,” Opt. Express 23(12), 16063–16070 (2015).
[Crossref]

H. Z. Yang, X. G. Qiao, Y. P. Wang, M. M. Ali, M. H. Lai, K. S. Lim, and H. Ahmad, “In-Fiber Gratings for Simultaneous Monitoring Temperature and Strain in Ultrahigh Temperature,” IEEE Photonics Technol. Lett. 27(1), 58–61 (2015).
[Crossref]

2014 (4)

2013 (1)

2012 (4)

F. C. Favero, L. Araujo, G. Bouwmans, V. Finazzi, J. Villatoro, and V. Pruneri, “Spheroidal Fabry-Perot microcavities in optical fibers for high-sensitivity sensing,” Opt. Express 20(7), 7112 (2012).
[Crossref]

P. A. R. Tafulo, P. A. S. Jorge, J. L. Santos, and O. Frazão, “Fabry–Pérot cavities based on chemical etching for high temperature and strain measurement,” Opt. Commun. 285(6), 1159–1162 (2012).
[Crossref]

P. Dragic, T. Hawkins, P. Foy, S. Morris, and J. Ballato, “Sapphire-Derived All-Glass Optical Fibers,” Nat. Photonics 6(9), 627–633 (2012).
[Crossref]

P. Dragic, J. Ballato, A. Ballato, S. Morris, T. Hawkins, P.-C. Law, S. Ghosh, and M. C. Paul, “Mass density and the Brillouin spectroscopy of aluminosilicate optical fibers,” Opt. Mater. Express 2(11), 1641–1654 (2012).
[Crossref]

2011 (2)

M. Deng, C. P. Tang, T. Zhu, and Y. J. Rao, “PCF-Based Fabry–Pérot Interferometric Sensor for Strain Measurement at High Temperatures,” IEEE Photonics Technol. Lett. 23(11), 700–702 (2011).
[Crossref]

S. Pevec and D. Donlagic, “All-fiber, long-active-length Fabry-Perot strain sensor,” Opt. Express 19(16), 15641–15651 (2011).
[Crossref]

2007 (1)

2006 (1)

2003 (1)

M. Huang, “Stress effects on the performance of optical waveguides,” Int. J. Solids Struct. 40(7), 1615–1632 (2003).
[Crossref]

1998 (1)

1971 (1)

R. Bruckner, “Properties and structure ofvitreous silica. II,” J. Non-Cryst. Solids 5(3), 177–216 (1971).
[Crossref]

Ahmad, H.

P. Zhang, H. Yang, Y. Wang, H. Liu, K. S. Lim, D. S. Gunawardena, and H. Ahmad, “Strain measurement at temperatures up to 800 degrees C using regenerated gratings produced in the highGe-doped and B/Ge co-doped fibers,” Appl. Opt. 56(22), 6073–6078 (2017).
[Crossref]

H. Z. Yang, X. G. Qiao, Y. P. Wang, M. M. Ali, M. H. Lai, K. S. Lim, and H. Ahmad, “In-Fiber Gratings for Simultaneous Monitoring Temperature and Strain in Ultrahigh Temperature,” IEEE Photonics Technol. Lett. 27(1), 58–61 (2015).
[Crossref]

Aichele, C.

Ali, M. M.

H. Z. Yang, X. G. Qiao, Y. P. Wang, M. M. Ali, M. H. Lai, K. S. Lim, and H. Ahmad, “In-Fiber Gratings for Simultaneous Monitoring Temperature and Strain in Ultrahigh Temperature,” IEEE Photonics Technol. Lett. 27(1), 58–61 (2015).
[Crossref]

Araujo, L.

Ballato, A.

Ballato, J.

Bartelt, H.

Bierlich, J.

Bourillot, E.

Bouwmans, G.

Bruckner, R.

R. Bruckner, “Properties and structure ofvitreous silica. II,” J. Non-Cryst. Solids 5(3), 177–216 (1971).
[Crossref]

Cao, K.

Chen, H. F.

H. F. Chen, D. N. Wang, and Y. Wang, “Simultaneous strain and temperature sensing using a slightly tapered optical fiber with an inner cavity,” Analyst 140(6), 1859–1862 (2015).
[Crossref]

Chen, W. P.

Y. Liu, D. N. Wang, and W. P. Chen, “Crescent shaped Fabry-Perot fiber cavity for ultra-sensitive strain measurement,” Sci. Rep. 6(1), 38390 (2016).
[Crossref]

Chen, X. P.

Dan, G.

David, T.

Dellith, J.

Deng, H. Y.

Deng, M.

M. Deng, C. P. Tang, T. Zhu, and Y. J. Rao, “PCF-Based Fabry–Pérot Interferometric Sensor for Strain Measurement at High Temperatures,” IEEE Photonics Technol. Lett. 23(11), 700–702 (2011).
[Crossref]

Donlagic, D.

Dragic, P.

Dragic, P. D.

Elsmann, T.

Farrell, G.

Favero, F. C.

Ferreira, M. S.

Finazzi, V.

Foy, P.

P. Dragic, T. Hawkins, P. Foy, S. Morris, and J. Ballato, “Sapphire-Derived All-Glass Optical Fibers,” Nat. Photonics 6(9), 627–633 (2012).
[Crossref]

Frazao, O.

Frazão, O.

P. A. R. Tafulo, P. A. S. Jorge, J. L. Santos, and O. Frazão, “Fabry–Pérot cavities based on chemical etching for high temperature and strain measurement,” Opt. Commun. 285(6), 1159–1162 (2012).
[Crossref]

Ghosh, S.

Gunawardena, D. S.

Habisreuther, T.

Hawkins, T.

Huang, M.

M. Huang, “Stress effects on the performance of optical waveguides,” Int. J. Solids Struct. 40(7), 1615–1632 (2003).
[Crossref]

Huang, Z.

Jorge, P. A. S.

P. A. R. Tafulo, P. A. S. Jorge, J. L. Santos, and O. Frazão, “Fabry–Pérot cavities based on chemical etching for high temperature and strain measurement,” Opt. Commun. 285(6), 1159–1162 (2012).
[Crossref]

Kido, L.

Klini, A.

Kobelke, J.

Kucera, C.

Lai, M. H.

H. Z. Yang, X. G. Qiao, Y. P. Wang, M. M. Ali, M. H. Lai, K. S. Lim, and H. Ahmad, “In-Fiber Gratings for Simultaneous Monitoring Temperature and Strain in Ultrahigh Temperature,” IEEE Photonics Technol. Lett. 27(1), 58–61 (2015).
[Crossref]

Lang, C.

Law, P.-C.

Lewis, E.

Li, Z.

Liang, H.

Liao, C.

Liao, X.

Lim, K. S.

P. Zhang, H. Yang, Y. Wang, H. Liu, K. S. Lim, D. S. Gunawardena, and H. Ahmad, “Strain measurement at temperatures up to 800 degrees C using regenerated gratings produced in the highGe-doped and B/Ge co-doped fibers,” Appl. Opt. 56(22), 6073–6078 (2017).
[Crossref]

H. Z. Yang, X. G. Qiao, Y. P. Wang, M. M. Ali, M. H. Lai, K. S. Lim, and H. Ahmad, “In-Fiber Gratings for Simultaneous Monitoring Temperature and Strain in Ultrahigh Temperature,” IEEE Photonics Technol. Lett. 27(1), 58–61 (2015).
[Crossref]

Litzkendorf, D.

Liu, H.

Liu, S.

Liu, Y.

C. Lang, Y. Liu, K. Cao, and S. Qu, “Temperature-insensitive optical fiber strain sensor with ultra-low detection limit based on capillary-taper temperature compensation structure,” Opt. Express 26(1), 477–487 (2018).
[Crossref]

Y. Liu, C. Lang, X. Wei, and S. Qu, “Strain force sensor with ultra-high sensitivity based on fiber inline Fabry-Perot micro-cavity plugged by cantilever taper,” Opt. Express 25(7), 7797–7806 (2017).
[Crossref]

Y. Liu, D. N. Wang, and W. P. Chen, “Crescent shaped Fabry-Perot fiber cavity for ultra-sensitive strain measurement,” Sci. Rep. 6(1), 38390 (2016).
[Crossref]

Y. Liu, S. L. Qu, W. G. Qu, and R. Y. Que, “A Fabry–Perot cuboid cavity across the fibre for high-sensitivity strain force sensing,” J. Opt. 16(10), 105401 (2014).
[Crossref]

Lorenz, A.

Mihailov, S. J.

Morris, S.

Mourelatos, Z. P.

Paul, M. C.

Pevec, S.

Pruneri, V.

Qiao, X. G.

H. Z. Yang, X. G. Qiao, Y. P. Wang, M. M. Ali, M. H. Lai, K. S. Lim, and H. Ahmad, “In-Fiber Gratings for Simultaneous Monitoring Temperature and Strain in Ultrahigh Temperature,” IEEE Photonics Technol. Lett. 27(1), 58–61 (2015).
[Crossref]

Qu, S.

Qu, S. L.

Y. Liu, S. L. Qu, W. G. Qu, and R. Y. Que, “A Fabry–Perot cuboid cavity across the fibre for high-sensitivity strain force sensing,” J. Opt. 16(10), 105401 (2014).
[Crossref]

Qu, W. G.

Y. Liu, S. L. Qu, W. G. Qu, and R. Y. Que, “A Fabry–Perot cuboid cavity across the fibre for high-sensitivity strain force sensing,” J. Opt. 16(10), 105401 (2014).
[Crossref]

Que, R. Y.

Y. Liu, S. L. Qu, W. G. Qu, and R. Y. Que, “A Fabry–Perot cuboid cavity across the fibre for high-sensitivity strain force sensing,” J. Opt. 16(10), 105401 (2014).
[Crossref]

Ran, Z. L.

Rao, Y. J.

M. Deng, C. P. Tang, T. Zhu, and Y. J. Rao, “PCF-Based Fabry–Pérot Interferometric Sensor for Strain Measurement at High Temperatures,” IEEE Photonics Technol. Lett. 23(11), 700–702 (2011).
[Crossref]

Z. L. Ran, Y. J. Rao, H. Y. Deng, and X. Liao, “Miniature in-line photonic crystal fiber etalon fabricated by 157 nm laser micromachining,” Opt. Lett. 32(21), 3071–3073 (2007).
[Crossref]

Roriz, P.

Rothhardt, M.

Santos, J. L.

M. S. Ferreira, P. Roriz, J. Bierlich, J. Kobelke, K. Wondraczek, C. Aichele, K. Schuster, J. L. Santos, and O. Frazao, “Fabry-Perot cavity based on silica tube for strain sensing at high temperatures,” Opt. Express 23(12), 16063–16070 (2015).
[Crossref]

P. A. R. Tafulo, P. A. S. Jorge, J. L. Santos, and O. Frazão, “Fabry–Pérot cavities based on chemical etching for high temperature and strain measurement,” Opt. Commun. 285(6), 1159–1162 (2012).
[Crossref]

Schuster, K.

Schwuchow, A.

Shen, F. B.

Tafulo, P. A. R.

P. A. R. Tafulo, P. A. S. Jorge, J. L. Santos, and O. Frazão, “Fabry–Pérot cavities based on chemical etching for high temperature and strain measurement,” Opt. Commun. 285(6), 1159–1162 (2012).
[Crossref]

Tang, C. P.

M. Deng, C. P. Tang, T. Zhu, and Y. J. Rao, “PCF-Based Fabry–Pérot Interferometric Sensor for Strain Measurement at High Temperatures,” IEEE Photonics Technol. Lett. 23(11), 700–702 (2011).
[Crossref]

Tang, J.

Tian, K.

Villatoro, J.

Wang, A. B.

Wang, D. N.

Y. Liu, D. N. Wang, and W. P. Chen, “Crescent shaped Fabry-Perot fiber cavity for ultra-sensitive strain measurement,” Sci. Rep. 6(1), 38390 (2016).
[Crossref]

H. F. Chen, D. N. Wang, and Y. Wang, “Simultaneous strain and temperature sensing using a slightly tapered optical fiber with an inner cavity,” Analyst 140(6), 1859–1862 (2015).
[Crossref]

Wang, G.

Wang, P.

Wang, Q.

Wang, X.

Wang, Y.

Wang, Y. P.

H. Z. Yang, X. G. Qiao, Y. P. Wang, M. M. Ali, M. H. Lai, K. S. Lim, and H. Ahmad, “In-Fiber Gratings for Simultaneous Monitoring Temperature and Strain in Ultrahigh Temperature,” IEEE Photonics Technol. Lett. 27(1), 58–61 (2015).
[Crossref]

Wang, Z.

Wang, Z. Y.

Wei, X.

Wondraczek, K.

Wu, J.

Wu, Y.

Xin, Y.

Yang, H.

Yang, H. Z.

H. Z. Yang, X. G. Qiao, Y. P. Wang, M. M. Ali, M. H. Lai, K. S. Lim, and H. Ahmad, “In-Fiber Gratings for Simultaneous Monitoring Temperature and Strain in Ultrahigh Temperature,” IEEE Photonics Technol. Lett. 27(1), 58–61 (2015).
[Crossref]

Yang, K.

Yang, W.

Yazd, N. S.

Yuan, P.

Zhang, L.

Zhang, P.

Zhang, P. H.

Zhang, Y.

Zhao, J.

Zhong, X.

Zhou, J.

Zhu, T.

M. Deng, C. P. Tang, T. Zhu, and Y. J. Rao, “PCF-Based Fabry–Pérot Interferometric Sensor for Strain Measurement at High Temperatures,” IEEE Photonics Technol. Lett. 23(11), 700–702 (2011).
[Crossref]

Analyst (1)

H. F. Chen, D. N. Wang, and Y. Wang, “Simultaneous strain and temperature sensing using a slightly tapered optical fiber with an inner cavity,” Analyst 140(6), 1859–1862 (2015).
[Crossref]

Appl. Opt. (4)

IEEE Photonics Technol. Lett. (2)

H. Z. Yang, X. G. Qiao, Y. P. Wang, M. M. Ali, M. H. Lai, K. S. Lim, and H. Ahmad, “In-Fiber Gratings for Simultaneous Monitoring Temperature and Strain in Ultrahigh Temperature,” IEEE Photonics Technol. Lett. 27(1), 58–61 (2015).
[Crossref]

M. Deng, C. P. Tang, T. Zhu, and Y. J. Rao, “PCF-Based Fabry–Pérot Interferometric Sensor for Strain Measurement at High Temperatures,” IEEE Photonics Technol. Lett. 23(11), 700–702 (2011).
[Crossref]

Int. J. Solids Struct. (1)

M. Huang, “Stress effects on the performance of optical waveguides,” Int. J. Solids Struct. 40(7), 1615–1632 (2003).
[Crossref]

J. Lightwave Technol. (1)

J. Non-Cryst. Solids (1)

R. Bruckner, “Properties and structure ofvitreous silica. II,” J. Non-Cryst. Solids 5(3), 177–216 (1971).
[Crossref]

J. Opt. (1)

Y. Liu, S. L. Qu, W. G. Qu, and R. Y. Que, “A Fabry–Perot cuboid cavity across the fibre for high-sensitivity strain force sensing,” J. Opt. 16(10), 105401 (2014).
[Crossref]

J. Opt. Soc. Am. B (1)

Nat. Photonics (1)

P. Dragic, T. Hawkins, P. Foy, S. Morris, and J. Ballato, “Sapphire-Derived All-Glass Optical Fibers,” Nat. Photonics 6(9), 627–633 (2012).
[Crossref]

Opt. Commun. (1)

P. A. R. Tafulo, P. A. S. Jorge, J. L. Santos, and O. Frazão, “Fabry–Pérot cavities based on chemical etching for high temperature and strain measurement,” Opt. Commun. 285(6), 1159–1162 (2012).
[Crossref]

Opt. Express (8)

Y. Wu, Y. Zhang, J. Wu, and P. Yuan, “Temperature-insensitive fiber optic Fabry-Perot interferometer based on special air cavity for transverse load and strain measurements,” Opt. Express 25(8), 9443–9448 (2017).
[Crossref]

F. C. Favero, L. Araujo, G. Bouwmans, V. Finazzi, J. Villatoro, and V. Pruneri, “Spheroidal Fabry-Perot microcavities in optical fibers for high-sensitivity sensing,” Opt. Express 20(7), 7112 (2012).
[Crossref]

Y. Liu, C. Lang, X. Wei, and S. Qu, “Strain force sensor with ultra-high sensitivity based on fiber inline Fabry-Perot micro-cavity plugged by cantilever taper,” Opt. Express 25(7), 7797–7806 (2017).
[Crossref]

C. Lang, Y. Liu, K. Cao, and S. Qu, “Temperature-insensitive optical fiber strain sensor with ultra-low detection limit based on capillary-taper temperature compensation structure,” Opt. Express 26(1), 477–487 (2018).
[Crossref]

S. Pevec and D. Donlagic, “All-fiber, long-active-length Fabry-Perot strain sensor,” Opt. Express 19(16), 15641–15651 (2011).
[Crossref]

T. Elsmann, A. Lorenz, N. S. Yazd, T. Habisreuther, J. Dellith, A. Schwuchow, J. Bierlich, K. Schuster, M. Rothhardt, L. Kido, and H. Bartelt, “High temperature sensing with fiber Bragg gratings in sapphire-derived all-glass optical fibers,” Opt. Express 22(22), 26825–26833 (2014).
[Crossref]

M. S. Ferreira, P. Roriz, J. Bierlich, J. Kobelke, K. Wondraczek, C. Aichele, K. Schuster, J. L. Santos, and O. Frazao, “Fabry-Perot cavity based on silica tube for strain sensing at high temperatures,” Opt. Express 23(12), 16063–16070 (2015).
[Crossref]

K. Tian, G. Farrell, X. Wang, W. Yang, Y. Xin, H. Liang, E. Lewis, and P. Wang, “Strain sensor based on gourd-shaped single-mode-multimode-single-mode hybrid optical fibre structure,” Opt. Express 25(16), 18885–18896 (2017).
[Crossref]

Opt. Lett. (2)

Opt. Mater. Express (1)

Optica (1)

Sci. Rep. (1)

Y. Liu, D. N. Wang, and W. P. Chen, “Crescent shaped Fabry-Perot fiber cavity for ultra-sensitive strain measurement,” Sci. Rep. 6(1), 38390 (2016).
[Crossref]

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Figures (12)

Fig. 1.
Fig. 1. The scheme diagram of the FPI.
Fig. 2.
Fig. 2. The model of the proposed FPI sensor.
Fig. 3.
Fig. 3. Block diagram of a unit volume of the SDF core in the force mechanical system.
Fig. 4.
Fig. 4. Calculated strain sensitivity of the SDF based FPI as a function of alumina content.
Fig. 5.
Fig. 5. The microscopic image of the sensor.
Fig. 6.
Fig. 6. The reflection spectrum with and without an etched air cavity.
Fig. 7.
Fig. 7. The experimental setup of the FPI for strain measurement at a high temperature.
Fig. 8.
Fig. 8. The FPI sensor responses to the applied strain.
Fig. 9.
Fig. 9. The FPI sensor responses to the temperature.
Fig. 10.
Fig. 10. Wavelength shifts of the FPI sensor for different annealing temperature.
Fig. 11.
Fig. 11. The responses of the FPI sensor to the applied strain at (a)700℃, 800℃, (b)900℃, 950, (c)1000℃.
Fig. 12.
Fig. 12. The sensitivities of loading and unloading strain at each tested temperature.

Tables (2)

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Table 1. Parameters used to calculate the strain sensitivity

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Table 2. The comparison of the highest operation temperature and the strain range

Equations (21)

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E o u t = E 0 ( R 1 + ( 1 η 1 ) ( 1 R 1 ) R 2 e j 2 β L ) ,
I λ = R 1 + ( 1 η 1 ) 2 ( 1 R 1 ) 2 R 2 + 2 ( 1 η 1 ) ( 1 R 1 ) R 1 R 2 cos ( 4 π n SDF L / λ + φ 0 ) ,
4 π n SDF L λ m = ( 2 m + 1 ) π ,
λ d i p = 4 n SDF L 2 m + 1 .
Δ λ d i p = 4 2 m + 1 ( n SDF Δ L + L Δ n SDF ) ,
Δ L = L ε z ,
Δ λ d i p = 4 2 m + 1 ( n SDF L ε z + L Δ n SDF ) = 4 n SDF L 2 m + 1 ( ε z + 1 n SDF Δ n SDF ) .
Δ λ d i p ε z = λ d i p ( 1 + 1 n SDF Δ n SDF ε z ) .
n SDF = m n A l 2 O 3 + ( 1 m ) n Si O 2 ,
ν c o r e = m ν A l 2 O 3 + ( 1 m ) ν Si O 2 ,
ν c l a d d i n g = ν Si O 2 .
( ε OC, σ OC ) = 1 n SDF 3 ( n A l 2 O 3 3 m ( ε O C A l 2 O 3 , σ O C A l 2 O 3 ) + n Si O 2 3 ( 1 m ) ( ε O C Si O 2 , σ O C Si O 2 ) ) ,
p 11 = ε OC + 2 σ OC 1 + 2 ν ,
p 12 = ε OC + 2 ν σ OC 1 2 ν .
ε c o r e , x = ε c o r e , y = ν c o r e ε z ,
ε c l a d d i n g , x = ε c l a d d i n g , y = ν c l a d d i n g ε z ,
Δ n z = 1 2 n SDF 3 ( p 12 ν c o r e ( p 11 + p 12 ) ) ε z .
Δ n x = 1 2 n SDF 3 ( p 12 ν c o r e ( p 11 + p 12 ) ) ( ε c l a d d i n g , x ε c o r e , x ) = 1 2 n SDF 3 ( p 12 ν c o r e ( p 11 + p 12 ) ) ( ν c o r e ν c l a d d i n g ) ε z ,
Δ n y = 1 2 n SDF 3 ( p 11 2 ν c o r e p 12 ) ( ε c l a d d i n g , x ε c o r e , x ) = 1 2 n SDF 3 ( p 11 2 ν c o r e p 12 ) ( ν c o r e ν c l a d d i n g ) ε z .
Δ n SDF = Δ n x + Δ n y + Δ n z .
Δ λ d i p ε = λ d i p { 1 1 2 n SDF 2 ( p 12 ν c o r e ( p 11 + p 12 ) + 1 2 n SDF 2 ( p 12 ν c o r e ( p 11 + p 12 ) + p 11 2 ν c o r e p 12 ) ( ν core ν c l a d d i n g ) } .

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