Abstract

In this letter, a highly sensitive bending sensor based on an embedded multimode D-shaped long period fiber grating (EMD-LPFG) is proposed. The novel sensor is applied to carry out vector bending measurement. The proposed LPFG is fabricated by polishing on the prepared structure which is formed by periodically splicing between single mode fiber (SMF) and multimode fiber (MMF). Since the cross section of the embedded MMF is D-shaped, we named it EMD-LPFG. Due to the asymmetric modulation of the refractive index on the fiber by the CO2 laser, the sensor has the ability to distinguish the bending directions, and the MMFs provide higher bending response. The experimental transmission spectrum can match the simulation results well. The experimental results show that the average bending sensitivities in three orthogonal directions are 70.21 nm/m−1 (0°), 9.75 nm/m−1 (90°), −12.04 nm/m−1 (180°) and 9.98 nm/m−1 (270°), respectively. Meanwhile, the temperature sensitivity is 30 pm/°C in the range of 25 °C to 75 °C. According to the ultra-compact structure with the total length of 2.5 mm, high bending sensitivity and ability to distinguish the bending direction, the novel sensor has potential in bending measurement.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Bending measurement plays a significant role in composite structures, such as mechanical engineering and structural health monitoring [13]. In recent years, due to the unique advantages including high sensitivity and corrosion resistance, various fiber structures used to configure sensors have been proposed to measure bending like Mach-Zehnder interferometer (MZI) based on photonic crystal fiber (PCF) [4], triple cladding quartz specialty fiber (TCQSF) structure [5], single mode fiber-multimode fiber-single mode fiber-long period grating (SMS-LPG) [6,7], multimode fiber-seven-core fiber-multimode fiber (MMF-SCF-MMF) structure [8] and single mode fiber-two-core fiber-single mode fiber (SMF-TCF-SMF) structure [9]. However, measuring curvature merely is not sufficient for actual applications, especially in some fields like robotic arms and human health monitoring [10,11], it is critical for the sensor to identify the bending direction.

Typically, the vector bending is achieved by two distinct methods. One method is implemented by fibers with special structures, such as homogeneous seven-core fiber [12,13], dual-tapered PCF [14], D-shaped fiber [15,16] and hollow eccentric fiber (HEF) [17]. The other method is to utilize the CO2 laser or UV laser [18] which could asymmetrically modulate the refractive index of fiber cladding and core. In 2005, Y. P. Wang and Y. J. Rao proposed a bending sensor consists of three long period fiber gratings (LPFGs). One LPFG prepared by UV-laser was used to measure curvature, and the other two LPFGs were prepared by CO2 lasers and were in charge of determining the bend-directions [19]. In 2012, P. C. Geng and W. G. Zhang reported the spatial cascaded orthogonal long period fiber gratings (SCO-LPFGs) fabricated by CO2 laser and established a three-dimensional orthogonal sensing coordinate system to measure curvature and distinguish bending directions [20]. In 2018, Y. X. Zhang proposed a V-shaped LPFG induced by CO2 laser, and the bending directions can be discriminated according to asymmetrical structure [21]. However, in the general case, compared with some fiber sensors for curvature measurement, the sensitivity of fiber sensors for vector bending measurement is inadequate to meet the accuracy required for engineering surveys.

In this article, a vector bending sensor with high sensitivity is proposed. The proposed sensor is configured by embedded multimode D-shaped long period fiber grating (EMD-LPFG). The fabrication process includes two steps. First, we splice 5 periods of SMF and MMF, and then the sample is polished for re-modulation by CO2 laser until stable resonant dip appears. The spectrum evolution during whole fabrication process is monitored and the final spectrum corresponds to simulation results. This sensor is proven to discriminate bending direction according to the asymmetric distribution of refractive index. Bending characteristic is experimentally measured in 4 directions, and the results show that the average bending sensitivities of proposed sensor reach 70.21 nm/m−1 (0°), 9.75 nm/m−1 (90°), −12.04 nm/m−1 (180°) and 9.98 nm/m−1 (270°) within the curvature measurement of 0∼0.88 m−1. In addition, the temperature response of proposed sensor is measured to be 30 pm/°C in the range of 25 °C to 75 °C. Therefore, depending on the high sensitivity and vector bending ability, the proposed sensor could be applied in the field of bending sensing.

2. Device fabrication

The entire experiment of the proposed EMD-LPFG consists of two steps: fabricating the combined fiber structure and polishing on the whole combined fiber structure for re-modulation.

Figure 1 shows the experimental equipment and process of splicing multiple SMFs and MMFs. Due to the precision required for fiber splicing, the fiber cutting system contains three precision 3D adjustment brackets, a fiber cleaver, and a set of microscopic imaging system. The fiber cleaver (Sumitomo Electric Industrial Co., Ltd. FC-6S) which fixed to the bracket is used to cut the fiber, and two adjustment brackets are used to fix the fiber. The microscopic imaging system is used to ensure the accuracy of the distance of each splicing point.

 figure: Fig. 1.

Fig. 1. Schematic diagram of the process for splicing SMFs and MMFs.

Download Full Size | PPT Slide | PDF

The entire fabrication process is divided into the following steps: in the first step, the SMF is placed on two holders to keep it taut. In the second step, a section of the SMF is cleaved and placed in the fusion splicer (Fujitsu, FSM-60S). The MMF which is prepared in advance is placed on the other side of fusion splicer and then splice the SMF and MMF. In the third step, the MMF is cut by fiber cleaver and the remaining length of the MMF is ensured to be 200 µm. The whole procedure is under the microscope to assure experiment accuracy. In the fourth step, another section of SMF is spliced on the aforementioned MMF and the SMF is cleaved for 300 µm, which is similar to the second step and third step. Repeat the above steps until the designed structure (the number of the MMF is 5) is prepared completely. After the production is finished, the accuracy of the experiment is checked by the high-precision optical microscope (Nikon, LV100 N). The transmission spectrum of the sample is measured and the result is shown in line named “original” of Fig. 4.

After the sample is obtained, the sample is placed on two three-dimensional displacement stages for re-modulation. The experimental system is shown in Fig. 2. The sample is fixed by the clamps, then the input end is connected to a super-continuum light source (SLS, 800–1750 nm), and the output end is connected to the optical spectrum analyzer (OSA, ANDO) to observe the spectrum changes. The CO2 laser (P-FB-30W) is used to re-modulate on the original sample. It is possible to carry out polishing by adjusting the program on the computer and the output power of the CO2 laser is fixed at 5%. During the whole fabrication process, a monitor system composed of a CCD and a screen is used to observe the depth of the polished area.

 figure: Fig. 2.

Fig. 2. Schematic diagram of the experimental setup for re-modulation.

Download Full Size | PPT Slide | PDF

The partial diagram of the EMD-LPFG is shown in Fig. 3, a plane which is parallel to the axis direction of the optical fiber is polished on the sample. The length of the plane is 2.5 mm and the depth is 15 µm.

 figure: Fig. 3.

Fig. 3. Structure diagram of the EMD-LPFG.

Download Full Size | PPT Slide | PDF

 figure: Fig. 4.

Fig. 4. The evolution of transmission spectrum during re-modulation.

Download Full Size | PPT Slide | PDF

The evolution of the transmission spectrum with re-modulation depth increasing is illustrated in Fig. 4. As the re-modulation frequency increased, the modulation depth gradually expands and the resonant dip appears near 1590 nm. When the re-modulation times reaches about 12, the resonant dip intensity is 15 dB and tends to be stable.

3. Principle and simulation

When the light transmits from the SMF to MMF, due to the large core diameter mismatch, the refractive index changes caused by material properties and the CO2 laser re-modulation, the partially fundamental mode (LP01) power couples into cladding mode. Thus, the mode coupling occurs between core mode and cladding mode.

In order to select the optimal re-modulation depth, the transmission spectrum and transmission light field distribution are simulated by the three-dimensional finite difference beam propagating method (3D-FD-BPM). In the simulation, the length of the SMF and MMF are 200 µm and 300 µm, the number of the MMF is 5, which is consistent with the parameters in the experiment. The core/cladding diameters of the SMF and MMF are 8/125 µm and 60/125 µm, the core/cladding refractive index of SMF and MMF are 1.4521/1.4468 and 1.4550/1.4500. In order to improve the accuracy of simulation calculation, the grid size and slice size for X, Y, Z (transmission direction) are 0.01 µm, 0.01 µm, 0.1 µm.

The schematic diagram of the light propagation within the EMD-LPFG can be illustrated in Fig. 5(a). The energy in the core is gradually coupled to the cladding with the spread of light. Due to the one-side polishing by CO2 laser, the optical field intensity distribution for XZ section is asymmetric, which determines the ability to achieve vector measurements of bending.

 figure: Fig. 5.

Fig. 5. (a) Simulated transmission light field distribution of the EMD-LPFG. (b) Simulated transmission spectrum of different re-modulation depths.

Download Full Size | PPT Slide | PDF

In addition, Fig. 5(b) shows the simulated transmission spectrum of re-modulation process. As the re-modulation depth increases, the resonant dip gradually appears. When the re-modulation depth reaches about 15 µm, amplitude of dip reaches its maximum. The resonant dip would appear as the phase condition matches, the phase matching condition of EMD-LPFG can be expressed as:

$${\lambda _{{\textrm{res}}}} = (n_{eff}^{co} - n_{eff}^{cl,m})\Lambda = \Delta n \cdot \Lambda .$$
where ${\lambda _{\textrm{res}}}$ is the resonant wavelength, $n_{eff}^{co}$ is the effective refractive index of the fiber core, and $n_{eff}^{cl,m}$ is the effective refractive index of m-th cladding mode of the fiber, Λ is the period of the grating.

In order to illustrate the principle of ability to achieve vector bending measurement, which is caused by CO2 laser, a schematic diagram is shown in Fig. 6. When the exposure side faces up, the direction is marked as 0° [22], the other three directions are defined as 90°, 180°, 270°. When the CO2 laser irradiates on the fiber, the refractive index distribution on the cross section of fiber exhibits asymmetric. According to Fig. 6(a), the refractive index modulation on the direction of 0° is the largest, the direction of 180° is the most unobvious, and the two orthogonal directions of 90° and 270° are moderate and equivalent theoretically. Therefore, the bending properties of 0°, 90°, 180° and 270° directions are measured experimentally.

 figure: Fig. 6.

Fig. 6. Schematic diagram of vector bending principle. (a) The modulation of refractive index with the influence of CO2 laser. (b) The schematic diagram of refractive index changes in different directions.

Download Full Size | PPT Slide | PDF

When the bending is applied to the sensor, because of the tiny curvature (0.88 m−1), the period variation can be ignored compared to the refractive index variation. Therefore, according to Eq. (1), the direction and degree of the resonant wavelength shifts are only related to the effective refractive index variation. The refractive index distribution of 0°, 90° and 180° directions caused by elasto-optical effect will increase or decrease, which is mainly determined by the fiber mode LP0m (m=8). As shown in Fig. 6(b), the simultaneous effects of bending and CO2 laser can be illustrated by coordinate system computation. The re-modulation of CO2 laser changes the refractive index on 0°, 90°, 180° directions inconsistently, which is marked as Δn1, Δn2 and Δn3. Because the refractive index change of the polished surface is the largest, the value of the Δn1 is the maximum. As for the 180° direction, the CO2 laser has little refractive index modulation on this side of the fiber, the value of the Δn2 is considered as 0 consequently. Therefore, on the coordinate axis, the intercept of the three line segments (blue-0°, green-90°, red-180°) are compared as: Δn1>Δn2>Δn3.

On the other hand, compared with the bending direction orthogonal to the core deviation direction, when the direction of applied bending is parallel to the core deviation direction, the core receives a stronger force, showing a more sensitive bending response. Therefore, when bending force is applied to the EMD-LPFG, the total refractive index change is shown as: Δn1′>Δn2′>0, Δn3′<0. As a result, the bending sensitivity of the 0° direction is maximum, the resonant wavelengths present the red and blue shift in 0°/90° and 180° directions, which is consistent with experimental results.

4. Experiment and discussion

Figure 7(a) shows the measurement process for bending characteristic. The EMD-LPFG is placed on the stable optical table, then the two ends of the grating are fixed by the clamp and rotator B. The two rotators are used to limit the position of the fiber and rotate the grating to measure bending in different directions. A weight is used to offset the stress generated during bending measurement. A metal sheet is placed on two positioning stages between grating and micrometer. The bending force is applied by adjusting micrometer. As illustrated in Fig. 7(b), the curvature C of the EMD-LPFG can be defined as:

$$C = \frac{1}{R} = \frac{{2d}}{{{d^2} + {L^2}}}.$$
where R is the bending curvature radius, d is the bending displacement, and L is half of the distance between the two stages. L is 120 mm in the experimental measurement.

 figure: Fig. 7.

Fig. 7. (a) Schematic diagram of bending measuring device. (b) Schematic diagram of curvature calculation.

Download Full Size | PPT Slide | PDF

The result of bending measurement is shown in Fig. 8. The initial resonant wavelength of the bending measurement experiment is chosen to be around 1583 nm. In the directions of 0° and 90°, the resonant wavelength exhibits clear red-shift as curvature increased and the resonant wavelength appears blue-shift with the increase of curvature in the 180° direction measurement. During the measurement process, the curvature changes 0.11 m−1 each time in the range of 0∼0.88 m−1. Since the measurement range of linear fitting is insufficient (0∼0.44 m−1), the quadratic polynomial fitting is used to describe the bending sensitivities. Figure 9 shows a standard deviation plot and fitting curve of the resonant wavelength shift against curvature. The average bending sensitivity of the 0° direction is calculated to be 70.21 nm/m−1. Similarly, the average bending sensitivities of the 90° direction, 180° direction and the 270° direction are 9.75 nm/m−1, −12.04 nm/m−1 and 9.98 nm/m−1, respectively.

 figure: Fig. 8.

Fig. 8. Bending characteristic of the EMD-LPFG. (a) Resonant dip shift of the 0° direction. (b) Resonant dip shift of the 90° direction. (c) Resonant dip shift of the 180° direction. (d) Resonant dip shift of the 270° direction.

Download Full Size | PPT Slide | PDF

 figure: Fig. 9.

Fig. 9. The fitting curve between the curvature and wavelengths for four directions.

Download Full Size | PPT Slide | PDF

Due to the influence of external environment temperature on measurement, the temperature characteristic is measured at the same time. The range of temperature measurement is from 35°C to 75°C for every 10°C, which is controlled by the thermostatic furnace (measurement accuracy: 0.1°C). Figure 10(a) shows the evolution of transmission spectra as temperature increased. As illustrated in Fig. 10(b), the results of the linear fit shows that the temperature sensitivity of the EMD-LPFG is 30 pm/°C, and the maximum temperature-curvature crosstalk is calculated as 0.003 m−1/°C. When EMD-LPFG is used as a curvature sensor, the bending measurement results are more accurate because of the low temperature crosstalk.

 figure: Fig. 10.

Fig. 10. Temperature characteristic of the EMD-LPFG. (a) Resonant dip shift under different temperatures. (b) The linear fit between the temperature and wavelength shifts.

Download Full Size | PPT Slide | PDF

To evaluate the bending performance of the EMD-LPFG, the comparison with recent bending sensors are listed in Table 1. It is clear from the Table 1 that the bending sensitivity of proposed structure is much higher than other bending sensors. Although the SMF-TCF-SMF [9] shows a higher sensitivity, the measurement range of curvature is only 0 to 0.27 m−1, and the sensor needs to splice a 5 cm long section of TCF between two SMF sections, which increase the length of the sensor greatly.

Tables Icon

Table 1. The performance comparison between our sensor and related sensors

5. Conclusion

In this article, we propose a vector bending sensor with high sensitivity. The proposed sensor is configured by EMD-LPFG, which is fabricated by splicing SMFs and MMFs alternately and the sample obtained is polished on one side by CO2 laser. According to the strong refractive index modulation of MMF, the sensor exhibits high bending sensitivity with a compact structure. Meanwhile, the CO2 laser re-modulation provides the ability to measure vector bending. In three orthogonal directions, the average bending sensitivities of the proposed sensor reach 70.21 nm/m−1 (0°), 9.75 nm/m−1 (90°), −12.04 nm/m−1 (180°) and 9.98 nm/m−1 (270°). Furthermore, the temperature sensitivity of 30 pm/°C is demonstrated. As a vector bending sensor with high sensitivities, the EMD-LPFG can be applied to multiple mechanical structures.

Funding

Natural Science Foundation of Heilongjiang Province (ZD2019H003); The Joint Research Fund in Astronomy under cooperative agreement between the National Natural Science Foundation of China (NSFC) and Chinese Academy of Sciences (CAS) (U1831115, U1931206, U2031130, U2031132).

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 may be obtained from the authors upon reasonable request.

References

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. Q. Wang and Y. Liu, “Review of optical fiber bending/curvature sensor,” Measurement 130, 161–176 (2018). [CrossRef]  

3. C. Majidi, R. Kramer, and R. J. Wood, “A non-differential elastomer curvature sensor for softer-than-skin electronics,” Smart Mater. Struct. 20(10), 105017 (2011). [CrossRef]  

4. M. Deng, C. P. Tang, T. Zhu, and Y. J. Rao, “Highly sensitive bend sensor base d on Mach-Zehnder interferometer using photonic crystal fiber,” Opt. Commun. 284(12), 2849–2853 (2011). [CrossRef]  

5. X. H. Fu, J. Wen, Y. P. Zhang, D. Wang, F. Liu, H. Y. Xie, G. W. Fu, and W. H. Bi, “Experimental and theoretical analysis of curvature sensor based on cladding mode resonance with triple cladding quartz specialty fiber,” Opt. Commun. 429, 5–11 (2018). [CrossRef]  

6. Q. H. Hu, S. Zhang, W. L. Yang, T. Geng, W. M. Sun, C. T. Sun, X. R. Jin, and L. B. Yuan, “Highly sensitive curvature sensor based on long period fiber grating with alternately splicing multiple single/multimode structure,” Opt. Fiber Technol. 37, 69–73 (2017). [CrossRef]  

7. S. Zhang, S. F. Deng, Z. M. Wang, C. T. Sun, X. D. Chen, Y. W. Ma, L. Zhao, C. L. Lu, T. Geng, W. L. Yang, and L. B. Yuan, “A miniature SMS-LPG bending sensor with high sensitivity based on multimode fiber embedded-LPG,” Sens. Actuators, A 295, 31–36 (2019). [CrossRef]  

8. Q. Wang and Y. Liu, “Optical fiber curvature sensor based on MMF-SCF-MMF structure,” Opt. Fiber Technol. 43, 1–5 (2018). [CrossRef]  

9. J. R. Guzman-Sepulveda and D. A. May-Arrioja, “In-fiber directional coupler for high-sensitivity curvature measurement,” Opt. Express 21(10), 11853–11861 (2013). [CrossRef]  

10. L. Jin, W. Jin, and J. Ju, “Directional bend sensing with a CO2-laser-inscribed long period grating in a photonic crystal fiber,” J. Lightwave Technol. 27(21), 4884–4891 (2009). [CrossRef]  

11. Y. P. Li, W. G. Zhang, S. Wang, L. Chen, Y. X. Zhang, B. Wang, T. Y. Yan, X. Y. Li, and W. Hu, “Bending vector sensor based on a pair of opposite tilted long-period fiber gratings,” IEEE Photonics Technol. Lett. 29(2), 224–227 (2017). [CrossRef]  

12. M. X. Hou, K. M. Yang, J. He, X. Z. Xu, S. Ju, K. K. Guo, and Y. P. Wang, “Two-dimensional vector bending sensor based on seven-core fiber Bragg gratings,” Opt. Express 26(18), 23770–23781 (2018). [CrossRef]  

13. D. Budnicki, I. Parola, L. Szostkiewicz, K. Markiewicz, Z. Holdynski, G. Wojcik, M. Makara, K. Poturaj, M. Kuklinska, P. Mergo, M. Napierala, and T. Nasilowski, “All-fiber vector bending sensor based on a multicore fiber with asymmetric air-hole structure,” J. Lightwave Technol. 38(23), 6685–6690 (2020). [CrossRef]  

14. Z. J. Tang, S. Q. Lou, X. Wang, W. Zhang, S. B. Yan, and Z. Xing, “High-performance bending vector and strain sensor using a dual-tapered photonic crystal fiber Mach-Zehnder interferometer,” IEEE Sens. J. 19(11), 4062–4068 (2019). [CrossRef]  

15. T. Allsop, A. Gillooly, V. Mezentsev, T. Earthgrowl-Gould, R. Neal, D. J. Webb, and I. Bennion, “Bending and orientational characteristics of long period gratings written in D-shaped optical Fiber,” IEEE Trans. Instrum. Meas. 53(1), 130–135 (2004). [CrossRef]  

16. D. H. Zhao, X. F. Chen, K. M. Zhou, L. Zhang, I. Bennion, W. N. MacPherson, J. S. Barton, and J. D. C. Jones, “Bend sensors with direction recognition based on long-period gratings written in D-shaped fiber,” Appl. Opt. 43(29), 5425–5428 (2004). [CrossRef]  

17. G. P. Mao, T. T. Yuan, C. Y. Guan, J. Yang, L. Chen, Z. Zhu, J. H. Shi, and L. B. Yuan, “Fiber Bragg grating sensors in hollow single- and two-core eccentric fibers,” Opt. Express 25(1), 144–150 (2017). [CrossRef]  

18. Y. H. Zhao, C. L. Wang, G. L. Yin, B. Q. Jiang, K. M. Zhou, C. B. Mou, Y. Q. Liu, L. Zhang, and T. Y. Wang, “Simultaneous directional curvature and temperature sensor based on a tilted few-mode fiber Bragg grating,” Appl. Opt. 57(7), 1671–1678 (2018). [CrossRef]  

19. Y. P. Wang and Y. J. Rao, “A novel long period fiber grating sensor measuring curvature and determining bend-direction simultaneously,” IEEE Sens. J. 5(5), 839–843 (2005). [CrossRef]  

20. P. C. Geng, W. G. Zhang, S. C. Gao, H. Zhang, J. L. Li, S. S. Zhang, Z. Y. 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]  

21. Y. X. Zhang, W. G. Zhang, T. Y. Yan, L. J. Bie, Y. S. Zhang, S. Wang, L. X. Kong, X. X. Kang, L. Yu, and P. C. Geng, “V-shaped long-period fiber grating high-sensitive bending vector sensor,” IEEE Photonics Technol. Lett. 30(17), 1531–1534 (2018). [CrossRef]  

22. L. Huang, X. Y. Meng, Y. H. Zhao, and Y. Q. Liu, “Temperature-insensitive directional bending sensors based on the interlaced tilted long-period gratings,” Opt. Commun. 447, 18–23 (2019). [CrossRef]  

References

  • View by:

  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. Q. Wang and Y. Liu, “Review of optical fiber bending/curvature sensor,” Measurement 130, 161–176 (2018).
    [Crossref]
  3. C. Majidi, R. Kramer, and R. J. Wood, “A non-differential elastomer curvature sensor for softer-than-skin electronics,” Smart Mater. Struct. 20(10), 105017 (2011).
    [Crossref]
  4. M. Deng, C. P. Tang, T. Zhu, and Y. J. Rao, “Highly sensitive bend sensor base d on Mach-Zehnder interferometer using photonic crystal fiber,” Opt. Commun. 284(12), 2849–2853 (2011).
    [Crossref]
  5. X. H. Fu, J. Wen, Y. P. Zhang, D. Wang, F. Liu, H. Y. Xie, G. W. Fu, and W. H. Bi, “Experimental and theoretical analysis of curvature sensor based on cladding mode resonance with triple cladding quartz specialty fiber,” Opt. Commun. 429, 5–11 (2018).
    [Crossref]
  6. Q. H. Hu, S. Zhang, W. L. Yang, T. Geng, W. M. Sun, C. T. Sun, X. R. Jin, and L. B. Yuan, “Highly sensitive curvature sensor based on long period fiber grating with alternately splicing multiple single/multimode structure,” Opt. Fiber Technol. 37, 69–73 (2017).
    [Crossref]
  7. S. Zhang, S. F. Deng, Z. M. Wang, C. T. Sun, X. D. Chen, Y. W. Ma, L. Zhao, C. L. Lu, T. Geng, W. L. Yang, and L. B. Yuan, “A miniature SMS-LPG bending sensor with high sensitivity based on multimode fiber embedded-LPG,” Sens. Actuators, A 295, 31–36 (2019).
    [Crossref]
  8. Q. Wang and Y. Liu, “Optical fiber curvature sensor based on MMF-SCF-MMF structure,” Opt. Fiber Technol. 43, 1–5 (2018).
    [Crossref]
  9. J. R. Guzman-Sepulveda and D. A. May-Arrioja, “In-fiber directional coupler for high-sensitivity curvature measurement,” Opt. Express 21(10), 11853–11861 (2013).
    [Crossref]
  10. L. Jin, W. Jin, and J. Ju, “Directional bend sensing with a CO2-laser-inscribed long period grating in a photonic crystal fiber,” J. Lightwave Technol. 27(21), 4884–4891 (2009).
    [Crossref]
  11. Y. P. Li, W. G. Zhang, S. Wang, L. Chen, Y. X. Zhang, B. Wang, T. Y. Yan, X. Y. Li, and W. Hu, “Bending vector sensor based on a pair of opposite tilted long-period fiber gratings,” IEEE Photonics Technol. Lett. 29(2), 224–227 (2017).
    [Crossref]
  12. M. X. Hou, K. M. Yang, J. He, X. Z. Xu, S. Ju, K. K. Guo, and Y. P. Wang, “Two-dimensional vector bending sensor based on seven-core fiber Bragg gratings,” Opt. Express 26(18), 23770–23781 (2018).
    [Crossref]
  13. D. Budnicki, I. Parola, L. Szostkiewicz, K. Markiewicz, Z. Holdynski, G. Wojcik, M. Makara, K. Poturaj, M. Kuklinska, P. Mergo, M. Napierala, and T. Nasilowski, “All-fiber vector bending sensor based on a multicore fiber with asymmetric air-hole structure,” J. Lightwave Technol. 38(23), 6685–6690 (2020).
    [Crossref]
  14. Z. J. Tang, S. Q. Lou, X. Wang, W. Zhang, S. B. Yan, and Z. Xing, “High-performance bending vector and strain sensor using a dual-tapered photonic crystal fiber Mach-Zehnder interferometer,” IEEE Sens. J. 19(11), 4062–4068 (2019).
    [Crossref]
  15. T. Allsop, A. Gillooly, V. Mezentsev, T. Earthgrowl-Gould, R. Neal, D. J. Webb, and I. Bennion, “Bending and orientational characteristics of long period gratings written in D-shaped optical Fiber,” IEEE Trans. Instrum. Meas. 53(1), 130–135 (2004).
    [Crossref]
  16. D. H. Zhao, X. F. Chen, K. M. Zhou, L. Zhang, I. Bennion, W. N. MacPherson, J. S. Barton, and J. D. C. Jones, “Bend sensors with direction recognition based on long-period gratings written in D-shaped fiber,” Appl. Opt. 43(29), 5425–5428 (2004).
    [Crossref]
  17. G. P. Mao, T. T. Yuan, C. Y. Guan, J. Yang, L. Chen, Z. Zhu, J. H. Shi, and L. B. Yuan, “Fiber Bragg grating sensors in hollow single- and two-core eccentric fibers,” Opt. Express 25(1), 144–150 (2017).
    [Crossref]
  18. Y. H. Zhao, C. L. Wang, G. L. Yin, B. Q. Jiang, K. M. Zhou, C. B. Mou, Y. Q. Liu, L. Zhang, and T. Y. Wang, “Simultaneous directional curvature and temperature sensor based on a tilted few-mode fiber Bragg grating,” Appl. Opt. 57(7), 1671–1678 (2018).
    [Crossref]
  19. Y. P. Wang and Y. J. Rao, “A novel long period fiber grating sensor measuring curvature and determining bend-direction simultaneously,” IEEE Sens. J. 5(5), 839–843 (2005).
    [Crossref]
  20. P. C. Geng, W. G. Zhang, S. C. Gao, H. Zhang, J. L. Li, S. S. Zhang, Z. Y. 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]
  21. Y. X. Zhang, W. G. Zhang, T. Y. Yan, L. J. Bie, Y. S. Zhang, S. Wang, L. X. Kong, X. X. Kang, L. Yu, and P. C. Geng, “V-shaped long-period fiber grating high-sensitive bending vector sensor,” IEEE Photonics Technol. Lett. 30(17), 1531–1534 (2018).
    [Crossref]
  22. L. Huang, X. Y. Meng, Y. H. Zhao, and Y. Q. Liu, “Temperature-insensitive directional bending sensors based on the interlaced tilted long-period gratings,” Opt. Commun. 447, 18–23 (2019).
    [Crossref]

2020 (1)

2019 (3)

Z. J. Tang, S. Q. Lou, X. Wang, W. Zhang, S. B. Yan, and Z. Xing, “High-performance bending vector and strain sensor using a dual-tapered photonic crystal fiber Mach-Zehnder interferometer,” IEEE Sens. J. 19(11), 4062–4068 (2019).
[Crossref]

S. Zhang, S. F. Deng, Z. M. Wang, C. T. Sun, X. D. Chen, Y. W. Ma, L. Zhao, C. L. Lu, T. Geng, W. L. Yang, and L. B. Yuan, “A miniature SMS-LPG bending sensor with high sensitivity based on multimode fiber embedded-LPG,” Sens. Actuators, A 295, 31–36 (2019).
[Crossref]

L. Huang, X. Y. Meng, Y. H. Zhao, and Y. Q. Liu, “Temperature-insensitive directional bending sensors based on the interlaced tilted long-period gratings,” Opt. Commun. 447, 18–23 (2019).
[Crossref]

2018 (6)

Y. H. Zhao, C. L. Wang, G. L. Yin, B. Q. Jiang, K. M. Zhou, C. B. Mou, Y. Q. Liu, L. Zhang, and T. Y. Wang, “Simultaneous directional curvature and temperature sensor based on a tilted few-mode fiber Bragg grating,” Appl. Opt. 57(7), 1671–1678 (2018).
[Crossref]

Y. X. Zhang, W. G. Zhang, T. Y. Yan, L. J. Bie, Y. S. Zhang, S. Wang, L. X. Kong, X. X. Kang, L. Yu, and P. C. Geng, “V-shaped long-period fiber grating high-sensitive bending vector sensor,” IEEE Photonics Technol. Lett. 30(17), 1531–1534 (2018).
[Crossref]

Q. Wang and Y. Liu, “Optical fiber curvature sensor based on MMF-SCF-MMF structure,” Opt. Fiber Technol. 43, 1–5 (2018).
[Crossref]

Q. Wang and Y. Liu, “Review of optical fiber bending/curvature sensor,” Measurement 130, 161–176 (2018).
[Crossref]

X. H. Fu, J. Wen, Y. P. Zhang, D. Wang, F. Liu, H. Y. Xie, G. W. Fu, and W. H. Bi, “Experimental and theoretical analysis of curvature sensor based on cladding mode resonance with triple cladding quartz specialty fiber,” Opt. Commun. 429, 5–11 (2018).
[Crossref]

M. X. Hou, K. M. Yang, J. He, X. Z. Xu, S. Ju, K. K. Guo, and Y. P. Wang, “Two-dimensional vector bending sensor based on seven-core fiber Bragg gratings,” Opt. Express 26(18), 23770–23781 (2018).
[Crossref]

2017 (3)

G. P. Mao, T. T. Yuan, C. Y. Guan, J. Yang, L. Chen, Z. Zhu, J. H. Shi, and L. B. Yuan, “Fiber Bragg grating sensors in hollow single- and two-core eccentric fibers,” Opt. Express 25(1), 144–150 (2017).
[Crossref]

Y. P. Li, W. G. Zhang, S. Wang, L. Chen, Y. X. Zhang, B. Wang, T. Y. Yan, X. Y. Li, and W. Hu, “Bending vector sensor based on a pair of opposite tilted long-period fiber gratings,” IEEE Photonics Technol. Lett. 29(2), 224–227 (2017).
[Crossref]

Q. H. Hu, S. Zhang, W. L. Yang, T. Geng, W. M. Sun, C. T. Sun, X. R. Jin, and L. B. Yuan, “Highly sensitive curvature sensor based on long period fiber grating with alternately splicing multiple single/multimode structure,” Opt. Fiber Technol. 37, 69–73 (2017).
[Crossref]

2015 (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]

2013 (1)

2012 (1)

2011 (2)

C. Majidi, R. Kramer, and R. J. Wood, “A non-differential elastomer curvature sensor for softer-than-skin electronics,” Smart Mater. Struct. 20(10), 105017 (2011).
[Crossref]

M. Deng, C. P. Tang, T. Zhu, and Y. J. Rao, “Highly sensitive bend sensor base d on Mach-Zehnder interferometer using photonic crystal fiber,” Opt. Commun. 284(12), 2849–2853 (2011).
[Crossref]

2009 (1)

2005 (1)

Y. P. Wang and Y. J. Rao, “A novel long period fiber grating sensor measuring curvature and determining bend-direction simultaneously,” IEEE Sens. J. 5(5), 839–843 (2005).
[Crossref]

2004 (2)

T. Allsop, A. Gillooly, V. Mezentsev, T. Earthgrowl-Gould, R. Neal, D. J. Webb, and I. Bennion, “Bending and orientational characteristics of long period gratings written in D-shaped optical Fiber,” IEEE Trans. Instrum. Meas. 53(1), 130–135 (2004).
[Crossref]

D. H. Zhao, X. F. Chen, K. M. Zhou, L. Zhang, I. Bennion, W. N. MacPherson, J. S. Barton, and J. D. C. Jones, “Bend sensors with direction recognition based on long-period gratings written in D-shaped fiber,” Appl. Opt. 43(29), 5425–5428 (2004).
[Crossref]

Allsop, T.

T. Allsop, A. Gillooly, V. Mezentsev, T. Earthgrowl-Gould, R. Neal, D. J. Webb, and I. Bennion, “Bending and orientational characteristics of long period gratings written in D-shaped optical Fiber,” IEEE Trans. Instrum. Meas. 53(1), 130–135 (2004).
[Crossref]

Bai, Z. Y.

Barton, J. S.

Bennion, I.

T. Allsop, A. Gillooly, V. Mezentsev, T. Earthgrowl-Gould, R. Neal, D. J. Webb, and I. Bennion, “Bending and orientational characteristics of long period gratings written in D-shaped optical Fiber,” IEEE Trans. Instrum. Meas. 53(1), 130–135 (2004).
[Crossref]

D. H. Zhao, X. F. Chen, K. M. Zhou, L. Zhang, I. Bennion, W. N. MacPherson, J. S. Barton, and J. D. C. Jones, “Bend sensors with direction recognition based on long-period gratings written in D-shaped fiber,” Appl. Opt. 43(29), 5425–5428 (2004).
[Crossref]

Bi, W. H.

X. H. Fu, J. Wen, Y. P. Zhang, D. Wang, F. Liu, H. Y. Xie, G. W. Fu, and W. H. Bi, “Experimental and theoretical analysis of curvature sensor based on cladding mode resonance with triple cladding quartz specialty fiber,” Opt. Commun. 429, 5–11 (2018).
[Crossref]

Bie, L. J.

Y. X. Zhang, W. G. Zhang, T. Y. Yan, L. J. Bie, Y. S. Zhang, S. Wang, L. X. Kong, X. X. Kang, L. Yu, and P. C. Geng, “V-shaped long-period fiber grating high-sensitive bending vector sensor,” IEEE Photonics Technol. Lett. 30(17), 1531–1534 (2018).
[Crossref]

Budnicki, D.

Chen, L.

Y. P. Li, W. G. Zhang, S. Wang, L. Chen, Y. X. Zhang, B. Wang, T. Y. Yan, X. Y. Li, and W. Hu, “Bending vector sensor based on a pair of opposite tilted long-period fiber gratings,” IEEE Photonics Technol. Lett. 29(2), 224–227 (2017).
[Crossref]

G. P. Mao, T. T. Yuan, C. Y. Guan, J. Yang, L. Chen, Z. Zhu, J. H. Shi, and L. B. Yuan, “Fiber Bragg grating sensors in hollow single- and two-core eccentric fibers,” Opt. Express 25(1), 144–150 (2017).
[Crossref]

Chen, X. D.

S. Zhang, S. F. Deng, Z. M. Wang, C. T. Sun, X. D. Chen, Y. W. Ma, L. Zhao, C. L. Lu, T. Geng, W. L. Yang, and L. B. Yuan, “A miniature SMS-LPG bending sensor with high sensitivity based on multimode fiber embedded-LPG,” Sens. Actuators, A 295, 31–36 (2019).
[Crossref]

Chen, X. F.

Deng, M.

M. Deng, C. P. Tang, T. Zhu, and Y. J. Rao, “Highly sensitive bend sensor base d on Mach-Zehnder interferometer using photonic crystal fiber,” Opt. Commun. 284(12), 2849–2853 (2011).
[Crossref]

Deng, S. F.

S. Zhang, S. F. Deng, Z. M. Wang, C. T. Sun, X. D. Chen, Y. W. Ma, L. Zhao, C. L. Lu, T. Geng, W. L. Yang, and L. B. Yuan, “A miniature SMS-LPG bending sensor with high sensitivity based on multimode fiber embedded-LPG,” Sens. Actuators, A 295, 31–36 (2019).
[Crossref]

Earthgrowl-Gould, T.

T. Allsop, A. Gillooly, V. Mezentsev, T. Earthgrowl-Gould, R. Neal, D. J. Webb, and I. Bennion, “Bending and orientational characteristics of long period gratings written in D-shaped optical Fiber,” IEEE Trans. Instrum. Meas. 53(1), 130–135 (2004).
[Crossref]

Fu, G. W.

X. H. Fu, J. Wen, Y. P. Zhang, D. Wang, F. Liu, H. Y. Xie, G. W. Fu, and W. H. Bi, “Experimental and theoretical analysis of curvature sensor based on cladding mode resonance with triple cladding quartz specialty fiber,” Opt. Commun. 429, 5–11 (2018).
[Crossref]

Fu, X. H.

X. H. Fu, J. Wen, Y. P. Zhang, D. Wang, F. Liu, H. Y. Xie, G. W. Fu, and W. H. Bi, “Experimental and theoretical analysis of curvature sensor based on cladding mode resonance with triple cladding quartz specialty fiber,” Opt. Commun. 429, 5–11 (2018).
[Crossref]

Gao, S. C.

Geng, P. C.

Y. X. Zhang, W. G. Zhang, T. Y. Yan, L. J. Bie, Y. S. Zhang, S. Wang, L. X. Kong, X. X. Kang, L. Yu, and P. C. Geng, “V-shaped long-period fiber grating high-sensitive bending vector sensor,” IEEE Photonics Technol. Lett. 30(17), 1531–1534 (2018).
[Crossref]

P. C. Geng, W. G. Zhang, S. C. Gao, H. Zhang, J. L. Li, S. S. Zhang, Z. Y. 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]

Geng, T.

S. Zhang, S. F. Deng, Z. M. Wang, C. T. Sun, X. D. Chen, Y. W. Ma, L. Zhao, C. L. Lu, T. Geng, W. L. Yang, and L. B. Yuan, “A miniature SMS-LPG bending sensor with high sensitivity based on multimode fiber embedded-LPG,” Sens. Actuators, A 295, 31–36 (2019).
[Crossref]

Q. H. Hu, S. Zhang, W. L. Yang, T. Geng, W. M. Sun, C. T. Sun, X. R. Jin, and L. B. Yuan, “Highly sensitive curvature sensor based on long period fiber grating with alternately splicing multiple single/multimode structure,” Opt. Fiber Technol. 37, 69–73 (2017).
[Crossref]

Ghandehari, M.

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]

Gillooly, A.

T. Allsop, A. Gillooly, V. Mezentsev, T. Earthgrowl-Gould, R. Neal, D. J. Webb, and I. Bennion, “Bending and orientational characteristics of long period gratings written in D-shaped optical Fiber,” IEEE Trans. Instrum. Meas. 53(1), 130–135 (2004).
[Crossref]

Guan, C. Y.

Guo, K. K.

Guzman-Sepulveda, J. R.

He, J.

Holdynski, Z.

Hou, M. X.

Hu, Q. H.

Q. H. Hu, S. Zhang, W. L. Yang, T. Geng, W. M. Sun, C. T. Sun, X. R. Jin, and L. B. Yuan, “Highly sensitive curvature sensor based on long period fiber grating with alternately splicing multiple single/multimode structure,” Opt. Fiber Technol. 37, 69–73 (2017).
[Crossref]

Hu, W.

Y. P. Li, W. G. Zhang, S. Wang, L. Chen, Y. X. Zhang, B. Wang, T. Y. Yan, X. Y. Li, and W. Hu, “Bending vector sensor based on a pair of opposite tilted long-period fiber gratings,” IEEE Photonics Technol. Lett. 29(2), 224–227 (2017).
[Crossref]

Huang, L.

L. Huang, X. Y. Meng, Y. H. Zhao, and Y. Q. Liu, “Temperature-insensitive directional bending sensors based on the interlaced tilted long-period gratings,” Opt. Commun. 447, 18–23 (2019).
[Crossref]

Jiang, B. Q.

Jin, L.

Jin, W.

Jin, X. R.

Q. H. Hu, S. Zhang, W. L. Yang, T. Geng, W. M. Sun, C. T. Sun, X. R. Jin, and L. B. Yuan, “Highly sensitive curvature sensor based on long period fiber grating with alternately splicing multiple single/multimode structure,” Opt. Fiber Technol. 37, 69–73 (2017).
[Crossref]

Jones, J. D. C.

Ju, J.

Ju, S.

Kang, X. X.

Y. X. Zhang, W. G. Zhang, T. Y. Yan, L. J. Bie, Y. S. Zhang, S. Wang, L. X. Kong, X. X. Kang, L. Yu, and P. C. Geng, “V-shaped long-period fiber grating high-sensitive bending vector sensor,” IEEE Photonics Technol. Lett. 30(17), 1531–1534 (2018).
[Crossref]

Kong, L. X.

Y. X. Zhang, W. G. Zhang, T. Y. Yan, L. J. Bie, Y. S. Zhang, S. Wang, L. X. Kong, X. X. Kang, L. Yu, and P. C. Geng, “V-shaped long-period fiber grating high-sensitive bending vector sensor,” IEEE Photonics Technol. Lett. 30(17), 1531–1534 (2018).
[Crossref]

Kramer, R.

C. Majidi, R. Kramer, and R. J. Wood, “A non-differential elastomer curvature sensor for softer-than-skin electronics,” Smart Mater. Struct. 20(10), 105017 (2011).
[Crossref]

Kuklinska, M.

Li, J. L.

Li, X. Y.

Y. P. Li, W. G. Zhang, S. Wang, L. Chen, Y. X. Zhang, B. Wang, T. Y. Yan, X. Y. Li, and W. Hu, “Bending vector sensor based on a pair of opposite tilted long-period fiber gratings,” IEEE Photonics Technol. Lett. 29(2), 224–227 (2017).
[Crossref]

Li, Y. P.

Y. P. Li, W. G. Zhang, S. Wang, L. Chen, Y. X. Zhang, B. Wang, T. Y. Yan, X. Y. Li, and W. Hu, “Bending vector sensor based on a pair of opposite tilted long-period fiber gratings,” IEEE Photonics Technol. Lett. 29(2), 224–227 (2017).
[Crossref]

Liu, F.

X. H. Fu, J. Wen, Y. P. Zhang, D. Wang, F. Liu, H. Y. Xie, G. W. Fu, and W. H. Bi, “Experimental and theoretical analysis of curvature sensor based on cladding mode resonance with triple cladding quartz specialty fiber,” Opt. Commun. 429, 5–11 (2018).
[Crossref]

Liu, Y.

Q. Wang and Y. Liu, “Review of optical fiber bending/curvature sensor,” Measurement 130, 161–176 (2018).
[Crossref]

Q. Wang and Y. Liu, “Optical fiber curvature sensor based on MMF-SCF-MMF structure,” Opt. Fiber Technol. 43, 1–5 (2018).
[Crossref]

Liu, Y. Q.

L. Huang, X. Y. Meng, Y. H. Zhao, and Y. Q. Liu, “Temperature-insensitive directional bending sensors based on the interlaced tilted long-period gratings,” Opt. Commun. 447, 18–23 (2019).
[Crossref]

Y. H. Zhao, C. L. Wang, G. L. Yin, B. Q. Jiang, K. M. Zhou, C. B. Mou, Y. Q. Liu, L. Zhang, and T. Y. Wang, “Simultaneous directional curvature and temperature sensor based on a tilted few-mode fiber Bragg grating,” Appl. Opt. 57(7), 1671–1678 (2018).
[Crossref]

Lou, S. Q.

Z. J. Tang, S. Q. Lou, X. Wang, W. Zhang, S. B. Yan, and Z. Xing, “High-performance bending vector and strain sensor using a dual-tapered photonic crystal fiber Mach-Zehnder interferometer,” IEEE Sens. J. 19(11), 4062–4068 (2019).
[Crossref]

Lu, C. L.

S. Zhang, S. F. Deng, Z. M. Wang, C. T. Sun, X. D. Chen, Y. W. Ma, L. Zhao, C. L. Lu, T. Geng, W. L. Yang, and L. B. Yuan, “A miniature SMS-LPG bending sensor with high sensitivity based on multimode fiber embedded-LPG,” Sens. Actuators, A 295, 31–36 (2019).
[Crossref]

Ma, Y. W.

S. Zhang, S. F. Deng, Z. M. Wang, C. T. Sun, X. D. Chen, Y. W. Ma, L. Zhao, C. L. Lu, T. Geng, W. L. Yang, and L. B. Yuan, “A miniature SMS-LPG bending sensor with high sensitivity based on multimode fiber embedded-LPG,” Sens. Actuators, A 295, 31–36 (2019).
[Crossref]

MacPherson, W. N.

Majidi, C.

C. Majidi, R. Kramer, and R. J. Wood, “A non-differential elastomer curvature sensor for softer-than-skin electronics,” Smart Mater. Struct. 20(10), 105017 (2011).
[Crossref]

Makara, M.

Mao, G. P.

Markiewicz, K.

May-Arrioja, D. A.

Meng, X. Y.

L. Huang, X. Y. Meng, Y. H. Zhao, and Y. Q. Liu, “Temperature-insensitive directional bending sensors based on the interlaced tilted long-period gratings,” Opt. Commun. 447, 18–23 (2019).
[Crossref]

Mergo, P.

Mezentsev, V.

T. Allsop, A. Gillooly, V. Mezentsev, T. Earthgrowl-Gould, R. Neal, D. J. Webb, and I. Bennion, “Bending and orientational characteristics of long period gratings written in D-shaped optical Fiber,” IEEE Trans. Instrum. Meas. 53(1), 130–135 (2004).
[Crossref]

Mou, C. B.

Napierala, M.

Nasilowski, T.

Neal, R.

T. Allsop, A. Gillooly, V. Mezentsev, T. Earthgrowl-Gould, R. Neal, D. J. Webb, and I. Bennion, “Bending and orientational characteristics of long period gratings written in D-shaped optical Fiber,” IEEE Trans. Instrum. Meas. 53(1), 130–135 (2004).
[Crossref]

Ou, J. P.

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]

Parola, I.

Poturaj, K.

Rao, Y. J.

M. Deng, C. P. Tang, T. Zhu, and Y. J. Rao, “Highly sensitive bend sensor base d on Mach-Zehnder interferometer using photonic crystal fiber,” Opt. Commun. 284(12), 2849–2853 (2011).
[Crossref]

Y. P. Wang and Y. J. Rao, “A novel long period fiber grating sensor measuring curvature and determining bend-direction simultaneously,” IEEE Sens. J. 5(5), 839–843 (2005).
[Crossref]

Shan, B. H.

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]

Shi, J. H.

Sun, C. T.

S. Zhang, S. F. Deng, Z. M. Wang, C. T. Sun, X. D. Chen, Y. W. Ma, L. Zhao, C. L. Lu, T. Geng, W. L. Yang, and L. B. Yuan, “A miniature SMS-LPG bending sensor with high sensitivity based on multimode fiber embedded-LPG,” Sens. Actuators, A 295, 31–36 (2019).
[Crossref]

Q. H. Hu, S. Zhang, W. L. Yang, T. Geng, W. M. Sun, C. T. Sun, X. R. Jin, and L. B. Yuan, “Highly sensitive curvature sensor based on long period fiber grating with alternately splicing multiple single/multimode structure,” Opt. Fiber Technol. 37, 69–73 (2017).
[Crossref]

Sun, W. M.

Q. H. Hu, S. Zhang, W. L. Yang, T. Geng, W. M. Sun, C. T. Sun, X. R. Jin, and L. B. Yuan, “Highly sensitive curvature sensor based on long period fiber grating with alternately splicing multiple single/multimode structure,” Opt. Fiber Technol. 37, 69–73 (2017).
[Crossref]

Szostkiewicz, L.

Tang, C. P.

M. Deng, C. P. Tang, T. Zhu, and Y. J. Rao, “Highly sensitive bend sensor base d on Mach-Zehnder interferometer using photonic crystal fiber,” Opt. Commun. 284(12), 2849–2853 (2011).
[Crossref]

Tang, Z. J.

Z. J. Tang, S. Q. Lou, X. Wang, W. Zhang, S. B. Yan, and Z. Xing, “High-performance bending vector and strain sensor using a dual-tapered photonic crystal fiber Mach-Zehnder interferometer,” IEEE Sens. J. 19(11), 4062–4068 (2019).
[Crossref]

Wang, B.

Y. P. Li, W. G. Zhang, S. Wang, L. Chen, Y. X. Zhang, B. Wang, T. Y. Yan, X. Y. Li, and W. Hu, “Bending vector sensor based on a pair of opposite tilted long-period fiber gratings,” IEEE Photonics Technol. Lett. 29(2), 224–227 (2017).
[Crossref]

Wang, C. L.

Wang, D.

X. H. Fu, J. Wen, Y. P. Zhang, D. Wang, F. Liu, H. Y. Xie, G. W. Fu, and W. H. Bi, “Experimental and theoretical analysis of curvature sensor based on cladding mode resonance with triple cladding quartz specialty fiber,” Opt. Commun. 429, 5–11 (2018).
[Crossref]

Wang, L.

Wang, Q.

Q. Wang and Y. Liu, “Review of optical fiber bending/curvature sensor,” Measurement 130, 161–176 (2018).
[Crossref]

Q. Wang and Y. Liu, “Optical fiber curvature sensor based on MMF-SCF-MMF structure,” Opt. Fiber Technol. 43, 1–5 (2018).
[Crossref]

Wang, S.

Y. X. Zhang, W. G. Zhang, T. Y. Yan, L. J. Bie, Y. S. Zhang, S. Wang, L. X. Kong, X. X. Kang, L. Yu, and P. C. Geng, “V-shaped long-period fiber grating high-sensitive bending vector sensor,” IEEE Photonics Technol. Lett. 30(17), 1531–1534 (2018).
[Crossref]

Y. P. Li, W. G. Zhang, S. Wang, L. Chen, Y. X. Zhang, B. Wang, T. Y. Yan, X. Y. Li, and W. Hu, “Bending vector sensor based on a pair of opposite tilted long-period fiber gratings,” IEEE Photonics Technol. Lett. 29(2), 224–227 (2017).
[Crossref]

Wang, T. Y.

Wang, X.

Z. J. Tang, S. Q. Lou, X. Wang, W. Zhang, S. B. Yan, and Z. Xing, “High-performance bending vector and strain sensor using a dual-tapered photonic crystal fiber Mach-Zehnder interferometer,” IEEE Sens. J. 19(11), 4062–4068 (2019).
[Crossref]

Wang, Y. P.

M. X. Hou, K. M. Yang, J. He, X. Z. Xu, S. Ju, K. K. Guo, and Y. P. Wang, “Two-dimensional vector bending sensor based on seven-core fiber Bragg gratings,” Opt. Express 26(18), 23770–23781 (2018).
[Crossref]

Y. P. Wang and Y. J. Rao, “A novel long period fiber grating sensor measuring curvature and determining bend-direction simultaneously,” IEEE Sens. J. 5(5), 839–843 (2005).
[Crossref]

Wang, Z. M.

S. Zhang, S. F. Deng, Z. M. Wang, C. T. Sun, X. D. Chen, Y. W. Ma, L. Zhao, C. L. Lu, T. Geng, W. L. Yang, and L. B. Yuan, “A miniature SMS-LPG bending sensor with high sensitivity based on multimode fiber embedded-LPG,” Sens. Actuators, A 295, 31–36 (2019).
[Crossref]

Webb, D. J.

T. Allsop, A. Gillooly, V. Mezentsev, T. Earthgrowl-Gould, R. Neal, D. J. Webb, and I. Bennion, “Bending and orientational characteristics of long period gratings written in D-shaped optical Fiber,” IEEE Trans. Instrum. Meas. 53(1), 130–135 (2004).
[Crossref]

Wen, J.

X. H. Fu, J. Wen, Y. P. Zhang, D. Wang, F. Liu, H. Y. Xie, G. W. Fu, and W. H. Bi, “Experimental and theoretical analysis of curvature sensor based on cladding mode resonance with triple cladding quartz specialty fiber,” Opt. Commun. 429, 5–11 (2018).
[Crossref]

Wojcik, G.

Wood, R. J.

C. Majidi, R. Kramer, and R. J. Wood, “A non-differential elastomer curvature sensor for softer-than-skin electronics,” Smart Mater. Struct. 20(10), 105017 (2011).
[Crossref]

Xie, H. Y.

X. H. Fu, J. Wen, Y. P. Zhang, D. Wang, F. Liu, H. Y. Xie, G. W. Fu, and W. H. Bi, “Experimental and theoretical analysis of curvature sensor based on cladding mode resonance with triple cladding quartz specialty fiber,” Opt. Commun. 429, 5–11 (2018).
[Crossref]

Xing, Z.

Z. J. Tang, S. Q. Lou, X. Wang, W. Zhang, S. B. Yan, and Z. Xing, “High-performance bending vector and strain sensor using a dual-tapered photonic crystal fiber Mach-Zehnder interferometer,” IEEE Sens. J. 19(11), 4062–4068 (2019).
[Crossref]

Xu, X. Z.

Yan, S. B.

Z. J. Tang, S. Q. Lou, X. Wang, W. Zhang, S. B. Yan, and Z. Xing, “High-performance bending vector and strain sensor using a dual-tapered photonic crystal fiber Mach-Zehnder interferometer,” IEEE Sens. J. 19(11), 4062–4068 (2019).
[Crossref]

Yan, T. Y.

Y. X. Zhang, W. G. Zhang, T. Y. Yan, L. J. Bie, Y. S. Zhang, S. Wang, L. X. Kong, X. X. Kang, L. Yu, and P. C. Geng, “V-shaped long-period fiber grating high-sensitive bending vector sensor,” IEEE Photonics Technol. Lett. 30(17), 1531–1534 (2018).
[Crossref]

Y. P. Li, W. G. Zhang, S. Wang, L. Chen, Y. X. Zhang, B. Wang, T. Y. Yan, X. Y. Li, and W. Hu, “Bending vector sensor based on a pair of opposite tilted long-period fiber gratings,” IEEE Photonics Technol. Lett. 29(2), 224–227 (2017).
[Crossref]

Yang, J.

Yang, K. M.

Yang, W. L.

S. Zhang, S. F. Deng, Z. M. Wang, C. T. Sun, X. D. Chen, Y. W. Ma, L. Zhao, C. L. Lu, T. Geng, W. L. Yang, and L. B. Yuan, “A miniature SMS-LPG bending sensor with high sensitivity based on multimode fiber embedded-LPG,” Sens. Actuators, A 295, 31–36 (2019).
[Crossref]

Q. H. Hu, S. Zhang, W. L. Yang, T. Geng, W. M. Sun, C. T. Sun, X. R. Jin, and L. B. Yuan, “Highly sensitive curvature sensor based on long period fiber grating with alternately splicing multiple single/multimode structure,” Opt. Fiber Technol. 37, 69–73 (2017).
[Crossref]

Yin, G. L.

Yu, L.

Y. X. Zhang, W. G. Zhang, T. Y. Yan, L. J. Bie, Y. S. Zhang, S. Wang, L. X. Kong, X. X. Kang, L. Yu, and P. C. Geng, “V-shaped long-period fiber grating high-sensitive bending vector sensor,” IEEE Photonics Technol. Lett. 30(17), 1531–1534 (2018).
[Crossref]

Yuan, L. B.

S. Zhang, S. F. Deng, Z. M. Wang, C. T. Sun, X. D. Chen, Y. W. Ma, L. Zhao, C. L. Lu, T. Geng, W. L. Yang, and L. B. Yuan, “A miniature SMS-LPG bending sensor with high sensitivity based on multimode fiber embedded-LPG,” Sens. Actuators, A 295, 31–36 (2019).
[Crossref]

Q. H. Hu, S. Zhang, W. L. Yang, T. Geng, W. M. Sun, C. T. Sun, X. R. Jin, and L. B. Yuan, “Highly sensitive curvature sensor based on long period fiber grating with alternately splicing multiple single/multimode structure,” Opt. Fiber Technol. 37, 69–73 (2017).
[Crossref]

G. P. Mao, T. T. Yuan, C. Y. Guan, J. Yang, L. Chen, Z. Zhu, J. H. Shi, and L. B. Yuan, “Fiber Bragg grating sensors in hollow single- and two-core eccentric fibers,” Opt. Express 25(1), 144–150 (2017).
[Crossref]

Yuan, T. T.

Zhang, H.

Zhang, L.

Zhang, S.

S. Zhang, S. F. Deng, Z. M. Wang, C. T. Sun, X. D. Chen, Y. W. Ma, L. Zhao, C. L. Lu, T. Geng, W. L. Yang, and L. B. Yuan, “A miniature SMS-LPG bending sensor with high sensitivity based on multimode fiber embedded-LPG,” Sens. Actuators, A 295, 31–36 (2019).
[Crossref]

Q. H. Hu, S. Zhang, W. L. Yang, T. Geng, W. M. Sun, C. T. Sun, X. R. Jin, and L. B. Yuan, “Highly sensitive curvature sensor based on long period fiber grating with alternately splicing multiple single/multimode structure,” Opt. Fiber Technol. 37, 69–73 (2017).
[Crossref]

Zhang, S. S.

Zhang, W.

Z. J. Tang, S. Q. Lou, X. Wang, W. Zhang, S. B. Yan, and Z. Xing, “High-performance bending vector and strain sensor using a dual-tapered photonic crystal fiber Mach-Zehnder interferometer,” IEEE Sens. J. 19(11), 4062–4068 (2019).
[Crossref]

Zhang, W. G.

Y. X. Zhang, W. G. Zhang, T. Y. Yan, L. J. Bie, Y. S. Zhang, S. Wang, L. X. Kong, X. X. Kang, L. Yu, and P. C. Geng, “V-shaped long-period fiber grating high-sensitive bending vector sensor,” IEEE Photonics Technol. Lett. 30(17), 1531–1534 (2018).
[Crossref]

Y. P. Li, W. G. Zhang, S. Wang, L. Chen, Y. X. Zhang, B. Wang, T. Y. Yan, X. Y. Li, and W. Hu, “Bending vector sensor based on a pair of opposite tilted long-period fiber gratings,” IEEE Photonics Technol. Lett. 29(2), 224–227 (2017).
[Crossref]

P. C. Geng, W. G. Zhang, S. C. Gao, H. Zhang, J. L. Li, S. S. Zhang, Z. Y. 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]

Zhang, Y. P.

X. H. Fu, J. Wen, Y. P. Zhang, D. Wang, F. Liu, H. Y. Xie, G. W. Fu, and W. H. Bi, “Experimental and theoretical analysis of curvature sensor based on cladding mode resonance with triple cladding quartz specialty fiber,” Opt. Commun. 429, 5–11 (2018).
[Crossref]

Zhang, Y. S.

Y. X. Zhang, W. G. Zhang, T. Y. Yan, L. J. Bie, Y. S. Zhang, S. Wang, L. X. Kong, X. X. Kang, L. Yu, and P. C. Geng, “V-shaped long-period fiber grating high-sensitive bending vector sensor,” IEEE Photonics Technol. Lett. 30(17), 1531–1534 (2018).
[Crossref]

Zhang, Y. X.

Y. X. Zhang, W. G. Zhang, T. Y. Yan, L. J. Bie, Y. S. Zhang, S. Wang, L. X. Kong, X. X. Kang, L. Yu, and P. C. Geng, “V-shaped long-period fiber grating high-sensitive bending vector sensor,” IEEE Photonics Technol. Lett. 30(17), 1531–1534 (2018).
[Crossref]

Y. P. Li, W. G. Zhang, S. Wang, L. Chen, Y. X. Zhang, B. Wang, T. Y. Yan, X. Y. Li, and W. Hu, “Bending vector sensor based on a pair of opposite tilted long-period fiber gratings,” IEEE Photonics Technol. Lett. 29(2), 224–227 (2017).
[Crossref]

Zhao, D. H.

Zhao, L.

S. Zhang, S. F. Deng, Z. M. Wang, C. T. Sun, X. D. Chen, Y. W. Ma, L. Zhao, C. L. Lu, T. Geng, W. L. Yang, and L. B. Yuan, “A miniature SMS-LPG bending sensor with high sensitivity based on multimode fiber embedded-LPG,” Sens. Actuators, A 295, 31–36 (2019).
[Crossref]

Zhao, Y. H.

L. Huang, X. Y. Meng, Y. H. Zhao, and Y. Q. Liu, “Temperature-insensitive directional bending sensors based on the interlaced tilted long-period gratings,” Opt. Commun. 447, 18–23 (2019).
[Crossref]

Y. H. Zhao, C. L. Wang, G. L. Yin, B. Q. Jiang, K. M. Zhou, C. B. Mou, Y. Q. Liu, L. Zhang, and T. Y. Wang, “Simultaneous directional curvature and temperature sensor based on a tilted few-mode fiber Bragg grating,” Appl. Opt. 57(7), 1671–1678 (2018).
[Crossref]

Zheng, S. J.

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]

Zhou, K. M.

Zhu, T.

M. Deng, C. P. Tang, T. Zhu, and Y. J. Rao, “Highly sensitive bend sensor base d on Mach-Zehnder interferometer using photonic crystal fiber,” Opt. Commun. 284(12), 2849–2853 (2011).
[Crossref]

Zhu, Z.

Appl. Opt. (2)

IEEE Photonics Technol. Lett. (2)

Y. X. Zhang, W. G. Zhang, T. Y. Yan, L. J. Bie, Y. S. Zhang, S. Wang, L. X. Kong, X. X. Kang, L. Yu, and P. C. Geng, “V-shaped long-period fiber grating high-sensitive bending vector sensor,” IEEE Photonics Technol. Lett. 30(17), 1531–1534 (2018).
[Crossref]

Y. P. Li, W. G. Zhang, S. Wang, L. Chen, Y. X. Zhang, B. Wang, T. Y. Yan, X. Y. Li, and W. Hu, “Bending vector sensor based on a pair of opposite tilted long-period fiber gratings,” IEEE Photonics Technol. Lett. 29(2), 224–227 (2017).
[Crossref]

IEEE Sens. J. (2)

Z. J. Tang, S. Q. Lou, X. Wang, W. Zhang, S. B. Yan, and Z. Xing, “High-performance bending vector and strain sensor using a dual-tapered photonic crystal fiber Mach-Zehnder interferometer,” IEEE Sens. J. 19(11), 4062–4068 (2019).
[Crossref]

Y. P. Wang and Y. J. Rao, “A novel long period fiber grating sensor measuring curvature and determining bend-direction simultaneously,” IEEE Sens. J. 5(5), 839–843 (2005).
[Crossref]

IEEE Trans. Instrum. Meas. (1)

T. Allsop, A. Gillooly, V. Mezentsev, T. Earthgrowl-Gould, R. Neal, D. J. Webb, and I. Bennion, “Bending and orientational characteristics of long period gratings written in D-shaped optical Fiber,” IEEE Trans. Instrum. Meas. 53(1), 130–135 (2004).
[Crossref]

J. Lightwave Technol. (2)

Measurement (2)

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]

Q. Wang and Y. Liu, “Review of optical fiber bending/curvature sensor,” Measurement 130, 161–176 (2018).
[Crossref]

Opt. Commun. (3)

M. Deng, C. P. Tang, T. Zhu, and Y. J. Rao, “Highly sensitive bend sensor base d on Mach-Zehnder interferometer using photonic crystal fiber,” Opt. Commun. 284(12), 2849–2853 (2011).
[Crossref]

X. H. Fu, J. Wen, Y. P. Zhang, D. Wang, F. Liu, H. Y. Xie, G. W. Fu, and W. H. Bi, “Experimental and theoretical analysis of curvature sensor based on cladding mode resonance with triple cladding quartz specialty fiber,” Opt. Commun. 429, 5–11 (2018).
[Crossref]

L. Huang, X. Y. Meng, Y. H. Zhao, and Y. Q. Liu, “Temperature-insensitive directional bending sensors based on the interlaced tilted long-period gratings,” Opt. Commun. 447, 18–23 (2019).
[Crossref]

Opt. Express (4)

Opt. Fiber Technol. (2)

Q. Wang and Y. Liu, “Optical fiber curvature sensor based on MMF-SCF-MMF structure,” Opt. Fiber Technol. 43, 1–5 (2018).
[Crossref]

Q. H. Hu, S. Zhang, W. L. Yang, T. Geng, W. M. Sun, C. T. Sun, X. R. Jin, and L. B. Yuan, “Highly sensitive curvature sensor based on long period fiber grating with alternately splicing multiple single/multimode structure,” Opt. Fiber Technol. 37, 69–73 (2017).
[Crossref]

Sens. Actuators, A (1)

S. Zhang, S. F. Deng, Z. M. Wang, C. T. Sun, X. D. Chen, Y. W. Ma, L. Zhao, C. L. Lu, T. Geng, W. L. Yang, and L. B. Yuan, “A miniature SMS-LPG bending sensor with high sensitivity based on multimode fiber embedded-LPG,” Sens. Actuators, A 295, 31–36 (2019).
[Crossref]

Smart Mater. Struct. (1)

C. Majidi, R. Kramer, and R. J. Wood, “A non-differential elastomer curvature sensor for softer-than-skin electronics,” Smart Mater. Struct. 20(10), 105017 (2011).
[Crossref]

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

Cited By

Optica participates in Crossref's Cited-By Linking service. Citing articles from Optica Publishing Group journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (10)

Fig. 1.
Fig. 1. Schematic diagram of the process for splicing SMFs and MMFs.
Fig. 2.
Fig. 2. Schematic diagram of the experimental setup for re-modulation.
Fig. 3.
Fig. 3. Structure diagram of the EMD-LPFG.
Fig. 4.
Fig. 4. The evolution of transmission spectrum during re-modulation.
Fig. 5.
Fig. 5. (a) Simulated transmission light field distribution of the EMD-LPFG. (b) Simulated transmission spectrum of different re-modulation depths.
Fig. 6.
Fig. 6. Schematic diagram of vector bending principle. (a) The modulation of refractive index with the influence of CO2 laser. (b) The schematic diagram of refractive index changes in different directions.
Fig. 7.
Fig. 7. (a) Schematic diagram of bending measuring device. (b) Schematic diagram of curvature calculation.
Fig. 8.
Fig. 8. Bending characteristic of the EMD-LPFG. (a) Resonant dip shift of the 0° direction. (b) Resonant dip shift of the 90° direction. (c) Resonant dip shift of the 180° direction. (d) Resonant dip shift of the 270° direction.
Fig. 9.
Fig. 9. The fitting curve between the curvature and wavelengths for four directions.
Fig. 10.
Fig. 10. Temperature characteristic of the EMD-LPFG. (a) Resonant dip shift under different temperatures. (b) The linear fit between the temperature and wavelength shifts.

Tables (1)

Tables Icon

Table 1. The performance comparison between our sensor and related sensors

Equations (2)

Equations on this page are rendered with MathJax. Learn more.

λ res = ( n e f f c o n e f f c l , m ) Λ = Δ n Λ .
C = 1 R = 2 d d 2 + L 2 .

Metrics