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Abstract
We propose a wide-range strain sensor based on Brillouin frequency and linewidth in a 50 cm-long As2Se3-polymethyl methacrylate (As2Se3-PMMA) hybrid microfiber with a core diameter of 2.5 µm. The distributed information over the hybrid microfiber is measured by a Brillouin optical time-domain analysis (BOTDA) system. The wide dynamic range strain from 0 to 15000 µɛ is enabled by measuring the Brillouin frequency and linewidth due to the low Young’s modulus of As2Se3 core and the high mechanical strength of PMMA cladding. The deformation of the As2Se3-PMMA hybrid microfiber is observed when the strain is greater than 1500 µɛ by measuring the distributed Brillouin frequency and Brillouin linewidth over the 50 cm-long hybrid microfiber. The measured errors based on the Brillouin frequency in the range of 0-1500 µɛ and 1500-15000 µɛ are 42 µɛ and 105 µɛ, respectively. The measured error based on the Brillouin linewidth is 65 µɛ at 0-1500 µɛ and the maximum error is 353 µɛ when the tensile strain is 15000 µɛ. No strain memory effect is observed compared with the polymer optical fiber due to Young’s modulus in As2Se3 is larger than that in polymer. Numerical simulations are developed to accurately predict the strain dependence of Brillouin frequency in the As2Se3-PMMA hybrid microfiber.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Optical fiber strain measurement plays an important role in structural health monitoring [1–3] and human motion detection [4]. Optical fiber sensors for measuring wide-range strain have been extensively demonstrated in the last few decades. A strain sensor with a wide-range of 20000${\,\mu \varepsilon }$ and an uncertainty of 33${\,\mu \varepsilon }$ has been proposed in a polymer optical fiber (POF) based on the multi-mode interference [5]. The POF sensor was measured based on an optical spectrum analyzer (OSA) which has limited resolution leading to low strain resolution of 1.73 pm$/{\mu \varepsilon }$ corresponding to 0.22 GHz$/{\mu \varepsilon }$. The wide-range strain was also measured based on Brillouin scattering in POF to improve the measurement resolution [6–8]. The POF has broad Brillouin spectrum linewidth as it is a multi-mode fiber, which requires high pump power; in addition, the POF strain sensor has a memory effect at wide dynamic range due to the low Young’s modulus, which affects its strain accuracy [9]. Recently, chalcogenide-PMMA hybrid optical fiber fabricated by using chalcogenide (As$_2$Se$_3$) as the core and PMMA as the cladding is attracting lots of attention. Coating PMMA on As$_2$Se$_3$ provides sufficient mechanical robustness and flexibility, which allows the fabrication of tapers with As$_2$Se$_3$ core diameters at the sub-wavelength scale. The fabrication of As$_2$Se$_3$-PMMA taper was proposed due to its ultrahigh nonlinearity $\gamma$=133$\,(Wm)^{-1}$ [10]. The tapered As$_2$Se$_3$-PMMA hybrid fiber has been reported for measuring ultrasound [11], transverse load [12], stimulated Brillouin scattering (SBS) [13], and supercontinuum [14]. Here, we are exploring the possibility of using As$_2$Se$_3$-PMMA hybrid microfiber based on BOTDA for wide-range strain sensing. As Young’s modulus for As$_2$Se$_3$ is 17.8 GPa [15], while the POF is 3.5 GPa [16], we do not observe the strain memory effect over the 15000${\,\mu \varepsilon }$ range. This means the strain measurement is repeatable, even though the uncertainty is higher. Taking the advantages of the high refractive index of As$_2$Se$_3$ for strong SBS amplification and low peak power requirement due to small core size fabrication for the single-mode operation has not been explored yet. The ultrahigh nonlinearity of As$_2$Se$_3$ also enables low peak power of pump pulse for SBS generation. The PMMA with mechanical flexibility protects the As$_2$Se$_3$ core and allows the wide-range strain sensing. To the best of our knowledge, the Brillouin frequency shift (BFS) and Brillouin linewidth dependence on strain over wide-range strain sensing in the As$_2$Se$_3$-PMMA hybrid microfiber has not been demonstrated yet. Due to the ultrahigh nonlinear coefficient and the small core size of the As$_2$Se$_3$-PMMA hybrid microfiber compared with POFs, the low power requirement in pump pulse for SBS generation makes it a promising candidate for wide-range strain sensing, which can be applied for monitoring civil infrastructures such as railway and bridge with steel structures that require large strain beyond that of SiO$_{2}$ limited to less than 1%.
In this paper, we demonstrate a wide-range strain sensor based on Brillouin frequency and linewidth in an As$_2$Se$_3$-PMMA hybrid microfiber of 50 cm long with a core diameter of 2.5 $\mu$m. BOTDA setup is employed for tensile strain sensing as it provides the location information. The fabrication process, Brillouin strain sensing principle, and the numerical simulations of the hybrid microfiber are introduced. Experimental results show that SBS is excited using only 8 dBm peak power of the pump pulse, and a wide-range strain up to 15000 ${\mu \varepsilon }$ is measured based on BFS and Brillouin linewidth. When the strain is larger than 1500 ${\mu \varepsilon }$, the hybrid microfiber is deformed which is detected by measuring the distributed BFS and Brillouin linewidth. The strain errors based on BFS measurement in the range of 0-1500 ${\mu \varepsilon }$ and 1500-15000 ${\mu \varepsilon }$ are 42 ${\mu \varepsilon }$ and 105 ${\mu \varepsilon }$, respectively. For strain dependence of Brillouin linewidth, the error is 65 ${\mu \varepsilon }$ at 0-1500 ${\mu \varepsilon }$ and the maximum error is 353 ${\mu \varepsilon }$ when the tensile strain is 15000 ${\mu \varepsilon }$.
2. Fabrication and sensing principle
2.1 Fabrication of As$_2$Se$_3$-PMMA fiber
The As$_2$Se$_3$-PMMA fiber is fabricated by the rod-in-tube drawing technique [17]. The fabrication requires the following steps. A 7 cm-long As$_2$Se$_3$ fiber is inserted into an elongated PMMA microtube before inserting it into a 13 cm-long PMMA tube which is placed in the oven before fabricating to eliminate moisture. The assembly is then heat-softened by a resistive heater at a constant temperature of 220 $^\circ$C to obtain an As$_2$Se$_3$-PMMA preform. Finally, the preform is drawn to a fiber with the As$_2$Se$_3$ core diameter of 21.25 $\mu$m and the PMMA cladding diameter of 1.2 mm. The photos of the initial PMMA tube, the elongated PMMA microtube, and the As$_2$Se$_3$ fiber are shown in Fig. 1(a). Figure 1(b) shows an optical microscope image of a polished As$_2$Se$_3$-PMMA fiber end facet without tapering.
Fig. 1. (a) Photos of the PMMA tube, the elongated PMMA microtube and the As$_2$Se$_3$ fiber. (b) Cross-section of an end polished As$_2$Se$_3$-PMMA fiber without tapering. (c) Schematic of 50 cm-long angle-coupled As$_2$Se$_3$-PMMA hybrid microfiber with a core diameter of 2.5$\,\mu$m.
2.2 Coupling and tapering of the As$_2$Se$_3$-PMMA fiber
The hybrid fiber is then angle coupled with single-mode fibers (SMF) before the tapering process. To suppress the undesired Fresnel reflection of the hybrid fiber$/$SMF interfaces and maximize the transmission coefficient, the end faces of the hybrid fiber and SMFs are polished at the angle of 5 degrees for the As$_2$Se$_3$-PMMA fiber and 10 degrees for SMFs. The butt-coupling interfaces are permanently fixed using UV-cured epoxy. The As$_2$Se$_3$-PMMA fiber is further tapered to a 50 cm-long microfiber with a core diameter of 2.5 $\mu$m using the heat-brush method [18]. The total loss of the tapered fiber is $\sim$ 4 dB, including a $\sim$ 2 dB insertion loss at hybrid fiber$/$SMF interfaces and a $\sim$ 2 dB propagation loss over 50 cm length. Figure 1(c) shows the schematic of the coupled As$_2$Se$_3$-PMMA hybrid microfiber, including a tapered waist-length of $L_{w}=50\,$cm, a core diameter of $D_{As{_2}Se{_3}}=2.5$ $\mu$m and a cladding diameter of $D_{PMMA}=141\,\mu$m.
2.3 Principle of Brillouin strain sensing
The relationship between the BFS ($\nu _{B}$) experienced by scattered light in the SBS process and longitudinal acoustic velocity ($V_{L}$) in the As$_2$Se$_3$-PMMA hybrid microfiber is given by [19]
3. Numerical simulations
An analytical model, refined by numerical simulation, is developed to predict strain dependence of BFS using the finite-element method (FEM). Here, fundamental optical mode and acoustic modes are calculated at the operating wavelength $\lambda _{p}=1550\,$nm by solving optical propagation and mechanical equations. These are written as [20]
where $E$ and $u_{j}$ are the spatial distribution of optical field and acoustic field, respectively, $n_{eff}$ is the effective refractive index of the optical mode, $V_{L,j}$ and $\beta _{a,j}$ are the longitudinal velocity and propagation constant of the $j$th acoustic mode, and $\Omega _{j}$ is the Brillouin frequency shift of the $j$th acoustic mode. The phase-matching condition leads to the relation $\beta _{a,j}\approx 2\beta _{opt}$, where $\beta _{opt}$ is the propagation constant of the optical mode. The parameters for calculating the optical and acoustic modes are shown in Table 1. The profiles of fundamental optical mode and two acoustic modes (L01 and L02) in the hybrid microfiber with the core diameter of 2.5 $\mu$m are plotted in Fig. 2(a). The large acoustic impedance difference between the As$_2$Se$_3$ core and the PMMA cladding confines the acoustic fields in the core (1.044$\times$10$^7$ kg/m$^2$/s for As$_2$Se$_3$ and 1.86$\times$10$^6$ kg/m$^2$/s for PMMA [21]). We also observe that the distribution of acoustic mode L02 tends to spread to the interface between the As$_2$Se$_3$ core and PMMA cladding. Since the longitudinal acoustic velocity of PMMA is greater than that of the core, the acoustic mode L02 has larger acoustic velocity than that of the acoustic mode L01, as shown in Fig. 2(b). Then the overlap between the fundamental mode and the $j$th acoustic mode is calculated using the acousto-optic coupling efficiency given by [22,23]Fig. 2. (a) Profiles of optical mode (blue) and acoustic modes L01 (black) and L02 (red). (b) The acoustic velocity of acoustic modes L01 (black) and L02 (red). (c) Simulated Brillouin spectrum of the hybrid fiber. (d) The electric field of the fundamental mode. (e,f) Acoustic mode L01 at 7.726 GHz and acoustic mode L02 at 7.854 GHz.
Table 1. As$_2$Se$_3$ and PMMA parameters used for Brilloin gain spectrum calculation.
According to Eq. (2), the change of effective refractive index $n_{eff}$ and longitudinal acoustic velocity $V_{L}$ is considered when calculating the strain dependence of BFS. For the isotropic material, such as fibers, subjected to the tensile strain $\varepsilon$, the longitudinal acoustic velocity $V_{L}^\varepsilon$ is given by [26]
where $V_{L}^0$ is the longitudinal acoustic velocity without strain and longitudinal acousto-elastic coefficient $K$ is given by4. Experimental results
4.1 Experiment setup and Brillouin spectra
To obtain location information and improve the accuracy of strain measurement, experiments are conducted by employing a BOTDA system. The strain sensor based on BFS and Brillouin linewidth can be measured at an accuracy of $\sim$ MHz/${\mu \varepsilon }$ instead of the OSA accuracy of $\sim$ GHz/${\mu \varepsilon }$ [30]. The spectrum of each location of the As$_2$Se$_3$-PMMA hybrid microfiber is measured using the distributed system, which allows us to measure the strain at which the microfiber is deformed. Figure 3 illustrates the BOTDA setup. The light source is a tunable optical fiber laser, and the operating wavelength is set to 1550 nm. The continuous wave (CW) light is divided by a 50:50 coupler into two paths. The upper path transfers light into a 20 ns pump pulse with a high extinction ratio (ER) using two electro-optic modulators (EOM) driven by a dual-channel function generator (FG). The signal to noise ratio of the BOTDA sensor system can be increased by using the high ER pump pulse. An Erbium-doped-fiber-amplifier (EDFA) is used to amplify the pulse to 8 dBm peak power. The amplified spontaneous emission (ASE) is then filtered out by a tunable filter. The pump pulse is injected into one end of the 50 cm-long microfiber through an optical circulator. In the lower path, the EOM generates two sidebands with a frequency shift from 7.5 to 7.9 GHz, corresponding to the BFS of the As$_2$Se$_3$-PMMA microfiber. The power of two sidebands is amplified by an EDFA, and then selected by a 2 GHz narrow bandwidth filter as the probe wave, whose frequency can be swept by a radio frequency (RF) generator. The probe wave is injected into the FUT opposite to the propagation direction of the pump. The two polarization controllers (PC) are used to change the polarization states of both of pump pulse and probe wave to make sure that they are co-polarized along with the microfiber. The FUT is fixed by two clamps to linear translation stages to induce the axial strain. The resulting backscattered signal is detected using a photodetector (PD), and the Brillouin spectra are recorded using an oscilloscope (OSC) with a 5 GS/s sampling rate.
Fig. 3. Experimental setup for strain measurement based on BOTDA in an As$_2$Se$_3$-PMMA hybrid mcirofiber. The abbreviations here denote: EOM, Electro-Optic Modulator; FG, Function Generator; EDFA, Erbium-Doped-Fiber-Amplifier; PC, Polarization Controller; RF, Radio Frequency. FUT, Fiber Under Test; PD, Photo Detector; OSC, Oscilloscope.
The backscattering trace is recorded in the time domain and is converted to frequency and length information using the sweeping range of RF generator and the sampling rate of OSC. All experimental results are measured at the room temperature of 22 $^\circ$C and the room humidity of 38%. Figure 4(a) shows the Brillouin spectrum in the 25 cm position of the As$_2$Se$_3$-PMMA microfiber with a core diameter of 2.5 $\mu$m without strain. The Brillouin spectrum is excited using only 8 dBm peak power of the pump pulse due to the ultrahigh nonlinearity and the small core size of the As$_2$Se$_3$-PMMA hybrid microfiber. The main peak of BFS is 7.728 GHz which is slightly different from that of the numerical simulation result of 7.726 GHz as the fabrication process gives the 10$\%$ error of the core diameter [13]. Figure 4(a) also shows a secondary peak at 7.848 GHz arising from the acoustic mode L02. Figure 4(b) shows the time-varying gain profile of the 7.728 GHz probe wave when the pump pulse with 20 ns linewidth passes through the 50 cm-long hybrid microfiber. The gain exists in the position from 0.5 to 1.5 m because of the 20 ns pump pulse corresponding to 1 m length. Although the pulse length is longer than that of the hybrid microfiber, the BFS and Brillouin linewidth difference in each position over the 50 cm-long hybrid microfiber can be clearly identified due to the non-uniformity of the microfiber. The distributed BFS and Brillouin linewidth are obtained from the Brillouin spectra by sweeping the frequency of the probe wave, as plotted in Fig. 4(c). The Stokes trace of the main peak is clearly shown in the distributed Brillouin spectrum, while the Stokes trace of the secondary peak is too weak to be seen as its small Brillouin gain.
Fig. 4. (a) Experimental normalized Brillouin spectrum in the 25 cm position of the microfiber with a core diameter of 2.5 $\mu$m (black circles) and Lorentzian fitting (red solid trace). (b) Stokes trace at 7.728 GHz. (c) Distributed Brillouin spectrum when sweeping the probe frequency from 7.5 to 7.9 GHz.
4.2 Strain dependence of Brillouin frequency and linewidth
The 50 cm-long As$_2$Se$_3$-PMMA microfiber is fixed by the two clamps to the linear translation stages with a resolution of 1 $\mu$m. The tensile strain is then induced by using the linear translation stages at steps of 100 $\mu$m, which corresponds to the tensile strain of 2000 ${\mu \varepsilon }$ for the fiber length of 50 cm. The experimental and simulated normalized Brillouin spectra at the 25 cm position of the As$_2$Se$_3$-PMMA microfiber with a core diameter of 2.5 $\mu$m for an increasing strain from 0 to 15000 ${\mu \varepsilon }$ are plotted in Fig. 5. We can observe that the experimental BFS (circles) decreases with increasing strain. It is related to the fact that increasing tensile strain reduces the longitudinal acoustic velocity as we expected in simulation. Remarkably close agreement on the strain dependence of BFS is obtained between the experimental and simulated results. Since the maximum difference of BFS between simulation and experiment in the range of 0-1500 ${\mu \varepsilon }$ is 2.5 MHz, the error is 95 ${\mu \varepsilon }$ in the comparison between numerical and the experimental results. The maximum difference of BFS is 10.4 MHz in the range of 1500-15000 ${\mu \varepsilon }$, which means the maximum error is 388 ${\mu \varepsilon }$. The plots in Fig. 5 also show that Brillouin gain shape is dramatically changed, and the Brillouin linewidth is broadened with increasing strain, unlike the SMF which has the constant linewidth with strain [31]. The linewidth of the spectra is constant in simulation as we did not consider the change of linewidth caused by the deformation of the microfiber.
Fig. 5. Experimental normalized Brillouin spectra (circles) and simulated Brillouin spectra (solid traces) of the hybrid microfiber with a core diameter of 2.5 $\mu$m for 0 ${\mu \varepsilon }$ (black), 3000 ${\mu \varepsilon }$ (red), 7000 ${\mu \varepsilon }$ (blue), 11000 ${\mu \varepsilon }$ (green) and 15000 ${\mu \varepsilon }$ (yellow).
The measured distributed BFS of the As$_2$Se$_3$-PMMA hybrid microfiber for increasing tensile strain is plotted in Fig. 6(a). The BFS in each position of the microfiber can be measured for the 20 ns pump pulse due to the non-uniform waist region of the microfiber. The horizontal dash lines represent the average values of the BFS over the 50 cm-long microfiber. The BFS in different positions of the hybrid microfiber without strain has tiny fluctuation, and the standard deviation is only 0.3 MHz due to the small non-uniformity of the As$_2$Se$_3$ core. The difference in BFS over the 50 cm-long microfiber can be clearly seen at 3000 ${\mu \varepsilon }$ as the great difference in core diameter in some positions resulting from the deformation of the microfiber at large strain. The microfiber is deformed at large strain due to low Young’s modulus of the As$_2$Se$_3$ and PMMA materials and the non-uniformity of the microfiber. The difference is noticeable at 9000 ${\mu \varepsilon }$ in which the standard deviation reaches 5.3 MHz. The standard deviations as a function of strain in the As$_2$Se$_3$-PMMA hybrid microfiber with core diameters of 2.5 $\mu$m and 2.3 $\mu$m are plotted in Fig. 6(b). The microfiber with a core diameter of 2.3 $\mu$m has a greater standard deviation than that of 2.5 $\mu$m even without strain as the large end-face reflection between the As$_2$Se$_3$-PMMA fiber and SMFs, which induces the gain fluctuation when measuring the Brillouin spectra. In Fig. 6(a), we observe that the BFS has a small difference at the center of the hybrid microfiber. Thus the Brillouin spectra at the 25 cm position of the hybrid microfiber with increasing axial strain are used for analyzing the BFS. Figure 6(c) and Figure 6(d) show the tensile strain dependence of the BFS in the As$_2$Se$_3$-PMMA microfiber with different core diameters in two strain ranges. Both of core diameters show that the BFS decreases linearly with the strain increases in the two ranges. The linear relation between strain and BFS can be related to the deformation only occurs at certain position of the microfiber and may not be reflected at central frequency. Strain coefficients of BFS in two ranges are shown in Table 2. The slopes in two ranges have a small difference of 0.0004 MHz/${\mu \varepsilon }$ for the fiber with a core diameter of 2.5 $\mu$m, which may be induced by the gain fluctuation at large strain and fitting errors.
Fig. 6. (a) Distributed BFS over the 50 cm-long microfiber with a core diameter of 2.5 $\mu$m in different strain values (circles), and the average BFS (horizontal dash lines). (b) Standard deviation for the increasing strain in the microfiber with the core diameter of 2.3 $\mu$m and 2.5 $\mu$m. (c) BFS versus the strain increase from 0 to 1500 ${\mu \varepsilon }$ in 25 cm position of the fiber with core diameters of 2.3 $\mu$m and 2.5 $\mu$m. (d) BFS versus the strain increase from 1500 to 15000 ${\mu \varepsilon }$ in 25 cm position of the fiber.
Table 2. Strain coefficients and errors of Brillouin frequency and linewidth of the As$_2$Se$_3$-PMMA microfiber with core diameters of 2.5 $\mu$m and 2.3 $\mu$m, respectively. C: Coefficient, BF: Brillouin frequency, BW: Brillouin linewidth.
Figure 7(a) shows the distributed Brillouin linewidth over the 50 cm-long As$_2$Se$_3$-PMMA hybrid microfiber at different tensile strain values. The Brillouin linewidth decreases in the same trend along the tapered fiber over the strain of 0-1500 ${\mu \varepsilon }$. There are two contributing factors for this decrease: 1) the PMMA cladding is non-uniform along the fiber during fabrication and tapering processes. The PMMA plays the role of an acoustic damper due to its large elastic loss and low density [13]. Thus, the large diameter of the PMMA induces small Brillouin linewidth; 2) the intensity of the pump pulse affects the Brillouin linewidth. The large Brillouin linewidth can be obtained for the low intensity of the pump pulse. When the pump pulse is launched into the fiber, the intensity of the pulse is gradually increased, which means the decrease of the Brillouin linewidth along the fiber. We observe that the linewidth broadens in a different trend at 3000 ${\mu \varepsilon }$ and it is obvious when the strain is 15000 ${\mu \varepsilon }$. This can be related to the combined effect of the decreased power with increasing strain and the deformation of the microfiber in large strain. For the As$_2$Se$_3$-PMMA microfiber, there are internal stress between As$_2$Se$_3$ core and PMMA cladding as PMMA has a large thermal coefficient comparing with the As$_2$Se$_3$. When the microfiber is elongated with small strain, it is not deformed. In the case, the power decreases linearly with strain due to PMMA cladding induced the stress on the As$_2$Se$_3$ core, which is similar to that in panda fiber where stress rods are pressed into the core leading to increased attenuation with strain [32]. The linear decreased power in the fiber under small strain from 0 to 1500 ${\mu \varepsilon }$ results in a linear increase of linewidth, as shown in Fig 7(b). The dependence between strain and linewidth in the range of 1500-15000 ${\mu \varepsilon }$ for two core diameters of the As$_2$Se$_3$-PMMA hybrid microfiber are shown in Fig. 7(c). The nonlinear relationship means that the hybrid microfiber is deformed in large strain. The non-uniform localized strain induced by the deformation of the hybrid microfiber enlarges the localized strain range resulting in the nonlinear broadened Brillouin linewidth. Strain coefficients and errors of Brillouin linewidth of the As$_2$Se$_3$-PMMA hybrid microfiber with core diameters of 2.3 $\mu$m and 2.5 $\mu$m are shown in Table 2.
Fig. 7. (a) Distributed Brillouin linewidth over the 50 cm-long microfiber the As$_2$Se$_3$-PMMA fiber with a core diameter of 2.5 $\mu$m for an increasing strain. (b) Linewidth versus the strain increase from 0 to 1500 ${\mu \varepsilon }$ in 25 cm position of the hybrid fiber with core diameters of 2.3 $\mu$m and 2.5 $\mu$m. (c) Linewidth versus the strain increase from 1500 to 15000 ${\mu \varepsilon }$ in 25 cm position of the hybrid fiber.
4.3 Relaxation and hysteresis measurement
The BFS as a function of time is measured at 7000 ${\mu \varepsilon }$ and 15000 ${\mu \varepsilon }$ in the As$_2$Se$_3$-PMMA microfiber with a core diameter of 2.5 $\mu$m, as shown in Fig. 8(a). We can see that the BFS at 7000 ${\mu \varepsilon }$ is constant with time, while the BFS at 15000 ${\mu \varepsilon }$ has a fluctuation with time induced by the Brillouin gain fluctuation at large strain. In two cases, no relaxation behavior is observed, which is different with the large strain sensor based on the POF as Young’s modulus in As$_2$Se$_3$ is larger than that in polymer. Figure 8(b) shows the BFS for both increasing and decreasing strain in the microfiber with a core diameter of 2.5 $\mu$m. The strain is increased to 15000 ${\mu \varepsilon }$ and then decreased to 0 ${\mu \varepsilon }$ in a step of 1000 ${\mu \varepsilon }$. It can be seen that the BFS shows the same value for both increasing and decreasing strain at < 9000 ${\mu \varepsilon }$; above this value, there is a slight difference in the strain cycle. The difference is due to the fluctuation of the BFS at large strain, as illustrated in Fig 8(a). The maximum difference is 4 MHz corresponding to the maximum error of 149 ${\mu \varepsilon }$, which is < 1% of the strain we measured. The error in the increasing and decreasing cycle is close to the error induced by the linear fitting of BFS at large strain range. Thus, the As$_2$Se$_3$-PMMA microfiber shows hysteresis free behavior and good repeatability for the wide-range strain measurement.
Fig. 8. (a) BFS as a function of time at 7000 ${\mu \varepsilon }$ and 15000 ${\mu \varepsilon }$ in 25 cm position of the hybrid fiber with the core diameter of 2.5 $\mu$m. (b) BFS versus the increasing and decreasing strain in 25 cm position of the hybrid fiber with the core diameter of 2.5 $\mu$m.
4.4 Temperature dependence of Brillouin frequency and linewidth
The dependence of Brillouin frequency and Brillouin linewidth on temperature variation is also investigated. Figure 9(a) shows the linear change of BFS with increasing temperature from 25 $^\circ$C to 55 $^\circ$C. The temperature sensitivity is -1.25 MHz/$^\circ$C, which is similar to the temperature measurement in the tapered dual-core As$_2$Se$_3$-PMMA fiber [33]. Figure 9(b) shows the Brillouin linewidth as a function of temperature. We can see that the Brilloin linewidth remains constant over the temperature range of 25 - 55 $^\circ$C as the As$_2$Se$_3$-PMMA microfiber is not deformed, which is different from the Brillouin linewidth change at large strain. Due to the different thermal expansion coefficient between the As$_2$Se$_3$ core and PMMA cladding, the strain is induced on the core by the cladding along the fiber. The fluctuation with a standard deviation of 0.4 MHz may be due to the thermally induced strain on the As$_2$Se$_3$ core.
Fig. 9. (a) BFS and (b) Brillouin linewidth as a function of temperature in 25 cm position of the hybrid fiber with the core diameter of 2.5 $\mu$m.
5. Conclusion
In conclusion, we have calculated and experimentally demonstrated a strain sensor based on Brillouin frequency shift and linewidth in a 50 cm-long As$_2$Se$_3$-PMMA microfiber with a core diameter of 2.5 ${\mu m}$ for wide-range strain measurement. Experimental results have demonstrated the linear strain dependence of the Brillouin frequency shift and nonlinear dependence of the linewidth in a wide-range strain up to 15000 ${\mu \varepsilon }$. The deformation of the hybrid microfiber is measured when the strain larger than 1500 ${\mu \varepsilon }$ by measuring the distributed Brillouin frequency shift and linewidth over the 50 cm-long hybrid microfiber. The calculated errors of strain dependence of BFS in range of 0-1500 ${\mu \varepsilon }$ and 1500-15000 ${\mu \varepsilon }$ are 42 ${\mu \varepsilon }$ and 105 ${\mu \varepsilon }$, respectively. The errors of strain based on linewidth are 65 ${\mu \varepsilon }$ from 0 to 1500 ${\mu \varepsilon }$ and 353 ${\mu \varepsilon }$ when the axial strain is 15000 ${\mu \varepsilon }$. In general, the As$_2$Se$_3$-PMMA hybrid microfiber provides huge potential for wide-range strain sensing.
Funding
China Scholarship Council; Natural Sciences and Engineering Research Council of Canada (06071-RGPIN-2015); Canada Research Chairs (75-67138).
Acknowledgment
The authors are thankful to Coractive Inc. for providing the As$_2$Se$_3$ fiber that is utilized in the fabrication of our single-core As$_2$Se$_3$-PMMA hybrid microfibers.
Disclosures
The authors declare no conflicts of interest.
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