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Abstract
An in-line Mach-Zehnder interferometer based on a multimode-fiber-assisted tapered open-cavity (TOC) is proposed. Light field distributions of the TOC were investigated using beam propagation method with different offsets and diameters of the taper waist. Bias and uniform taper (BT and UT)-based structures were fabricated and compared using one- and two-step arc-discharge methods, and comprehensive tests were then conducted considering axial-strain. The experimental results show that the UT structure has more than −45 pm/µɛ linear wavelength shift with the applied axial-strain. Owing to its compact size and low cost, the proposed sensor is promising for axial-strain-related high-precision engineering applications.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Fiber-optic axial-strain sensors have been widely used in civil engineering, environmental monitoring, aerospace, and other fields [1–4], owing to their compactness, high sensitivity, anti-electromagnetic interference, and good repeatability. Many structures have been extensively reported and investigated based on long-period fiber gratings [5–7], fiber Bragg gratings (FBGs) [8,9], and photonic crystal fibers (PCFs) [10,11]. However, the axial-strain response a for typical optical fiber sensor is merely 1–2 pm/µɛ [12,13]. To enhance sensitivity, the chemical etching method has been frequently adopted and 5.5 pm/µɛ sensitivity is gained in an etched-FBG based scheme [14–16]. Also, the down-taper based structures have been reported to improve strain response, which are prepared by arc-discharge technique with the merits of safety, time-saving and high repeatability in fabrication [17]. For instance, Dong et al. proposed a tapered hollow-core fiber (THCF) structure, and the strain sensitivity increased to 2.7 pm/µɛ in the range of 0–2100 µɛ [18]. Hou and Fan prepared tapered structures based on multimode fiber (MMF) and PCF, and their strain sensitivities reached approximately 6 pm/µɛ [19,20]. Furthermore, André et al. verified a sensitivity of more than −20 pm/µɛ in a single mode taper multimode-single mode (STMS) structure when the waist diameter was approximately 15 µm [21]. In addition, Han fabricated a liquid-filled high-birefringence PCF with a sensitivity of 25 pm/µɛ [22].
Recently, the open-cavity-based axial-strain sensors, regarded as a competitive candidate for the applications of lab-on-fiber, have attracted much attention owing to their ultracompact size (less than 1 mm) and ultrahigh sensitivity [23]. Wu et al. proposed a hollow-core silica tube (HCST)-based open-cavity structure using a large lateral offset splicing method, and the maximum sensitivity was 28.95 pm/µɛ [24]. Gao et al. demonstrated a microfiber-assisted Fabry-Perot interferometer (FPI) and obtained a sensitivity of 160 nm/N [25]. Nan et al. realized a parallel dual open-cavity structure based on the Vernier effect, and the strain sensitivity was further enhanced to −43.2 pm/µɛ [23]. But most open-cavity structures suffer high insertion loss because of the limitation of a less than 9 µm core diameter of single-mode fiber (SMF) [26–32]. To improve the quality rate, multimode fiber assisted (MFA) open-cavity structures have been reported to gain high contrast of fringes and applied in refractive index (RI) measurements [33,34]. In previous work, a new open-cavity structure based on the joint assistance (JA) of multimode fibers and microfibers was developed for axial-strain sensing, and the switchable intensity/wavelength demodulation was proved to be achieved by suitably selecting the cavity length, but with lower wavelength sensitivity (approximately 5.51 pm/µɛ) [35].
In this study, to improve sensitivity, a novel MFA-based open-cavity Mach-Zehnder interferometer (MZI) is proposed. It was completed experimentally using arc-discharged large lateral core-offset splicing and taper techniques. The light field distribution of the tapered open-cavity (TOC) was investigated using the beam propagation method with varied offsets and waist diameters. Bias taper (BT)- and uniform taper (UT)-based structures were fabricated and compared using one- and two-step arc-discharge methods, and their axial-strain characteristics were comprehensively tested. The experimental results show that the axial-strain responses of the BT and UT structures were negatively proportional to the waist diameter. With a diameter of approximately 30 µm, a maximum sensitivity of −46.7 pm/µɛ was achieved in the UT structure. As a result, the detection resolution of ∼ 0.2 µɛ can be achieved with the cross-sensitivity of 1.82-µɛ/°C.
2. Principle and simulation
A schematic diagram of the TOC structure is shown in Fig. 1. It consists of lead-in and lead-out SMFs, two pieces of MMF (MMF-1 and MMF-2), and a short section of tapered SMF (T-SMF). Figure 1(a) shows that the incident light from the lead-in SMF expands in MMF-1 and is split by offset joint 1 (OJ1) to transmit the cladding of the T-SMF and air cavity, respectively. Because of the obvious RI difference between the air and fiber cladding, a significant phase difference is generated when the two beams reach offset joint 2 (OJ2). The beams are recoupled at MMF-2, and a typical Mach-Zehnder interferometer is formed.
According to the theory of dual-beam interference [36], the intensity of an in-line MZI can be expressed as
where Ia and Icl are the light intensities in the air-cavity and the fiber cladding of the T-SMF, respectively. Here, Δφ = 2πΔneff La /λ is the phase difference between the modes of cladding and air-cavity, where λ is the incident wavelength, Δneff is the difference in effective RI between air and fiber cladding, and La is the length of the air-cavity (which is also the length of T-SMF).When Δφ = (2m+1)π (m = 1,2,3…), the resonance wavelength (λm) is
In addition, the free spectral range (FSR) of the fringes can be expressed as
The normalized extinction ratio (ER) of fringes is depicted as
Equation (4) reaches its maximum when Ia = Icl. Furthermore, for an axial-strain test, it is assumed that the total length of the structure (i.e., the distance between two fixed points) is LS= LSMF + LMMF1 + LMMF2 + La, where LSMF is the sum of the lengths of the lead-in and lead-out SMFs, and LMMF1 and LMMF2 are the lengths of MMF-1 and MMF-2, respectively. The applied axial-strain is then defined as S = ΔLS/LS, where ΔLS is the variation of LS. From a previous report [37], the strain applied to a silica fiber structure is directly dependent on the cross-sectional area. Thus, the axial-strain of the TOC can be approximately written as
To obtain a higher ER of the fringes, the parameters of the fabrication and structure should be carefully selected. Thus, the light field distribution of the TOC structure was firstly simulated using the beam propagation method by the software of R-Soft with different offset values (denoted by α). The RIs of the background and air-cavity were 1.0. The center wavelength of the incident light was 1550 nm, and the initial cavity length was fixed at 1000 µm. The lengths of lead-in and lead-out SMFs were same and equal to 0.2 mm for ease of observation. In addition, based on previous research [38], the lengths of MMF-1 and MMF-2 were set to 0.5 mm to avoid possible multimode interference and increase the effective beam expansion diameter. And the grid size of simulation was set 50 nm to ensure precision and accuracy. Other simulation parameters are shown in Table 1, where nco and ncl are the RIs of the fiber core and fiber cladding. The simulation results of the untapered TOC (i.e., dt = dM =125 µm) are shown in Fig. 2.
Table 1. Main Parameters of Simulation.
As shown in Fig. 2, when α < 20 µm, no air-cavity forms, and the light transmits only in the core and cladding of the T-SMF. The smaller air-cavity is formed only when α reaches 40 µm, but with a small light energy. When α = 60 µm, the light energy is almost evenly distributed in the air-cavity and fiber cladding, which means that the maximum ER may be obtained. The quantitative results are shown in Fig. 3(a), and the light energy of cladding and the air-cavity energy are 0.45 A.U. when α = 62.5 µm. Figure 3(b) shows that the corresponding maximum ER can reach approximately 21.9 dB theoretically.
Furthermore, under the state of α = 62.5 µm, the light field distributions of TOC structures with different waist diameters were studied and are shown in Fig. 4. It is clear that the decreased dt (from 80 to 10 µm) caused a dramatic loss of cladding energy in the region of the taper waist. Figure 5(a) shows that the cladding energy quickly but linearly decreased with the reduction in dt. As a result, the matched energy distribution between the air-cavity and cladding was broken. In Fig. 5(b), compared with the case of dt = 80 µm, the deduction of ER exceeds 50% when dt = 10 µm, which worsens the detection resolution of the sensors [39]. Thus, the waist diameter trade-off should be carefully considered between the ER of fringes and axial-strain sensitivity. In addition, the minimum waist diameter was set to approximately 30 µm in the subsequent fabrication and experiments because of the ultralow fusion efficiency and quality rate when dt < 20 µm.
3. Fabrication
Based on the results in Section 2, the TOC structure was fabricated by arc-discharged large lateral offset splicing and taper techniques, with the parameters of α = 62.5 µm, dt = 30–80 µm and LMMF1 = LMMF2 = 0.4 mm. For comparison, the BT and UT structures were fabricated via one- and two-step arc-discharge methods, respectively. As shown in Fig. 6(a), the MFA-based large lateral offset structure was first fabricated by a commercial fusion splicer in manual mode.
The MMF (Nurfen, MM-S105/125-22A) and lead-in/lead-out SMF (Corning, SMF-28) were adopted, forming the MFA structure in mismatch mode with a loss of approximately 0.1 dB. Then, as shown in Fig. 6(b), an MFA-based open-cavity was completed by connection with a piece of SMF (with a length of 500–2000µm) using a large lateral offset splicing method. Furthermore, in the taper mode, the in-cavity SMF was stretched, and a bias-tapered open-cavity was realized when only one side of the motor was axially moved. As shown in the micro-image in Fig. 6(b), the waist diameter was approximately 60 µm. The total length of taper area was approximately 600 µm, and the down and up transition areas were 245.7 and 349.86 µm, respectively. The key fabrication parameters of the BT structure were set as follows: the predischarge intensity and time were 248 bit and 50 ms, respectively, the main discharge intensity and time were 248 bit and 2000ms, respectively, the waiting time was 400 ms, the splicing speed was 1 µm/ms, and the splicing length was 180–490 µm.
As shown in Fig. 6(c), in the fabrication of the UT structure, two identical segments of a large lateral offset structure were first completed and spliced together with the auto-mode of the SMF. Then, the two sides of the motor of the fusion splicer were moved simultaneously under the taper mode, and the open-cavity that formed was uniformly stretched with the key parameters for the taper structure as follows: the predischarge intensity and time were 40 bit and 180 ms, respectively, the main discharge intensity and time were 70 bit and 2200 ms, the waiting time was 1200–1800ms, and the splicing speed was 0.17 µm/ms. As shown in the micro-image of Fig. 6(c), the total length of the taper area was approximately 500 µm, and the taper waist was located at the middle of the T-SMF with a diameter of 60 µm. Clearly, the above two-step process of arc-discharge is somewhat complicated. Moreover, it was found that a clear bubble-like pitfall existed at the taper waist of the UT structure. Such pitfall resulted from two continuous arc-discharges at the splicing point may cause an extra loss of light energy in the cladding of the T-SMF, but may enhance the sensing performance of axial-strain [40,41].
Several untapered TOC structures with different La were fabricated to obtain a suitable cavity length, and the corresponding micro images are shown in Fig. 7(a). Their transmission and spatial frequency spectra are shown in Figs. 7(b) and (c), respectively. Clearly, with the addition of La, the FSR values of the transmission spectra are reduced from 11.22 to 2.805 nm. There is a unique dominated peak occurring in the corresponding spatial frequency spectrum, with a line width of approximately 0.02 nm−1 when La < 1538 µm. However, the maximum ER value is approximately 17 dB (less than the theoretical value of 21.9 dB) because of the possible splicing and insertion loss, and it continuously decreased to 9.34 dB because the loss of light energy in the air-cavity is positively proportional to the increased La. In addition, because the length of a taper area fabricated by arc-discharge is usually larger than 600 µm [17], La = ∼ 1100 µm was set in the subsequent fabrication and experiments.
Fig. 7. (a) Micro images, (b) transmission, and (c) spatial frequency spectra of untapered TOC with different La.
Furthermore, a variety of BT and UT structures were fabricated with similar cavity lengths (La = ∼ 1100 µm) and different dt values. Their micro images, transmission spectra, and spatial frequency spectra are shown in Figs. 8 and 9, respectively. Comparatively, in the BT and UT structures, the maximum change of FSR was within 0.34 nm because of the 103 µm difference in cavity length, which is very close to the theoretical value obtained from Eq. (3). For spatial frequency spectra, although dt varied from 30 to 60 µm, there was a main dominant peak with a line width of < 0.024 nm−1 in the BT structure, but with an average line width of approximately 0.014 nm−1 in the UT structure, indicating that a more uniform period of fringes can be provided in the range of 1525–1565 nm. Nevertheless, with the reduced dt, the ER values increased from 7.45 to 11.83 dB in the BT structures but decreased in the UT structures from 10.37 to 6.71 dB. Compared with the result in Fig. 7, when dt = ∼ 30 µm, the deduction in terms of ER was merely approximately 1.3 dB in the BT structure. However, the deduction was sharply increased by approximately 49% and was equal to around 6.45 dB in the UT structure, which is approximately consistent with the result obtained in Fig. 5(b). These results indicate that the one-step arc-discharged taper method can effectively alleviate the possible energy loss of fiber cladding, although the diameter is dramatically reduced by more than 90 µm. In addition, some more obvious sub-dominant peaks occurring in both BT and UT structures are also possibly resulted from the energy loss of dominant cladding mode, which leads more pre-dominant cladding modes interfere with the fundamental mode in air-cavity.
Fig. 8. (a) Micro images, (b) transmission, and (c) spatial frequency spectra of BT structures with varied dt.
Fig. 9. (a) Micro images, (b) transmission, and (c) spatial frequency spectra of UT structures with varied dt.
4. Experiments and discussion
The experimental setup for axial-strain sensing is shown in Fig. 10, which is mainly completed by a micro-motion controller (MMC, Newport, Model ESP-300, with a minimum accuracy of 0.1 µm). The fabricated BT and UT structures were placed horizontally on the platform of the MMC and quickly fixed by UV glue. The distance between the two fixed points was LS = 10.4 cm. The sensor unit was connected with a broadband source (CONNET VENUS, with the range of 1525‒1565 nm) and an optical spectrum analyzer (OSA, Agilent 86142B, with a resolution of 0.01 nm/0.01 dB) by the lead-in and lead-out SMFs. Comprehensive axial-strain tests were then performed, and the experimental results are shown in Figs. 11 and 12. With the increased axial-strain, the transmission spectra of the BT and UT structures blue-shifted uniformly, but the intensity of the fringes also fluctuated. In BT structures, the wavelength shift and intensity fluctuation are relatively small.
Fig. 11. Transmission spectra of axial-strain responses with different waist diameters of BT structure.
Figure 13(a) shows that when dt = 30.1, 40.85, 60.89, and 80.45 µm, the axial-strain sensitivities in the BT structures were −18.04, −9.6, −8.29, and −4.22 pm/µɛ, respectively, with the linearity of > 0.96. According to Fig. 13(b), the intensity variation was merely ±0.06 dB when dt = 80.45 µm, and the largest fluctuation occurring at dt = 40.85 µm was constrained within approximately 2.28 dB. A higher axial-strain response occurred in UT structures in terms of wavelength and intensity owing to the slight defect caused by the double arc-discharge at the splicing point of the T-SMF. Figure 13(c) reveals that the axial-strain sensitivities of UT structures with dt = 30.12, 43.1, 60.34, and 80.1 µm were −46.7, −24.3, −20.7, and −8.3 pm/µɛ, respectively, with the linearity from 0.93 to 0.98. As a result, a detection limit of 0.214 µɛ can be obtained in the UT structure when a 0.01 nm resolution of OSA is adopted. The intensity of the fringes changed significantly and linearly with the added axial-strain, especially when dt = 30 and 80 µm. Figure 13(d) shows that the maximum of −0.0645 dB/µɛ was gained in the structure of dt = 30 µm with the linearity of 0.97 in the range of 0–110 µɛ. This means that the UT structure has the potential for intensity modulation in axial-strain-related measurements. Furthermore, the performances of the BT and UT structures were compared. Figure 14(a) shows that consistent with the results in Section 2, the strain sensitivities of the two TOC structures are nonlinearly negative-proportional to the waist diameter. The maximum strain sensitivity of the BT structure is less than 20 pm/µɛ, because of a weak pitfall of fusion caused by one-step arc-discharge preparation. Comparatively, more than 150% improvement (e.g., $\frac{46.7 - 18.04}{18.04}{ = 1}{.59}$@dt = 30.1 µm) is achieved in the UT structures when dt is 30–40 µm. Nevertheless, Figs. 14(b) and (c) reveal that the penalty in the linearity and linear range decreased in the UT structures.
Fig. 13. Relationship between (a) wavelength and (b) intensity and axial-strain in BT structures, and relationship between (c) wavelength and (d) intensity and axial-strain in UT structures.
Furthermore, the BT and UT structures with dt = ∼ 30 µm were placed in a temperature chamber (LICHEN, DFD-700). Their temperature responses were tested in the range of 30–40 °C. Figure 15 shows that the wavelength dips were uniformly red-shifted with an increase in temperature. The temperature sensitivity of the BT structure was 94.71 pm/°C with the linearity of 0.995. For the UT structure, it is 85 pm/°C with the linearity of 0.98. Therefore, by calculation, the corresponding cross-sensitivities are 5.25 and 1.82 µɛ/°C, respectively. Moreover, in the BT structure, the intensity of the dip linearly decreased by approximately 1.2 dB as the temperature increased, and the corresponding sensitivity was −0.124 dB/°C with ultrahigh linearity. Comparatively, the intensity sensitivity of the UT structure decreased to −0.0879 dB/°C but with a fluctuation of 1.95 dB, which means that the double arc-discharge process truly affects the mechanism of the TOC structure.
Additionally, from previous work [42], the measured variation with respect to the axial-strain and temperature can be effectively discriminated by the inverse matrix method, as shown in Eq. (7).
In addition, Table 2 gives a performance comparison of fiber-optic strain sensors in terms of the sensitivity, detection resolution, and cross-sensitivity of temperature (the 0.01-nm resolution is adopted). Clearly, compared with conventional structures (e.g., SMF, TCF and MMF), the micro and open-cavity-based schemes dramatically enhance the axial-strain sensitivity to more than 25 pm/µɛ. Without the Vernier effect, the UT structure achieves a response of −46.7 pm/µɛ with ultralow detection resolution (0.214 µɛ) and crosstalk (approximately 1.82 µɛ/°C). It is believed that the UT structure will be very competitive for high-precision axial-strain sensing under the state of well-controlled ambient temperature. Additionally, although the strain response is lower than 20 pm/µɛ, the BT structure is also very promising in the axial-strain-related engineering applications owing to the merits of ease of fabrication and stability.
Table 2. Performance Comparisons of the Reported Fiber-Optic Axial-Strain Sensors.
5. Conclusion
A novel TOC-based MZI was developed to improve axial-strain response. BT and UT structures were completed by one- and two-step arc-discharge methods, respectively. The structural parameters were optimized experimentally, and the performance comparisons of the BT and UT structures were conducted comprehensively with respect to axial-strain and temperature. The results show that the axial-strain response can be dramatically enhanced by reducing the diameter of the tapered waist. The maximum sensitivities for the BT and UT structures reached −18.04 and −46.7 pm/µɛ, respectively. For the temperature response, the similar sensitivity of ∼ 90 pm/°C was obtained for both structures. Thus, approximately 0.2 µɛ detection resolution was achieved by the UT structure, with a cross-sensitivity of 1.82 µɛ/°C. The proposed TOC scheme is an effective solution for high-precision axial-strain-related measurements and engineering monitoring.
Funding
National Natural Science Foundation of China (61675066); The Project of the Central Government Supporting the Reform and Development of Local Colleges and Universities (2020YQ01); The Graduate Innovation Research Project of Heilongjiang University (YJSCX2021-065HLJU).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but maybe obtained from the authors upon reasonable request.
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