Fiber-optic strain sensors have demonstrated their potentials in structural health monitoring^[1–3] because they are small in size, corrosion-resistant, immune to electromagnetic interference, and highly sensitive compared with the traditional ones based on mechanical and electronic technologies^[4–8]. However, strain measurements are prone to being affected by changes in the ambient environment such as temperature fluctuations. Many methods have been proposed for avoiding temperature crosstalk^[9–11], and, in practical applications, these often involve the simultaneous measurement of temperature and strain. One of the most common techniques for simultaneous measurement of strain and temperature involves cascaded structures such as inline interference structures cascaded with polarization-maintaining fibers and multimode fibers^[12], cascaded gratings^[13–15], cascaded Fabry–Pérot (FP) interferometers (FPIs)^[16–18], and in-line modal interferometers^[19–21]. These sensors perform simultaneous measurement using a crossing-matrix method and phase demodulation based on path-matching interferometers. Nevertheless, such structures are large, complex, difficult to fabricate, and fragile. Therefore, a structure or mechanism is needed to overcome these shortcomings.

Antiresonance (AR) is generated through an AR reflecting fiber—a photonic bandgap waveguide with a core of low refractive index^[22], the thickness of the layer with high refractive index, and the refractive index itself, which dominate the corresponding spectral characteristics ^[23]. With the introduction of the AR reflecting optical waveguide (ARROW) model^[22], the AR reflecting fiber has been gradually applied in the field of optical fiber sensing. Various structures of AR reflecting fibers have been reported, such as photonic crystal fibers^[24–26], Kagome fibers^[27,28], hollow-core fibers (HCFs) with two eccentric cores^[29,30] for temperature^[29,31], pressure^[32], and curvature^[30] sensing, and simple HCFs^[23,31,32]. However, most of these approaches can only achieve the measurement of a single parameter by directly tracing the shift of the transmission spectrum based on the AR mechanism. Therefore, temperature crosstalk in complex environments cannot be avoided. In fact, FP interference along the axial direction is ignored by these approaches, because it is too weak in forward transmission as a result of the large amplitude difference between the two forward beams on the two reflecting surfaces in the FP interference. However, it could potentially be used for double-parameter sensing. In the process of reflection, FP interference is dominant in a relatively short HCF, and AR is only generated when the length of the HCF is greater than a critical length. As a result, the reflection spectrum is comprised of spectral components caused by FP interference and AR if an HCF is long enough, and this can be utilized for double-parameter sensing.

In this Letter, a dual-parameter fiber-optic sensor simultaneously measuring strain and temperature is proposed. The sensor works properly with the help of FP interference and AR mechanisms within the AR reflecting fiber constructed from single-mode fiber (SMF)–HCF–SMF. The specific structure comprises an axial FP cavity formed by the hollow core and a radial FP cavity by the cladding of an HCF, in which the FP interference and AR are generated. It is observed that the reflection spectra are composed of an FP-modulated AR envelope. Since the FP and AR mechanisms within the HCF are solely sensitive to strain and temperature, respectively, this configuration allows the proposed sensor to perform simultaneous measurement. To the best of our knowledge, this is the first time that a combination of FP interference and AR mechanism in an AR reflecting fiber has been applied to the simultaneous measurement of strain and temperature.

The proposed sensor was composed of an HCF, the cladding thickness and outer diameter of which were 25 µm and 125 µm, respectively. The HCF was sandwiched between two SMFs to form an AR reflecting fiber, as shown in Fig. 1(a). Several steps including fiber cleaving and splicing were required to prepare the proposed sensor. First, two SMFs were spliced onto each end of an HCF (TSP050150, Polymicro Technologies, USA), respectively, with a fiber splicer (FSM-80S, Fujikura, Japan). Second, the fabricated fiber segment was placed under a microscope, and an HCF of the desired length to form the cavity was cleaved. Finally, another SMF was spliced onto the HCF obtained from the second step. The fabricated sensor is exhibited in Fig. 1(b), together with the end face of the HCF used in the experiment.

Regarding the HCF part illustrated in Fig. 1(a), it has a length of L and consists of an air core with a refractive index of n0 and a cladding of n2. 2r is the inner diameter, and d is the cladding thickness. Likewise, n1 denotes the refractive index of the core and n2 the cladding for the SMF. The air cavity between the interface of SMF1 and HCF (M1) and the interface of HCF and SMF2 (M2) forms an axial FPI. In the case of an FPI that is made of optical fibers, its reflection spectrum is simplified to superposition of I1 reflected back from M1, and I2 reflected back from M2 as a result of low reflectivity at each interface. Similarly, its transmission spectrum can also be assumed to be the interference between first transmitted light I3 and second transmitted light I4. However, after being reflected twice by M1 and M2, the intensity of I4 is too weak to form interference with I3. Therefore, the FP interference is quite weak in transmission, and FP interference was not observed in the structure.

The AR mechanism in the SMF–HCF–SMF structure can be interpreted by the ARROW model^[22]. According to this model, the capillary can be considered an FPI along the radial direction, in which the inner wall and outer wall of cladding make up the silica FPI generating AR. The typical resonant wavelengths λm can be given as^[22]λm(AR)=2dmn22−n02,(1)where m denotes the resonant order. The wavelengths of peak intensity for the axial FPI are known as^[23]λm(FP)=2Lmn0.(2)

A transmission spectrum of the proposed sensor with an HCF of 2050 µm in length is shown in Fig. 1(c). This shows that sharp dips occur at the resonant wavelengths of AR and indicates that FP interference is weak enough to be ignored in the forward propagation. The transmission energy of the AR mechanism will also be reflected by M2. However, AR mechanisms take effect and contribute to the reflection spectrum only if the HCF is longer than a certain length because AR is the result of the interference of two beams—the first reflected light at the air–silica interface, I5, and the light reflected back from the silica–air interface, I6 [see Fig. 1(a)]. The periodic dips in the AR spectrum can be interpreted as constructive interference formed in the HCF cladding. The critical length for AR generation is written as^[23]Lc=n02+n22−n12(rn12−n22+2dn12−n02).(3)

Therefore, AR and FP interference both contribute to the reflection spectrum if the critical condition, L≥Lc, is satisfied, resulting in a superposed reflection spectrum by axial FP and AR. The superposition is expected to achieve the fine fringes modulated by a broad envelope. The corresponding reflection spectrum is shown in Fig. 1(d), where the HCF was 450 µm in length, and the red dotted lines show the extracted envelope caused by AR, between which the high-frequency fine fringes caused by FP interference are.

In this sensor, these two mechanisms, axial FP interferometry and the AR mechanism, are used to measure strain and temperature. For an FPI sensor, the sensitivity for a physical quantity X is given by ΔλΔX=λ(1nΔnΔX+1LΔLΔX).(4)

Since the refractive index variation of air is negligible when the temperature changes compared to that of silica^[33], it is convenient to obtain the temperature dependence of the sensor by leaving out the air index variation, which can be derived from Eq. (1), expressed as

∂λm(AR)∂T=2dn2mn22−n02∂n2∂T,(5)where ∂n2/∂T is the thermo-optic coefficient of cladding material of HCF.

The cavity length of an FPI varies with the axial strain applied to it. However, L has no effect on λm(AR) according to Eq. (1). Therefore, only the fine fringes of the reflection spectra in FP interference will shift when the strain changes. The strain sensitivity S of an FP cavity can be expressed as^[9]S=kεLFP+LSMFLSMFAFPASMF+LFP,(6)where kε is the strain coefficient, LFP and LSMF are the lengths of the HCF and SMF, respectively, and AFP and ASMF are the cross-sectional areas of the HCF and SMF, respectively. From this equation, if AFP is smaller than ASMF, then the strain sensitivity will increase with decreasing LFP. It should be noted that a longer air-cavity FPI reduces the visibility of the interference fringes because of greater losses, whereas AR is generated only if the length of HCF is greater than the critical length. Furthermore, the critical length and the strain sensitivity both increase as the thickness of the HCF decreases. Therefore, there is a tradeoff between the fringe visibility and the strain sensitivity of the sensor.

To study the effect of temperature and strain acting on the sensor, theoretical calculations were conducted^[16,23]. Figures 2(a) and 2(b) show the calculated reflection spectra of the proposed sensor under different temperature and strain, respectively. Specifically, Figs. 2(c) and 2(d) show the spectra with the increased temperature, where the AR envelope has a red shift of 25 pm/°C, while the FP fringe response for temperature is only 0.7 pm/°C. Using the same analysis for strain tests, FP fringes evidently shift toward longer wavelengths with a strain response of 2.7 pm/µε, while a response −0.52pm/με is obtained from the AR envelope, as shown in Figs. 2(c) and 2(d). Consequently, it is acceptable to assume, in principle, that the AR envelope is solely sensitive to temperature, and the FP fringe is solely sensitive to strain.

Figure 3 exhibits an experimental setup for the purpose of testing the temperature responses, where a broadband light source (BBS, ASE, FiberLake, China) was connected to Port 1 of the optical circulator (OC), the fabricated sensor to Port 2, and the optical spectral analyzer (OSA, AQ6370C, Yokogawa, Japan) to Port 3. The light over a wavelength range 1250–1650 nm from the BBS was launched in the sensor and finally reflected back into the OSA and recorded. The sensor was placed in an oven (SG XL 1200, SIOM, China) that increased the temperature from 40°C to 190°C at intervals of 20°C. The sensor was not subject to external forces during the temperature test.

The AR envelope was extracted by linking the highest or lowest points of each peak or valley in the reflection spectrum of the sensor. Figure 4(a) shows the evolution of one dip of the extracted envelope with increasing temperature, where the spectrum shifts towards longer wavelengths. Figure 4(b) shows the evolution of the FPI fine fringes with respect to temperature. It indicates that the temperature does not influence the FP fringes of the sensor. The results are consistent with the calculations. By tracing the dips of the envelope in Fig. 4(a), the temperature-induced wavelength shift was obtained and is plotted in Fig. 4(c), where a linear relationship is demonstrated. The temperature sensitivity of the AR mechanism was 21.11 pm/°C, and the temperature response of the FP fringe was estimated to be 0.35 pm/°C.

The strain responses were also investigated with the experimental setup described in Fig. 5. Two ends of fibers that connect the sensor were fixed on a fiber-optic platform and a translation stage with glue, respectively, and the distance between two fixed points was set to 25 cm. The length of the fiber between the two glued points was gradually increased by changing the axial position of the translation stage. The extended length was increased from 5 µm to 300 µm with steps of 50 µm, and the reflection spectrum was recorded immediately in each step. The longitudinal strain ε was calculated usingε=ΔLL′,(7)where L′ is the original length between two fixed points, and ΔL is the extended length in the axial direction. From Eq. (7), the longitudinal strain ε that was applied to the sensor was increased from 0 to 1200 µε with steps of 200 µε. During the strain test, the temperature was maintained at 25°C.

Figure 6(a) shows a single valley of the AR envelopes under different strains, from which a clear red shift in the FPI fine fringes occurs as the strain is increased. This is because when the axial strain is applied to the sensor, the cavity length of the axial FPI increases. According to Eq. (2), the reflection spectrum should shift toward longer wavelengths with the increasing FP cavity length L. A linear relationship between the strain and the wavelength shift was found, as shown in Fig. 6(c), and the sensitivity of the FPI was 2 pm/µε. Additionally, the strain response of the AR envelope was calculated to be −0.55pm/με. Therefore, compared to the temperature responses, the AR envelope experienced a little movement with changes in strain, and only the amplitude changed as a result of the drift in the FPI spectrum, as shown in Fig. 6(b), which coincides with the calculations.

The temperature and strain responses of the sensor envelope will not be affected because the measurement mechanisms of the two parameters are independent. To experimentally demonstrate this, another sensor was fabricated from an HCF with a length of 600 µm and the inner and outer diameters of 75 and 125 µm, respectively. Two ends of the sensor were fixed to the translation stages, and a heating platform was placed below it so the ambient temperature of the sensor could be changed. When the temperature reached 30°C, 50°C, and 70°C, the position of the translation stage was changed to apply strain to the sensor, and the applied strain range was 0–1000 µε. The spectra were recorded with a step of 200 µε. The strain response curves at three different temperatures are shown in Fig. 7(a), and the sensitivities of the sensor at these different temperatures were 1.41, 1.37, and 1.37 pm/µε, respectively, which indicates that the measurement of strain is independent of temperature. Figure 7(b) shows temperature responses of the AR envelope during the strain test when the applied strain was 200 µε, the result of which was estimated to be 21 pm/°C.

A simultaneous measurement of strain and temperature is allowed by comparing the reflection spectra detected in changing environmental conditions to the original calibration one. This scheme works because the FP- and AR-based spectra are almost solely sensitive to their specific measurements, the corresponding crosstalk of which was estimated to be 0.026°C/µε for the AR envelope and 0.175 µε/°C for the FP fringe.

To investigate the repeatability of the proposed sensor, we conducted three temperature and strain experiments, each separated by 3 h, using a sensor with an HCF 445 µm in length. Strain measurement was found to be repeatable, as shown in Fig. 8(a), and the repeatability error was estimated to be 0.54%. The strain sensitivities from the three separate tests were 1.86, 1.84, and 1.84 pm/µε. The temperature sensitivities, calculated for two tests, were 22.70 and 22.72 pm/°C, indicating good repeatability, as illustrated in Fig. 8(b).

The temporal stability of the proposed sensor was also investigated. Measurements were taken continuously for 24 h under the same temperature and strain conditions. The spectral changes in the AR envelope of the sensor’s reflectance spectrum around 1408 and 1565 nm and the spectral fringe changes in the FPI spectrum around 1450 and 1550 nm are shown in Fig. 8(c). The positions of the two troughs in the AR envelope varied by 0.2 and 0.4 nm, respectively, whereas the positions of the two troughs in the FP spectrum were almost constant, demonstrating that the strain measurement obtained from FP interference is extremely stable.

In summary, we have proposed and demonstrated an FP- and AR-based dual-parameter sensor with an SMF–HCF–SMF configuration. This system can simultaneously measure strain and temperature due to different spectral sensitivities of FP interference and AR mechanism, which occurr in the air core and cladding, respectively, to strain and temperature. The experimental results show that the temperature sensitivity of our system was 21.11 pm/°C, and the strain sensitivity was 2 pm/µε. The corresponding crosstalk was 0.026°C/µε and 0.175 µε/°C. Moreover, the proposed sensor is small, simple, robust, and reliable, making it a good candidate for structural health monitoring of buildings, tunnels, and many other structures.