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We present a novel dual-channel fiber optic interferometer based on intermodal interference from single-mode fiber (SMF) bending. This dual-channel interferometer has simple structure, consisting of two bare fiber semicircular bending regions with different bending radiuses connected by a section of straight fiber. A dual-channel interferometer with bending radiuses of 4 mm and 4.3mm is fabricated and refractive index (RI) sensing is realized by measuring the wavelength shift of the resonance dips in the transmission spectrum of the dual-channel interferometer. In the RI range of 1.3403 to 1.3726, the corresponding RI sensitivities for these two channels are 207 and 245nm/RIU (refractive index unit) and the RI resolutions are about 6.57 × 10−5 RIU and 5.55 × 10−5 RIU, respectively.
© 2015 Optical Society of America
1. Introduction
Fiber optic RI sensors have been extensively investigated recently due to their potential applications in biological, food, and chemical industry and their distinctive advantages over traditional RI sensors, such as high sensitivity, miniature size, and immunity to electromagnetic interference [1]. Many fiber optic refractometer configurations have been studied, including optical fiber coil resonators [2], short period fiber gratings [3, 4], long period gratings [5], multimode interference structures [6–10], microfiber interferometer [11–13], waist-deformed fiber taper interferometers [14], in-fiber femtosecond laser micromachining microhole interferometers [15], side-polished plastic optical fibers [16], solid-core photonic crystal fiber based microfluidic refractive index sensors [17], and silica-nanowire tips [18]. Especially, Yang et al proposed a single-mode-multimode-single-mode fiber structure with a new concept of leaky mode interference [19]. However, its modulation is based on the output light intensity, which is easily affected by laser power fluctuations and external perturbations. In addition, the measureable refractive index range from 1.46 to 1.55 is very high with limited applications. Although some of these devices provide high RI sensitivities, most of them require sophisticated demodulation schemes and bulky optical setups, which increase the cost and complexity of fabrication and operation.
In addition, the multiplexing capability is an important inherent advantage of fiber optic sensors that has been rarely demonstrated for RI sensing. Recently, multi-channel fiber sensors are the subject of considerable research [20]. Compared to other fiber optic sensors that can be easily multiplexed such as temperature and strain sensors [21], multi-channel fiber RI sensors have rarely been reported. In [1], a cascaded photonic crystal fiber interferometer for refractive index sensing is proposed. The sensor fabrication involves simple cleaving and splicing processes, but the resonance wavelengths located at different spectral positions are difficult to be controlled by the splicing process; a dual-channel fiber optic surface Plasmon resonance sensor for biological applications has also been studied [22], the sensor multiplexing mechanism depends on gold and polymer coating films, which need costly or complex procedures. Most of the previously published investigations on bent fibers focused on the prediction and reduction of bend loss, which is viewed as an adverse effect for light transmission [23–25]. Recently, there are some studies employing bent fibers as optical sensing elements based on bending fiber [26–30], they can be divided into two main subtypes: intensity demodulated [26, 27] and wavelength demodulated [28–31]. Although intensity based light modulation is easily affected by light source or external environments, the intensity modulation based sensors are unfavorable for the realization of multi-channel simultaneous detection. The special treatments for fiber play an important role in the wavelength modulation based sensors. Especially, a RI sensor based on a C-shaped ultrathin fiber taper is proposed in [28], which provides a higher RI sensitivity, the C-shape bent fiber fabrication contains complex process, including fiber stretching and ultrathin fiber bending; S-like fiber tapers-based Mach-Zehnder interferometers have been proposed for sensing applications due to their low cost and simple fabrication process [29], but the cladding diameter must be reduced by tapering process which increases the complexity of sensor fabrication and multiplexing. Previously, we present a fiber-optic refractometer based on leaky-mode generation from fiber bending [30]. The interferometer is simply constructed by using a standard single-mode fiber with two fiber bending regions connected by a section of straight fiber. It has advantages of simple configuration, easy fabrication and low cost. However, the issue of multiplexing still exists.
In this letter, we propose and demonstrate a dual-channel fiber optic refractometer based on intermodal interference from single-mode fiber (SMF) bending. Each channel consists of a section of semicircular bare standard SMF with a selected bending radius. The dual-channel fiber optic refractometer has many distinctive advantages over RI sensors based on bending fiber [26–31], such as simple configuration, easy fabrication and ease of multiplexing. Above all, the multiplexing is a unique feature of the dual-channel sensor based on the advantage integration of simple configuration (intensity demodulated) and comparable high sensitivity (wavelength demodulated). Experimental results show that the proposed sensor has high sensitivity to the RIs of the surrounding environment, and the resonance wavelengths shifted towards the longer wavelength as the RI increases. Compared with other aforementioned fiber optic refractometers, the fabrication of the dual-channel fiber optic interferometer is simple and cost-effective, which makes it a good candidate for multi-channel RI simultaneous measurement.
2. Sensor design and operating principle
The intermodal interference based fiber optic sensor multiplexing mechanics from bent-fiber leaky-mode generation and its related analyses are illustrated in Fig. 1. The sensor structure is schematically shown in Fig. 1(a). It consists of two sections of semicircular bare standard SMFs with different selected bending radiuses separated by a section of straight fiber of several centimeters long. The protective coating of the bending sections was stripped off, except for the separation fiber between the bending sections. The absence of the protective coating of the bending sessions will be beneficial to the high interference visibility and interaction between the surroundings and the optical field. Due to the presence of the protective coating of the separation section, the residual cladding modes from the first channel, which would perturb the signal of another channel, are strongly attenuated by the coating. At the input end of the semicircular bare SMF, the cladding modes are excited and propagate as several cladding modes in the cladding, and the cladding modes re-couple back to the core mode at the termination of the semicircular bare SMF, where all the cladding modes interfere with the core mode. Therefore, the different optical paths of the core mode and cladding modes form an intermodal interferometer. As shown in Fig. 1(a), when the core mode enters the semicircular bare SMF region, the light power is split into two portions: firstly, due to the bending, the light is partially leaked into the cladding where several cladding modes are excited and propagate along the fiber; secondly, the light that has not leaked to the cladding continues to propagates as the core mode. At the end of semicircular bare SMF region, the cladding modes are coupled back to the core mode where interference occurs. It is known that the effective RIs of the cladding modes depend on the RI of the surrounding medium. This will lead to the transmission spectrum changes as the surrounding RI changes. The picture of the fiber configuration with 5mm bending radius when it was illuminated by a visible laser light source is shown in Fig. 1(b). We observed that the light gradually leaked out fiber core when propagate in bend segment, and there is a recouple point at the end of semicircular bare SMF region, which will lead the interference between core mode and cladding modes. In addition, using an Rsoft software, we simulate transverse mode profiles of the bent fiber, Fig. 1(c) shows the transverse mode profiles of a single-mode fiber with 5mm bending radius, it illustrated that the bend will induce mode leakage and transmission loss.
Fig. 1 Illustration of multiplexing of intermodal interference based on fiber leaky-mode generation. (a) Schematic diagram of bent-fiber based intermodal interference; (b) Fiber leakage caused by bending; (c) transverse mode profiles with 5mm bending radius.
At the spectral dips, the phase difference between the core and the mth-order cladding mode after propagating through a semicircular bare standard SMFs with a selected bending radius R can be written as:
where nco,eff and ncl,m,eff are the effective RIs of the fundamental mode and the mth-order cladding mode, respectively. Δneff = nco,eff - ncl,m,eff is the effective RI difference between the fundamental mode and the mth-order cladding mode, C is the length of semicircular SMF, D is the wavelength of the transmission dip, and k is an integer. Depending on the phase difference between the core mode and cladding mode, destructive or constructive interference can occur. When strong destructive interference occurs, the interference pattern will show in the transmitted spectrum. Since the effective RI of the cladding mode depends on the external RI, when the sensor is subjected to external RI perturbation, the transmission dip wavelength will shift. Surrounding RI changes can be detected and evaluated by measuring this resonance wavelength shift. The sensitivity of the transmission dip to the change of external RI can be deduced from Eq. (1) as:To verify the proposed model, we used a commercial standard SMF (Coning, SMF-28) to fabricate the designed sensor. The polymer coating layers of the separation section between the bending sections were retained. The polymer protective coating can absorb the residual cladding modes, and eliminate the crosstalk between the signals of the two channels.
To determine the selected appropriate bending radiuses and understand the influence of the bending radius on the optical spectra, we investigated the spectra of the individual configurations with different bending radiuses. Figure 2 illustrates transmission spectra of the configurations with different bending radiuses. In Fig. 2(a), there is an obvious dip with a resonance depth of ~15 dB located at 1566.6nm. Figure 2(b) shows an interference pattern that includes only one narrow dip with about 18dB resonance depth at the long end of the wavelength range. In order to verify that it has enough measurement range, this configuration is immersed in deionized water. The dips shown in Figs. 2(c) and 2(d) are very broad, leading to reduced resolution for RI sensing. Transmission spectra shown in Figs. 2(a) and 2(b) are more suitable for sensing. In order to avoid the crosstalk between the channels (the resonance wavelengths of the channels are located at different spectral positions) and achieve high precision detection (the resonance wavelengths of the channels with the narrow bandwidth and high depth) [32–34], bending radiuses of 4 mm and 4.3 mm were selected for the two semicircular bending fiber sections which function as the intermodal interferometers. Small bending radiuses will induce large attenuation and reduce the multiplexing; however, the multiplexing can be improved by appropriate bending radiuses which will reduce both precision detection and detection range, as shown in Figs. 2(c) and 2(d).
3. Experiments and discussion
The spectral characteristics of the single-channel fiber optic refractometer with 4.3mm bending radius was experimentally investigated, as shown in Fig. 3. NaCl solutions with different concentration were prepared as the RI samples. The temperature around the refractometer head is maintained at 20°C. The responses to different surrounding RIs are shown in Fig. 3(a). Figure 3(a) shows that as the surrounding RI increases, the dip wavelength shifts toward to the longer wavelength. The inset of Fig. 3(a) presents the dip wavelength as a function of the surrounding RI. The experimental verification demonstrated that the bent fiber interferometer can be used as a high-sensitivity RI sensor. For the initial experiment, we used a U-shape groove to fix the bent fiber, but this method brings other problems, such as difficulty cleaning and inadequate contact between fiber and liquids. After repeated attempts, we adopted to fix the fiber on the glass substrate, and the glue dropped upon the section with protective coating, hence, the glue will not affect the performance and the mode transmission of the sensor structure. Then, we investigate the polarization properties of the bent fiber by changing the incident light polarization. We use a polarizer to obtain the polarized light, and modify its polarization by adjusting polarization controller. The polarization of the incident light influences the transmission spectrum. As shown in Fig. 3(b), the transmission spectrum bandwidth decreases when polarized light is used. In addition, an inset of Fig. 3(b) illustrates spatial spectra; from the inset, we deduced that the mode coupling and interference mainly occur between the core mode and the single dominant higher-order mode. Even the bent fiber based interferometer is multi-mode interference, the coupling between core mode and different high-order modes excited by bending is obviously different; and the power will be primarily distributed in the individual higher-order modes. The interferometer transmission can be modeled as a two-mode interference process.
Fig. 3 Spectral characteristics of single-channel sensor (4.3mm bending radius). (a) Spectra when the sensor is immersed in varying RI liquid. Inset: RI responses of the sensor. (b) Transmission spectra variation by adjusting light polarization with a polarization controller (PC). Inset: Spatial spectrum.
Figure 4 shows the typical transmission spectra of the individual interferometer with 4mm and 4.3mm bending radius and the resultant dual-channel interferometer with 4mm and 4.3mm bending radiuses. It is shown that there is only one obvious dip at 1566.6nm appearing on the transmission spectrum (named as Channel 2) when the first semicircular bending fiber section with 4mm bending radius is formed. Then another semicircular bending fiber section with 4.3mm bending radius was created (labeled as Channel 1). Even the visibility of Channel 1 has a slightly degrade due to the loss induced by the Channel 2, the visibility of the fringes meets the detecting requirements of the demodulation system during RI measurement.
Fig. 4 The spectra of the individual 4mm and 4.3mm bending radius and the dual-channel sensor when Channel 1 is immersed in deionized water and Channel 2 is in air.
The RI sensing of the dual-channel fiber optic refractometer was experimentally investigated. The responses of Channel 1 to different surrounding RIs are shown in Fig. 5(a), when Channel 1 was immersed into the solution with different RIs and the RI of the medium surrounding Channel 2 was maintained at 1.3565 during the RI measurement. Figure 5(a) shows that, as the surrounding RI increases, the dip wavelength of the Channel 1 showed red shift and the total wavelength shift was up to 6.7nm; the dip wavelength of Channel 2 was largely unchanged. The inset of Fig. 5(a) presents the dip wavelength shift versus the surrounding RI for both channels. The dip wavelengths of the Channel 1 increased linearly as the RI increased from 1.3403 to 1.3726. From the linear fit, the RI sensitivity is 207nm/RIU for Channel 1. In this setup, a self-developed OSI (optical sensing interrogator) sends a broadband light to the fiber, the transmitted light signal is detected by the photoelectric converter in the OSI, and demodulated by DAQ (Data acquisition unit) and software, then display the spectra signal on computer. Considering that the wavelength resolution of the OSI is 4pm, the resolution of the RI measurement is estimated to be 6.57 × 10−5 RIU [32–34].
Fig. 5 (a) The spectra of the dual-channel sensor when Channel 1 is immersed in varying RI liquid and Channel 2 is in 1.3565 RI throughout the measurement. Inset: RI responses of the dual channels. (b) The spectra of the dual Channel sensor when Channel 2 is immersed in varying RI liquid and Channel 1 is immersed in liquid with 1.3726 RI throughout the measurement. Inset: RI responses of the dual channels.
After experimental demonstration of the RI sensing of Channel 1, we used the same procedure to investigate Channel 2 responses of the dual-channel sensor. The spectrum responses of Channel 2, when Channel 2 was immersed into the solutions with different RIs and Channel 1 was in liquid with constant RI of 1.3726, are shown in Fig. 5(b), It is shown that the dip wavelength of Channel 2 shifted to longer wavelengths while the surrounding RI increased from 1.3403 to 1.3726. There was no obvious wavelength change for the dip of Channel 1. The inset of Fig. 5(b) shows the dip wavelengths versus surrounding RIs. The dip wavelengths of Channel 2 increased by 8nm while the surrounding RI increased from 1.3403 to 1.3726. The corresponding RI sensitivity is calculated to be 245nm/RIU and the corresponding RI measurement resolution is about 5.55 × 10−5 RIU. Due to the spectrum interference between dual channels during RI sensing, there is some overlap on the spectra of dual channels. To avoid this spectrum overlap between dual channels, the sensing ranges corresponding to different channels are readdressed as follow: Channel 2 (1.3403-1.3630), Channel 1 (1.3565-1.3721). We verify the repeatability of this fiber device during the measurement process, when a channel is immersed in varying RI liquid, another channel is immersed in a random RI throughout the measurement; the experiment result indicates that the spectrum of this channel will be in accordance with that when this channel as the measurement channel.
In practical applications, temperature cross-sensitivity is an important issue for many RI sensors; as illustrated in Fig. 6, we investigate the temperature response of the dual-channel structure. The structure is mounted on a glass plate immersed into deionized water. Our experiment is performed by increasing the liquid temperature gradually from 13°C to 36°C, with a temperature interval of 1 °C. Figure 6(a) presents the transmission spectra versus temperature changes. As shown in Fig. 6(a), the dip wavelengths moved toward short wavelength. Additionally, the inset of Fig. 6(b) shows that the spectrum is constant when the temperatures are below 24°C. From Fig. 6(a), the spectrum evolution is faster when the temperatures exceed 24°C. The temperature response is shown in Fig. 6(b), when the temperature exceed 24°C, the resonance wavelengths moved toward shorter wavelengths as temperature increased, giving average temperature sensitivity of −260 and −250pm/°C for Channel 1 and Channel 2, respectively. The temperature sensitivity of Channel 1 is similar to that of Channel 2. When Channel 1 is used as a RI sensing channel, the Channel 2 can function as a reference channel to solve the temperature and RI cross-sensitivity. The different temperature response under different temperature range is induced by the thermal properties of the glue. This conclusion demonstrates that this sensor is more appropriate for RI measurement at lower temperature and it can realize the temperature-insensitive RI sensing.
Fig. 6 Temperature Responses. (a) Transmission spectra with increasing temperature. (b) Relationship between temperature and wavelength shift. Inset is the transmission spectra when temperatures are below 24°C.
4. Conclusion
In summary, we proposed and demonstrated a novel fiber optic refractometer by using a cladding mode generation mechanism in bent fibers. The optical interferences are generated from two bare fiber semicircular bending regions with different bending radiuses in a single mode fiber separated by s span of single-mode fiber with absorptive coating and the two bare fiber semicircular bending regions are used as the sensing channels for RI measurement. We fabricated a dual-channel interferometer prototype with 4mm and 4.3mm bending radius combination. The RI sensing is completed by measuring the wavelength shift of the resonance dips in its transmission spectrum. In the RI range from 1.3403 to 1.3726, the corresponding RI sensitivities are 207 and 245 nm/RIU for the Channel 1 and Channel 2, respectively, and the RI measurement resolutions are about 6.57 × 10−5 RIU and 5.55 × 10−5 RIU, respectively. We investigated the temperature response of this structure. When the temperature exceeded 24°C, the dip wavelengths moved toward short wavelength direction as temperature increased, giving average temperature sensitivity of −260 and −250pm/°C for Channel 1 and Channel 2, respectively. In addition, this temperature response demonstrated that this sensor is more appropriate for RI measurement at lower temperature, which it can realize the temperature-insensitive RI sensing. Future work will be focused on sensor optimization and packaging to further enhance sensor performance, and sensor multiplexing for more channel measurements.
Acknowledgments
The authors would like to acknowledge the financial supports from the National Nature Science Foundation of China (Nos. 61137005 and 11474043).
References and links
1. J. L. Lim, D. J. J. Hu, P. P. Shum, and Y. Wang, “Cascaded photonic crystal fiber interferometers for refractive index sensing,” IEEE Photon. J. 4(4), 1163–1169 (2012). [CrossRef]
2. F. Xu and G. Brambilla, “Demonstration of a refractometric sensor based on optical microfiber coil resonator,” Appl. Phys. Lett. 92(10), 101126 (2008). [CrossRef]
3. X. Zhang, W. Peng, Y. Liu, and L. Pan, “Core–cladding mode recoupling based fiber optic refractive index sensor,” Opt. Commun. 294(3), 188–191 (2013). [CrossRef]
4. S. M. Lee, S. S. Saini, and M. Y. Jeong, “Simultaneous measurement of refractive index, temperature, and strain using etched-core fiber Bragg grating sensors,” IEEE Photon. Technol. Lett. 22(19), 1431–1433 (2010). [CrossRef]
5. X. Shu, L. Zhang, and I. Bennion, “Sensitivity characteristics of long period fiber gratings,” J. Lightwave Technol. 20(2), 255–266 (2002). [CrossRef]
6. Q. Wu, Y. Semenova, B. Yan, Y. Ma, P. Wang, C. Yu, and G. Farrell, “Fiber refractometer based on a fiber Bragg grating and single-mode-multimode-single-mode fiber structure,” Opt. Lett. 36(12), 2197–2199 (2011). [CrossRef] [PubMed]
7. R. Jha, J. Villatoro, and G. Badenes, “Ultrastable in reflection photonic crystal fiber modal interferometer for accurate refractive index sensing,” Appl. Phys. Lett. 93(19), 191106 (2008). [CrossRef]
8. L. C. Li, L. Xia, Z. H. Xie, and D. M. Liu, “All-fiber Mach-Zehnder interferometers for sensing applications,” Opt. Express 20(10), 11109–11120 (2012). [CrossRef] [PubMed]
9. J. Shi, S. Xiao, M. Bi, L. Yi, and P. Yang, “Discrimination between strain and temperature by cascading single-mode thin-core diameter fibers,” Appl. Opt. 51(14), 2733–2738 (2012). [CrossRef] [PubMed]
10. J. Wu, Y. Miao, B. Song, K. Zhang, W. Lin, H. Zhang, B. Liu, and J. Yao, “Temperature-insensitive optical fiber refractometer based on multimode interference in two cascaded no-core square fibers,” Appl. Opt. 53(22), 5037–5041 (2014). [CrossRef] [PubMed]
11. F. Xu, P. Horak, and G. Brambilla, “Optical microfiber coil resonator refractometric sensor,” Opt. Express 15(12), 7888–7893 (2007). [CrossRef] [PubMed]
12. J. Wo, G. Wang, Y. Cui, Q. Sun, R. Liang, P. P. Shum, and D. Liu, “Refractive index sensor using microfiber-based Mach-Zehnder interferometer,” Opt. Lett. 37(1), 67–69 (2012). [CrossRef] [PubMed]
13. W. B. Ji, H. H. Liu, S. C. Tjin, K. K. Chow, and A. Lim, “Ultrahigh sensitivity refractive index sensor based on optical microfiber,” IEEE Photon. Technol. Lett. 24(20), 1872–1874 (2012). [CrossRef]
14. P. Lu, L. Men, K. Sooley, and Q. Chena, “Tapered fiber Mach-Zehnder interferometer for simultaneous measurement of refractive index and temperature,” Appl. Phys. Lett. 94(13), 131110 (2009). [CrossRef]
15. Y. Wang, M. Yang, D. N. Wang, S. Liu, and P. Lu, “Fiber in-line Mach-Zehnder interferometer fabricated by femtosecond laser micromachining for refractive index measurement with high sensitivity,” J. Opt. Soc. Am. B 27(3), 370–374 (2010). [CrossRef]
16. L. Bilro, N. J. Alberto, L. M. Sá, J. de Lemos Pinto, and R. Nogueira, “Analytical analysis of side-polished plastic optical fiber as curvature and refractive index sensor,” J. Lightwave Technol. 29(6), 864–870 (2011). [CrossRef]
17. D. K. C. Wu, B. T. Kuhlmey, and B. J. Eggleton, “Ultrasensitive photonic crystal fiber refractive index sensor,” Opt. Lett. 34(3), 322–324 (2009). [CrossRef] [PubMed]
18. S. Pevec and D. Donlagic, “Nanowire-based refractive index sensor on the tip of an optical fiber,” Appl. Phys. Lett. 102(21), 213114 (2013). [CrossRef]
19. R. P. Murphy, S. W. James, and R. P. Tatam, “Multiplexing of fiberoptic long-period grating-based interferometric sensors,” J. Lightwave Technol. 25(3), 825–829 (2007). [CrossRef]
20. D. Barrera, J. Villatoro, V. P. Finazzi, G. A. Cárdenas-Sevilla, V. P. Minkovich, S. Sales, and V. Pruneri, “Lowloss photonic crystal fiber interferometers for sensor networks,” J. Lightwave Technol. 28(24), 3542–3547 (2010). [CrossRef]
21. G. A. Cárdenas-Sevilla, V. Finazzi, J. Villatoro, and V. Pruneri, “Photonic crystal fiber sensor array based on modes overlapping,” Opt. Express 19(8), 7596–7602 (2011). [CrossRef] [PubMed]
22. W. Peng, S. Banerji, Y. C. Kim, and K. S. Booksh, “Investigation of dual-channel fiber-optic surface plasmon resonance sensing for biological applications,” Opt. Lett. 30(22), 2988–2990 (2005). [CrossRef] [PubMed]
23. J. H. Harris and P. F. Castle, “Bend loss measurements on high numerical aperture single-mode fibers as a function of wavelength and bend radius,” J. Lightwave Technol. 4(1), 34–40 (1986). [CrossRef]
24. R. Morgan, J. S. Barton, P. G. Harper, and J. D. C. Jones, “Wavelength dependence of bending loss in monomode optical fibers: Effect of the fiber buffer coating,” Opt. Lett. 15(17), 947–949 (1990). [CrossRef] [PubMed]
25. Y. Murakami and H. Tsuchiya, “Bending losses of coated single-mode optical fibers,” IEEE J. Quantum Electron. 14(7), 495–501 (1978). [CrossRef]
26. A. Iadicicco, D. Paladino, S. Campopiano, W. J. Bock, A. Cutolo, and A. Cusano, “Evanescent wave sensor based on permanently bent single mode optical fiber,” Sens. Actuators B Chem. 155(2), 903–908 (2011). [CrossRef]
27. P. Wang, Y. Semenova, Q. Wu, G. Farrell, Y. Ti, and J. Zheng, “Macro bending single-mode fiber-based refractometer,” Appl. Opt. 48(31), 6044–6049 (2009). [CrossRef] [PubMed]
28. H. M. Luo, X. W. Li, W. W. Zou, W. N. Jiang, and J. P. Chen, “Modal interferometer based on a C-shaped ultrathin fiber taper for high-sensitivity refractive index measurement,” Appl. Phys. Express 5(1), 012502 (2012). [CrossRef]
29. R. Yang, Y. S. Yu, Y. Xue, C. Chen, Q. D. Chen, and H.-B. Sun, “Single S-tapered fiber Mach-Zehnder interferometers,” Opt. Lett. 36(23), 4482–4484 (2011). [CrossRef] [PubMed]
30. X. Zhang and W. Peng, “Fiber optic refractometer based on leaky-mode interference of bent fiber,” IEEE Photon. Technol. Lett. 27(1), 11–14 (2015). [CrossRef]
31. G. Liu, K. Li, P. Hao, W. Zhou, Y. Wu, and M. Xuan, “Bent optical fiber taper for refractive index detection with a high sensitivity,” Sens. Actuators A Phys. 201, 352–356 (2013). [CrossRef]
32. I. M. White and X. Fan, “On the performance quantification of resonant refractive index sensors,” Opt. Express 16(2), 1020–1028 (2008). [CrossRef] [PubMed]
33. C. Wu, M. L. Tse, Z. Liu, B. O. Guan, C. Lu, and H. Y. Tam, “In-line microfluidic refractometer based on C-shaped fiber assisted photonic crystal fiber Sagnac interferometer,” Opt. Lett. 38(17), 3283–3286 (2013). [CrossRef] [PubMed]
34. C. Wu, Z. Liu, A. P. Zhang, B. O. Guan, and H. Y. Tam, “In-line open-cavity Fabry-Pérot interferometer formed by C-shaped fiber fortemperature-insensitive refractive index sensing,” Opt. Express 22(18), 21757–21766 (2014). [CrossRef] [PubMed]
