Open Access
Add to BibSonomy
Abstract
A sensitive one-dimensional vector bending fiber-optic sensor based on self-referenced antiresonant reflecting guidance mechanism has been proposed and experimentally demonstrated. Two symmetric air holes in the hollow-core photonic crystal fiber (HCPCF) were infiltrated with refractive index matching liquids with different refractive indices, which formed a self-referenced anti-resonant reflecting optical waveguide. The bending of the HCPCF induces a wavelength shift of lossy dip in the transmission spectrum. Specially, the one-dimensional bending orientation can be detected through the wavelength interval between two lossy dips due to the asymmetric refractive index change of the silica cladding for two resonators. The bending sensitivities are 4.86 and −4.84 nm/m−1 for the curvatures of the 0° and 180° bending orientations in a bending range from 0 to 0.88 m−1, respectively. Moreover, the temperature and strain crosstalk of the proposed sensor can be eliminated through the compensated self-referenced anti-resonant reflecting optical waveguide. The proposed fiber sensor can be used for the monitoring of the structural health of infrastructures.
© 2017 Optical Society of America
1. Introduction
In smart structure monitoring, bending is one of the most critical mechanical parameters for the monitoring of the structural health of bridges, dams, pile foundations, and other infrastructures [1–3]. In recent years, fibre optic bending sensors have attracted a great deal of research due to their particular characteristics, such as high sensitivity, compact size, and immunity to electromagnetic interference [4].
The well-known fibre optic bending sensors are based on various fibre gratings, such as fibre Bragg gratings [5], tilted fibre Bragg gratings [6], and long-period fibre gratings (LPFG) [7]. In general, although grating-based fibre-optic bending sensors possess high sensitivity and small size, they always suffer from serious cross-perturbation, such as temperature or strain [8]. Other well-known fibre-optic bending sensors are based on fibre interferometers. In-line Mach–Zehnder interferometers (MZI) are formed by splitting and recombining different optical modes (core mode and cladding modes), such as fibre lateral offset splicing [9], fibre taper [10], photonic crystal fibre collapsing [11], dual-core fibre [12], or LPFG pair [13]. Besides, supermodes interference is very sensitive to external bending in multicore optical fibres (MCFs). Thus three-core MCFs or even seven-core MCFs have been used to generate the supermodes excited by the fundamental mode of the input single mode fibre (SMF) [14, 15]. The interferometer-based fibre-optic bending sensors not only possess high sensitivity, but also distinguish the bending orientation. However, some interferometer-based bending sensors are also impaired by cross-sensitivity to temperature or axial strain, just like the grating-based fibre-optic bending sensors [16].
In this paper, we proposed a sensitive one-dimensional vector bending sensor based on a self-referenced anti-resonant reflecting optical waveguide (ARROW). Two symmetric air holes in the hollow-core photonic crystal fibre (HCPCF) were infiltrated with refractive index matching liquids (RIMLs) with different refractive indices, which formed a self-referenced ARROW. The bending of the sensor induces a change in the resonant condition of double-layered Fabry–Pérot resonators, and the one-dimensional bending orientation can be detected through the wavelength interval between two lossy dips. Moreover, the temperature and strain cross-sensitivity can be eliminated through the self-referenced ARROW.
2. Fabrication of the self-referenced ARROW
An optical micrograph of the HCPCF used in the proposed sensor is shown in Fig. 1(a). The core is an air hollow octagon with a side length of 18 μm, and the cladding is an air-ring with a diameter of 105 μm. The air-ring cladding is composed of eight hollow holes with an inner diameter of 35 μm. The diameter of the outer cladding is 190 μm, as shown in Fig. 1(b).
Then two symmetric air holes in the air-ring cladding of the HCPCF were infiltrated with RIMLs, respectively. Firstly, a section of the SMF was spliced to the HCPCF in order to block all air holes. During the arc fusion (arc power of 18mA, gap of 10 µm, and arc duration of 140 ms), the junction in the HCPCF was tapered slightly, with air holes still existed. Then the SMF was cut by use of femtosecond laser irradiation, and the length of the remaining SMF was ~10 µm. After that, the HCPCF was rotated, and the femtosecond laser was focused on the end face of the SMF. An air channel 1 was drilled in the SMF through the cleaved end face. This air channel 1 was aligned to one air hole in the air-ring cladding. Then, the drilled SMF was immersed into the RIML (Cargille Laboratories) with the refractive index of 1.440, which was infiltrated into one air hole in the air-ring cladding by using the capillary force through the air channel, as shown schematically in Fig. 2(a). Noted that in some other type of PCFs with small air holes (1~5 µm), it is very difficult to let the liquid get through the PCF air holes, hence an external air pressure is often needed. However, in the proposed HCPCF, the size of the inflltrated air hole is as large as 35µm, which could be filled with liquid very easily without the external air pressure. In the experiment the average velocity of the infiltration is 15 µm/min. Thus the entire infiltration time was ~20 h, and one air hole in the HCPCF with a length of 18 cm was infiltrated with the RIML, as shown in Fig. 2(b). The remaining SMF was cut off by using a conventional fibre cleaver.
Fig. 2 (a) The air channel1 for the infiltration of the RIML (1.440). (b) The RIML (1.440)-infiltrated HCPCF. (c) The air channel2 for the infiltration of the RIML (1.420). (d) The RIML (1.440) and RIML (1.420) -infiltrated HCPCF.
Then the cleaved end of the HCPCF was spliced with another section of the SMF, and a second air channel 2 was also drilled in the cleaved surface of the SMF by using the same method. The air channel 2 was aligned to a symmetric air hole of the first RIML infiltrated air hole in the air-ring cladding, and the other RIML with the refractive index of 1.420 was infiltrated into the second air hole by using capillary force, as shown in Fig. 2(c). In this way, two symmetric air holes in the air-ring cladding were infiltrated with RIMLs with different refractive indices, as shown in Fig. 2(d).
After the infiltration procedure was completed, the remaining SMF was also cut off. Then the well-cleaved HCPCF with a length of 12 cm was spliced with SMFs by using a conventional fibre splicer (S183PM, Fitel). Besides, the other HCPCF with a length of 12 cm was also infiltrated with RIML with a refractive index of 1.420 only in one air hole in the air-ring cladding in order to compare the HCPCFs between one and two RIML-infiltrated air holes.
3. Principle of the proposed sensor
The light is confined in the air core of the HCPCF with the air ring cladding due to the mode mismatching [17, 18]. However, once the RIML was infiltrated into the air-ring cladding, the refractive index of the core was less than that of the cladding. Thus the core mode oscillates and radiates through the cladding of the RIML and silica. The RIML-infiltrated air holes and the silica can be described as a double-layered Fabry–Pérot etalon [19], as shown in Fig. 3(a). When the wavelengths cannot satisfy the resonant condition of the resonator, the guided light is reflected back by the resonator, and the guided light is confined in the air core of the HCPCF, as shown in Fig. 3(b). When the wavelengths satisfy the resonant condition, the guided light is transmitted through the Fabry–Pérot resonator and leaks out of the cladding of the HCPCF, as shown in Fig. 3(c). In the proposed sensor, two symmetric air holes in the air-ring cladding of the HCPCF were infiltrated with different RIMLs. Thus there are two Fabry–Pérot resonators in the HCPCF (resonator A (1.440) and resonator B (1.420) in Fig. 3(a)). Thus periodic and narrow lossy dips corresponding to the resonant conditions of the two double-layered Fabry–Pérot resonators occur in the transmission spectrum [19]. The wavelength of the lossy dips can be expressed as [20]:
where andare resonant wavelengths for the RIML1- (1.440) and RIML2-(1.420) infiltrated resonator, is the diameter of the air hole in the air-ring cladding, is the thickness of the silica, , , , and are the refractive indices of the air, RIML1, RIML2, and silica, respectively, and is the resonance order. According to Eq. (1) and (2), lossy dips at the resonate condition were calculated as 1534.27 and 1554.52 nm corresponding to the resonator A (1.440), and 1545.15 and 1565.03 nm corresponding to resonator B (1.420).Fig. 3 (a) Schematic diagram of the cross-section of the RIMLs-infiltrated HCPCF. (b) Anti- resonant condition. (c) Resonant condition.
The experimental setup of the fibre-optic bending sensor is shown in Fig. 4(a). The light source is an amplified spontaneous emission (ASE) source with wavelength covering 1525-1565 nm, and the output power is 20 mW. The transmission spectrum of the sensor was interrogated by using an optical spectrum analyzer (OSA) (AQ6370B, Agilent Technologies). The transmission spectra of a section of the HCPCF with RIML (1.420) infiltrated in one air hole and with RIMLs (1.440 and 1.420) infiltrated in two air holes were investigated first, as shown in Fig. 4(b). The transmission powers of the RIML-infiltrated HCPCF with two resonators (−34.7 dB) are reduced significantly compared with that of the RIML-infiltrated HCPCF with one resonator (−22.4 dB). Two narrow lossy dips exist in the transmission spectrum of the RIML-infiltrated HCPCF in one air hole, indicating the leaky effect of one resonator in the HCPCF. The wavelengths of the lossy dips are 1543.83 and 1562.87 nm, respectively, corresponding to the resonator B with the RIML refractive index of 1.420. For the HCPCF with RIML infiltrated in two air holes, four narrow lossy dips exist in the transmission spectrum. The wavelengths of lossy dips A, B, C, and D, are 1533.06, 1543.26, 1552.68 nm, and 1562.27 nm, respectively, which are in good agreement with the theoretical predictions (1534.27, 1545.15, 1554.52 and 1565.03 nm). Lossy dips B and D are in good agreement with that of the RIML-infiltrated HCPCF with one resonator, indicating that lossy dips B and D correspond to the resonator B (1.420) while lossy dips A and C correspond to resonator A (1.440). It should be noted that the mode interference in the HCPCF should also be considered, which would generate a sinusoidal interferogram in the transmission spectrum. However, in Fig. 4(b), there are only lossy dips corresponding to the leaky modes in the transmission spectrum without the sinusoidal interferogram. Therefore, in the proposed sensor, the mode interference is too weak to influence the transmission spectrum. The RIML-infiltrated HCPCF was fixed to a stainless steel sheet, of which two ends were fixed to the centre of a rotatable disc that could be turned to rotate the fibre separately to an arbitrary orientation. Two rotators were fixed on two translation stages, which could be moved to generate the bending of the fibre. The fibre at 0° ( + Y) bending orientation is defined when the lossy dip A presents a maximum blue shift. In contrast, fibre bending at 180° (-Y) orientation is defined when the lossy dip B presents a maximum blue shift. The 90° ( + X) and 270°(–X) orientations are vertical with respect to the 0° and 180° orientations. A schematic of the bending orientations is shown in Fig. 4(c).
Fig. 4 (a) Schematic of the experimental setup. (b) The transmission spectra of a section of HCPCF with RIML infiltrated in one air hole and two air holes. (c) The definition of the bending orientation.
The principle of the fibre optic vector bending sensor can be contributed to the asymmetric distribution of the refractive index in the HCPCF. Figure 5(a) shows the refractive index profile of a curved HCPCF with a curvature of 0.88 m−1 along the + Y direction, which is performed by COMSOL FEM. Thus, the refractive index distribution of the HCPCF can be expressed as: when the fibre is bent in the + Y direction, where is the initial effective index of the HCPCF when it is straight and is the curvature of the HCPCF, which can be expressed as [13]: .and are half of the reduced and initial distance of the two fibre holders, respectively. When the HCPCF is bent, the refractive index of the outer cladding is changed due to the photoelastic effect of the silica cladding, which results in a wavelength shift of the lossy dip due to the variation of the resonant condition. However, because of the asymmetric distribution of the refractive index change for the HCPCF, the wavelength shifts for two double-layered Fabry–Pérot resonators differ significantly. When the HCPCF is bent along the + Y direction, the lossy dip A shifts to shorter wavelength because effective index of the silica cladding outside the resonator A decreases induced by the stretching [21]. On the contrary, the lossy dip B shifts to longer wavelength because effective index of the silica cladding outside the resonator B increases induced by the compression [21], as shown in Fig. 5(a). Therefore, the wavelength interval between two adjacent lossy dips A and B for two different resonators is increased. When the HCPCF is bent along the -Y direction, the refractive index distribution is opposite to that of the + Y direction, as shown in Fig. 5(b) (compression of resonator A and stretching of resonator B). Hence the lossy dip A and B shift to longer and shorter wavelength, respectively, and the wavelength interval between two adjacent lossy dips A and B for two different resonators is decreased. Therefore, the bending curvature and the one-dimensional bending orientation can be measured by interrogating the wavelength interval between two lossy dips.
For temperature and axial strain cross-perturbation, the refractive index change of silica claddings outside both the resonator A and resonator B are identical due to the same thermo-optic coefficient and optoelastic constant, and lossy dips A and B of two resonators shift to shorter or longer wavelength simultaneously. Therefore, a self-referenced ARROW is formed between the RIML1 and RIML2 -infiltrated HCPCF, and the temperature or strain cross-sensitivity can be eliminated by calculating the wavelength interval between two lossy dips of the self-referenced ARROW.
4. Experiment and discussion
The curvature sensitivity of the fibre optic bending sensor was investigated first. The RIML-infiltrated HCPCF was bent in the + Y direction (0°). The transmission spectra are shown in Fig. 6(a). Obviously, lossy dips A and B are shifted towards shorter and longer wavelength, respectively. Figure 6(b) shows the relationship between the wavelength shift of lossy dips A and B and the bending. The bending sensitivities of lossy dips A and B are −2.34 and 2.53 nm/m−1, indicating different resonant condition of the two resonators due to the asymmetric distribution of the refractive index change for the HCPCF. The wavelength interval between two lossy dips is increased. The sensitivity of the wavelength interval is 4.86 nm/m−1 when the HCPCF was bent in the + Y direction, as shown in Fig. 6(e). Then the RIML-infiltrated HCPCF was also bent in the -Y direction (180°), and transmission spectra are shown in Fig. 6(c). As in the -Y direction, lossy dips A and B are shifted towards longer and shorter wavelengths due to the opposite refractive index distribution of the HCPCF compared to that in the + Y direction. The sensitivity of the lossy dip A and B are 2.45 nm/m−1 and −2.39 nm/m−1, as shown in Fig. 6(d). The wavelength interval between two lossy dips is decreased. The sensitivity of the wavelength interval is −4.84 nm/m−1 when the HCPCF was bent in the -Y direction, as shown in Fig. 6(e). Therefore, the one-dimensional bending orientation can be detected through the increasing or decreasing of the wavelength interval between two lossy dips A and B. The sensitivity of the proposed sensor is higher than previous results of −0.754 nm/m−1 which is based on the method of the lateral offset splicing [22], 1.23 nm/m−1 which is based on the method of the LPFG [23], or 1 nm/m−1 which is based on the method of the intermodal interference [24]. When the RIML-infiltrated HCPCF was bent in the + X and –X directions (90° and 270°), the wavelength intervals were almost constant due to the symmetric refractive index distribution, as shown in Fig. 6(f) (the relative standard variation of the wavelength interval is only 0.73%).
Fig. 6 (a) Transmission spectra and (b) wavelength shift of the HCPCF bent in the + Y direction. (c) Transmission spectra and (d) wavelength shift of the HCPCF bent in the -Y direction. (e) Wavelength interval with the HCPCF bending. (f) Wavelength shift of the HCPCF bent in the + X and –X directions.
The temperature dependence of the fibre optic bending sensor was also researched. The RIML infiltrated HCPCF was fixed in an environmental chamber whose temperature range was adjusted from 20 to 80°C. Figure 7(a) and (b) show transmission spectra of the proposed sensor with different temperature for ascending and descending order. Although both lossy dips A and B shift to longer (ascending) or shorter (descending) wavelength simultaneously, it can be observed that the wavelength interval is almost fixed due to the same refractive index change for two silica claddings of resonator A and B at different temperature, as shown in Fig. 7(c) and (d). The standard variation of the wavelength interval is only 0.01 nm in the temperature range of 20 to 80 °C for both ascending and descending order.
Fig. 7 Transmission spectra of the proposed sensor with different temperature in (a) ascending order, and (b) descending order. The wavelength shift of lossy dips A and B and wavelength interval between two lossy dips in (c) ascending order, and (d) descending order.
The influence of the axial strain for the fiber optic bending sensor was also investigated. The axial strain of this sensor was measured by moving one translation stage, which could stretch the HCPCF to generate the axial strain. The axial strain in the RIML infiltrated HCPCF can be calculated by according to Hooke’s law, where is the applied force, is the cross-sectional area of fiber, and is the Young’s modulus of silica (~72 GPa) [25]. Figure 8(a) and (b) show transmission spectra of the proposed sensor with different axial strain for ascending and descending order. Although both lossy dips A and B shift to shorter (ascending) or longer (descending) wavelength simultaneously, it can be observed that the wavelength interval is also fixed due to the same refractive index change for two silica claddings of resonator A and B with different axial strain, as shown in Fig. 8(c) and (d). The standard variation of the wavelength difference is only 0.02 nm in the axial strain range of 200 to 1000μεfor both ascending and descending order. Therefore, the proposed sensor could compensate for the temperature and axial strain change, which overcomes the temperature and axial strain cross-sensitivity of many fibre bending sensors.
Fig. 8 Transmission spectra of the proposed sensor with different axial strain in (a) ascending order, and (b) descending order. The wavelength shift of lossy dip A and B and wavelength interval between two lossy dips in (c) ascending order, and (d) descending order.
For the analysis of polarization of the proposed sensor, we measured the polarization-dependent loss (PDL) of the RIML infiltrated HCPCF. The PDL is defined as the maximum change in the transmitted power for polarizations. A tunable laser diode (81980A, Agilent Technologies) with wavelength covering 1450 nm-1750 nm was used as the light source, and the output power was 20 mW. A polarization controller (PC030, Thorlabs) was used to control the polarization of the light source. A powermeter (PM20, Thorlabs) with a resolution of 0.01 dB was used to measure the intensity of the transmission spectrum. We measured the PDL of the RIML infiltrated HCPCF with the wavelength range from 1525 nm to 1565 nm, as shown in Fig. 9. The RIML infiltrated HCPCF shows a dramatically PDL value (from 1.47 to 6.38 dB), which is mainly attributed to the asymmetry structure of the RIML infiltrated HCPCF used in experiments.
5. Conclusion
In conclusion, a temperature and axial strain -compensated one-dimensional vector bending fibre optic sensor based on self-referenced anti-resonant reflecting optical waveguide has been proposed and experimentally demonstrated. Two air holes in the HCPCF were infiltrated with RIML with different refractive indices, which formed two resonators in an ARROW. The bending of the HCPCF induces a wavelength shift of lossy dip in the transmission spectrum, and the one-dimensional bending orientation can be detected through the wavelength interval between two lossy dips. The bending sensitivities are 4.86 and −4.84 nm/m−1 for the curvature of the 0° and 180° bending orientations in the bending range of 0–0.88 m−1, respectively. Moreover, this device exhibits low crosstalk of the temperature and axial strain. The proposed fibre sensor can be used for monitoring the structural health of infrastructures.
Funding
National Natural Science Foundation of China (NSFC) (No. 61601436, 61675203, 61377064, 61401432, 61501425); Beijing Natural Science Foundation (4174108); National Basic Research Program of China (No. 2015CB352100); Research Equipment Development Project of Chinese Academy of Sciences (No. YZ201508).
References and links
1. S. J. Zheng, B. H. Shan, M. Ghandehari, and J. P. Ou, “Sensitivity characterization of cladding modes in long-period gratings photonic crystal fiber for structural health monitoring,” Measurement 72, 43–51 (2015). [CrossRef]
2. S. J. Zheng, Y. N. Zhu, and S. Krishnaswamy, “Fiber humidity sensors with high sensitivity and selectivity based on interior nanofilm-coated photonic crystal fiber long-period gratings,” Sens. Actuat B 176, 264–274 (2013). [CrossRef]
3. S. J. Zheng, “Long-period fiber grating moisture sensor with nano-structured coatings for structural health monitoring,” Struct. Health Monitor. Int. J. 14(2), 148–157 (2015). [CrossRef]
4. D. Feng, X. Qiao, and J. Albert, “Off-axis ultraviolet-written fiber Bragg gratings for directional bending measurements,” Opt. Lett. 41(6), 1201–1204 (2016). [CrossRef] [PubMed]
5. W. Cui, J. Si, T. Chen, and X. Hou, “Compact bending sensor based on a fiber Bragg grating in an abrupt biconical taper,” Opt. Express 23(9), 11031–11036 (2015). [CrossRef] [PubMed]
6. T. Guo, L. Shao, H. Y. Tam, P. A. Krug, and J. Albert, “Tilted fiber grating accelerometer incorporating an abrupt biconical taper for cladding to core recoupling,” Opt. Express 17(23), 20651–20660 (2009). [CrossRef] [PubMed]
7. P. Geng, W. Zhang, S. Gao, H. Zhang, J. Li, S. Zhang, Z. Bai, and L. Wang, “Two-dimensional bending vector sensing based on spatial cascaded orthogonal long period fiber,” Opt. Express 20(27), 28557–28562 (2012). [CrossRef] [PubMed]
8. G. Mao, T. Yuan, C. Guan, J. Yang, L. Chen, Z. Zhu, J. Shi, and L. Yuan, “Fiber Bragg grating sensors in hollow single- and two-core eccentric fibers,” Opt. Express 25(1), 144–150 (2017). [CrossRef] [PubMed]
9. Z. Ou, Y. Yu, P. Yan, J. Wang, Q. Huang, X. Chen, C. Du, and H. Wei, “Ambient refractive index-independent bending vector sensor based on seven-core photonic crystal fiber using lateral offset splicing,” Opt. Express 21(20), 23812–23821 (2013). [CrossRef] [PubMed]
10. S. Zhang, W. Zhang, S. Gao, P. Geng, and X. Xue, “Fiber-optic bending vector sensor based on Mach-Zehnder interferometer exploiting lateral-offset and up-taper,” Opt. Lett. 37(21), 4480–4482 (2012). [CrossRef] [PubMed]
11. C. Shen, C. Zhong, Y. You, J. Chu, X. Zou, X. Dong, Y. Jin, J. Wang, and H. Gong, “Polarization-dependent curvature sensor based on an in-fiber Mach-Zehnder interferometer with a difference arithmetic demodulation method,” Opt. Express 20(14), 15406–15417 (2012). [CrossRef] [PubMed]
12. H. Qu, G. F. Yan, and M. Skorobogatiy, “Interferometric fiber-optic bending/nano-displacement sensor using plastic dual-core fiber,” Opt. Lett. 39(16), 4835–4838 (2014). [CrossRef] [PubMed]
13. J. Villatoro, A. Van Newkirk, E. Antonio-Lopez, J. Zubia, A. Schülzgen, and R. Amezcua-Correa, “Ultrasensitive vector bending sensor based on multicore optical fiber,” Opt. Lett. 41(4), 832–835 (2016). [CrossRef] [PubMed]
14. W. Shin, Y. L. Lee, B.-A. Yu, Y.-C. Noh, and T. J. Ahn, “Highly sensitive strain and bending sensor based on in-line fiber Mach-Zehnder interferometer in solid core large mode area photonic crystal fiber,” Opt. Commun. 283(10), 2097–2101 (2010). [CrossRef]
15. G. Salceda-Delgado, A. Van Newkirk, J. E. Antonio-Lopez, A. Martinez-Rios, A. Schülzgen, and R. Amezcua Correa, “Compact fiber-optic curvature sensor based on super-mode interference in a seven-core fiber,” Opt. Lett. 40(7), 1468–1471 (2015). [CrossRef] [PubMed]
16. W. Shin, Y. L. Lee, B. A. Yu, Y. C. Noh, and T. J. Ahn, “Highly sensitive strain and bending sensor based on inline fiber Mach–Zehnder interferometer in solid core large mode area photonic crystal fiber,” Opt. Commun. 283(10), 2097–2101 (2010). [CrossRef]
17. F. Benabid, J. C. Knight, G. Antonopoulos, and P. S. J. Russell, “Stimulated Raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298(5592), 399–402 (2002). [CrossRef] [PubMed]
18. N. M. Litchinitser, S. C. Dunn, B. Usner, B. J. Eggleton, T. P. White, R. C. McPhedran, and C. M. de Sterke, “Resonances in microstructured optical waveguides,” Opt. Express 11(10), 1243–1251 (2003). [CrossRef] [PubMed]
19. N. M. Litchinitser, A. K. Abeeluck, C. Headley, and B. J. Eggleton, “Antiresonant reflecting photonic crystal optical waveguides,” Opt. Lett. 27(18), 1592–1594 (2002). [CrossRef] [PubMed]
20. B. You, J. Y. Lu, J. H. Liou, C. P. Yu, H. Z. Chen, T. A. Liu, and J. L. Peng, “Subwavelength film sensing based on terahertz anti-resonant reflecting hollow waveguides,” Opt. Express 18(18), 19353–19360 (2010). [CrossRef] [PubMed]
21. K. Nagano, S. Kawakami, and S. Nishida, “Change of the refractive index in an optical fiber due to external forces,” Appl. Opt. 17(13), 2080–2085 (1978). [CrossRef] [PubMed]
22. Q. D. Huang, Y. Q. Yu, X. J. Li, X. Chen, Y. F. Zhang, W. Zhou, and C. L. Du, “Micro-bending vector sensor based on six-airhole grapefruit microstructure fiber using lateral offset splicing,” Opt. Express 23(3), 3010–3019 (2015). [CrossRef] [PubMed]
23. P. Saffari, T. Allsop, A. Adebayo, D. Webb, R. Haynes, and M. M. Roth, “Long period grating in multicore optical fiber: an ultra-sensitive vector bending sensor for low curvatures,” Opt. Lett. 39(12), 3508–3511 (2014). [CrossRef] [PubMed]
24. S. Li, Z. Wang, Y. Liu, T. Han, Z. Wu, C. Wei, H. Wei, J. Li, and W. Tong, “Bending sensor based on intermodal interference properties of two-dimensional waveguide array fiber,” Opt. Lett. 37(10), 1610–1612 (2012). [CrossRef] [PubMed]
25. R. Gao, Y. Jiang, and L. Jiang, “Multi-phase-shifted helical long period fiber grating based temperature-insensitive optical twist sensor,” Opt. Express 22(13), 15697–15709 (2014). [CrossRef] [PubMed]
