Abstract

A micro-fabricated Mach–Zehnder interferometer in optical fiber is demonstrated for bend sensing in four orthogonal directions. The intensity of the resonant dip exhibits a linear response to curvature in a logarithmic unit within a large range from 0 to 9 m−1, and the sensitivities obtained are 0.42 dB/m−1, 0.186 dB/m−1, −0.41dB/m−1, −0.265 dB/m−1, in the directions of 0°, 90°, 180°, and 270°, respectively. The temperature-induced curvature error is only ~0.012 m−1/°C in the bending directions of 0° and 180°. The device is compact, robust and efficient in operation.

© 2017 Optical Society of America

1. Introduction

Optical fiber bend sensors have drawn increased research attention in the structural health monitoring and mechanical engineering, due to their advantages of small size, low cost, operation flexibility and resistance to corrosion. Various types of bend sensor have been developed, such as those based on fiber Bragg grating (FBG) [1, 2], tilted FBG [3, 4], long period fiber grating (LPFG) [5–7] and fiber in-line Mach-Zehnder interferometer (MZI). MZI based bend sensors are featured with high sensitivity and ease of fabrication. However, in most of the configurations of MZI bend sensors such as single mode fiber (SMF)-multimode fiber (MMF)-SMF structure [8], a pair of identical fused tapers [9], two peanut-shape structures [10] and dual abrupt-tapers [11], the bending direction is still needed to be determined. Recently, S. Zhang et al. demonstrated a directional bend sensor based on lateral-offset splicing and an up-taper [12]. Z. Ou et al. proposed a bending vector sensor based on seven-core photonics crystal fiber (PCF) [13]. H. F. Chen et al. presented a directional bend sensor based on selectively infiltrated PCF [14]. J. Kong presented a bending sensor based on FBGs inscribed on the connection joint of eccentric-core fiber (ECF) and SMF [15]. D. Feng presented an off-axis ultraviolet-written FBG for directional bending measurements [16]. However, the structure based on lateral-offset splicing is difficult to control accurately, and the seven-core PCF and eccentric-core fiber are of high cost. Moreover, the fabrication of selectively infiltrated PCF and off-axis written FBG are relatively complicated.

In our previous work, a fiber in-line MZI sensor based on a hollow ellipsoid is proposed [17], and it can be used for bend sensing within a small range, from 0 to 2.88m−1. In this paper, we demonstrated that the device has the excellent capability for directional bend sensing with a large curvature range from 0 to 9 m−1. The interesting feature of the device is that the surface of the hollow ellipsoid at one end reflects the light traveling in the fiber core to the air-cladding interface, and the surface of the hollow ellipsoid at the other end reflects the light from the air-cladding interface back into the fiber core. When the fiber is bent in different directions, the shape of the air-cladding interface becomes concave and convex according to the bending orientations of 0° and 180°, respectively. The intensity of the resonant dip in the transmission spectrum of the MZI exhibits a linear response to curvature. The device is compact, robust and efficient in operation.

2. Sensor design and fabrication

The principle of the proposed MZI is shown in Fig. 1(a). Part of the input light in the fiber core is reflected at the left surface of the hollow ellipsoid, and propagates along the path AB. When it reaches the interface between the fiber cladding and air, it is reflected again, and propagates along the path BC. Finally it encounters on the right surface of the hollow ellipsoid, and is reflected into the fiber core. The other part of the input light propagates through the hollow ellipsoid, along the path AC. As the light beams traveling along the two paths are recombined, a fiber in-line MZI is formed [17]. Although point B actually represents a small region at the fiber cladding and air interface, and a number of reflects light paths exist, their differences are small.

 figure: Fig. 1

Fig. 1 Schematic diagram of the fiber in-line MZI (a), and the microscope image (b).

Download Full Size | PPT Slide | PDF

The transmission intensity of the MZI can be expressed by the theory of two-beam interference as

T=I1+I2+2I1I2cos[2πΔ(nL)/λ]
where I1 represents the light intensity of the transmitted beam (AC), I2 denotes the light intensity of the reflected beam (AB-BC), λ is the operating wavelength, and Δ(nL) is the optical path difference between the two interferometer beams. The minimum intensity appears at the wavelengths
λm=2Δ(nL)/(2m+1)
where m is an integer. And the separation between the two dips in the spectrum is

S=λm2/Δ(nL)

As the reflection of the interface between the fiber cladding and air is influenced by the external parameters, such as refractive index and curvature, the intensity of the light beam traveling along BC will be varied, and hence the transmission intensity of the MZI will be changed.

The hollow ellipsoid was fabricated by use of femtosecond (fs) laser micromachining and fusion splicing techniques. The fs laser pulses with the wavelength of 800 nm, pulse width of 120 fs and repetition rate of 1 kHz were focused onto a cleaved fiber end by a 20X objective lens with NA value of 0.5 and working distance of 2.1 mm. The SMF is placed on a computer-controlled translation stage with a resolution of 40 nm. A CCD camera (Nikon, Japan) was used to monitor the micromachining process. A micro square centered at 20 µm away from the center of the cleaved fiber end, with side length of 30 µm and depth of 40 µm, was inscribed by fs laser pulses with energy of ~3 µJ [14]. After the micromachining process was completed, the micro-square was cleaned by use of ethanol to remove the dust. The fiber end with micro-square was then fusion spliced together with another cleaved SMF end without micro structure to form a hollow ellipsoid. The fusion splicer used was FSM-45P (Fujikura, Japan), and the parameters of fusion splicing employed were the same as those used for splicing two SMFs. After fusion splicing, a hollow ellipsoid with the major axis length of 50 µm and the minor axis length of 40 µm was formed in the fiber, as shown in Fig. 1(b). Because of the high temperature of the air in the fusion splicing process, the size and shape of the microstructure are changes and in particular, the size of the hollow ellipsoid is enlarged. The fabrication process is described in Fig. 2. The insertion loss of the device is about 28dB.

 figure: Fig. 2

Fig. 2 Diagrams of the fabrication process.

Download Full Size | PPT Slide | PDF

3. Experimental setup

The experimental setup to investigate the bending response of the proposed MZI is schematically shown in Fig. 3(a). The light from a broadband source (BBS) is introduced into the MZI structure and the transmission spectrum obtained is recorded by an optical spectrum analyzer (OSA). The MZI structure is positioned in the middle of a section of SMF, and the two ends of the SMF are fixed by the two fiber holders. As the translation stage can be moved inward, the fiber bends toward the expected direction and is normally approximated as a circular arc. Two weights of 2g are attached to both sides of the fiber closely to ensure the fiber bending orientation. The applied curvature (C) could be defined as [5]:

C=2d/(d2+L2)
where d is the bending displacement of the center of the MZI and L is half of the distance between the two fiber holders. To avoid the temperature cross sensitivity, the MZI was placed in temperature-controlled environment with a fixed temperature of 24°C. Figure 3(b) shows the four fiber orientations used in the experiment.

 figure: Fig. 3

Fig. 3 Experimental setup (a), and four bending orientations (b).

Download Full Size | PPT Slide | PDF

4. Results and discussions

In the transmission spectrum of the MZI, there are two resonant dips, and the resonant wavelength dip at ~1552 nm was selected to monitor the response of the MZI in the bending direction of 0°, 90°, 180° and 270°, respectively. The curvature range applied to the fiber device during the experiment was from 0 to 9 m−1. Figure 4(a) and Fig. 4(b) show the transmission spectrum of the MZI corresponding to the curvature changed with the fiber orientation of 0° and 180°, respectively. It can be clearly observed that the bending responses of the sensor are sensitive to the fiber orientations.

 figure: Fig. 4

Fig. 4 (a) Spectral variations in 0° bending, (b) in 180° bending, (c) the diagram of concave bending, (d) the diagram of convex bending.

Download Full Size | PPT Slide | PDF

When the MZI is fixed at 0° orientation, the intensity of the resonant dip is increased with the increase of applied curvature, whereas it is decreased with the increase of applied curvature, in the case of 180° orientation. This can be explained as follows. When the curvature is applied on the sensor device with the orientation of 0° or 180°, the fiber surface becomes concave or convex, as shown in Fig. 4(c) and Fig. 4(d), respectively. When the fiber is bent in the direction of 0°, the fiber surface is equivalent to a concave mirror, which has the effect of concentrating light. When the fiber is bent in the direction of 180°, the fiber surface is operated like a convex mirror, which diverges light.

As shown in Fig. 4, the separation of the two dips is ~16.4nm, which agrees well with the calculated results from Eq. (3). The length of AC path is ~45µm, the length of AB-BC path can be calculated from the Pythagorean theorem of right triangle, ~133µm. Thus the optical path difference is: nclad × (AB + BC) - nair × AC = 1.46 × 133-1.0 × 45 = 149.18µm. By adopting theis value into Eq. (3), the separation obtained is 16.15nm. The frequency spectra for the bending directions of 0° and 180 o are obtained by use of fast Flourier transform (FFT) method, as shown in Fig. 5(a) and 5(b) respectively. It can be clearly observed that there is one peak in the interference spectrum besides zero frequency, and the mode intensity increases in 0° bending direction while decreasing in 180° bending direction. This demonstrates that the proposed sensor is a two-beam MZI.

 figure: Fig. 5

Fig. 5 Frequency spectra in 0° bending (a), and in 180° bending (b).

Download Full Size | PPT Slide | PDF

As the reflection of the interface between the fiber cladding and air is influenced by bending, the intensity of the light beam traveling along AB-BC path is varied, and hence the transmission intensity of the MZI is changed with bending, which explains that the intensity is a function of bending. Thus the fiber bending mainly changes the intensity of the reflected beam (AB-BC), the optical path difference has little change, and hence there is no significant phase change in different bend conditions.

The transmission spectra of the varied curvatures in the bending directions of 90° and 270° are shown in Fig. 6, where the intensity variation of the resonant dip is clearly observed; however, the dip wavelength is still kept as a constant. Thus the dip wavelength intensity can be used to characterize the response of the device to the curvature change. The intensity difference of ~0.8dB in the two spectra is noticed, which could be caused by the difference of the residue stress remained within the fiber when the bent fiber is returned from maximum curvature to zero curvature. The responses of the device in the four bending directions are shown in Fig. 7, where it can be observed that the intensity of the resonant dip is linearly changed with the curvature for any of the bending directions in logarithmic unit (dB). The sensitivities in the directions of 0° and 180° are 0.42 dB/m−1 and −0.41 dB/m−1 respectively, close to a constant, which demonstrates the symmetric property of the concave and convex reflection. When the fiber device is bent in the directions of 90° and 270°, the bending sensitivities obtained are 0.186dB/m−1 and −0.265dB/m−1, respectively. Theoretically, the bending sensitivities in these two directions should be similar, and the error may come from the fact that the hollow ellipsoid is not positioned in symmetry in these two directions during the test. However, the bending in these two directions has less effect on the shape of the reflection interface, and hence the bending sensitivities of the two directions are small. The results obtained indicate that we can determine the bending direction by the intensity change process, to see if the intensity change is increased or decreased, and the amount of change is small or large. For instance, the intensity variations for the bending directions of 0 degree and 180 degree are the largest but in opposite directions.

 figure: Fig. 6

Fig. 6 Spectral variations in 90° bending (a), and in 270° bending (b).

Download Full Size | PPT Slide | PDF

 figure: Fig. 7

Fig. 7 Intensity variations in the four bending directions.

Download Full Size | PPT Slide | PDF

The maximum bending applied in the experiment is 9.0 m−1, and as the bending experiment has been carried out for many times, the good robustness of the device can be ensured. To enable a multi-point sensing, more sensor heads have to be fabricated along the fiber length. Different sensor heads would produce different transmission spectra or in other words, wavelength dips would appear at different locations in the transmission spectra, which could be utilized for multi-point sensing. If a laser diode with the wavelength of 1552 nm is used as a light source, the optical spectrum analyzer will not be needed, and we can use a power meter to detect the intensity, which could be very cost-effective for practical application. As the sensor is intensity-demodulated, the power fluctuation has great impact on the sensitivity. To eliminate the effect of power fluction, a reference wavelength intensity can be used. For example, the neighbor wavelength dips (1552nm and 1558nm) can be used. Compared with other bend sensors reported [12–16], the sensitivity of our proposed sensor is higher than the ones in [13–15] and lower than the ones in [12,16]. However, our proposed sensor is more compact, robust and efficient in operation.

The temperature cross-sensitivity is always a concern in optical fiber bending sensors. We also measured the temperature response of the proposed sensor, which is shown in Fig. 8. When the temperature is increased from 24°C to 70°C,the wavelength of the resonant dip shifts ~0.4 nm, and the intensity varies ~0.24 dB, which correspond to the temperature sensitivities of 8.5 pm/°C and 0.005 dB/°C, respectively. Thus, the temperature-induced curvature error is only ~0.012 m−1/°C in the bending directions of 0° and 180°. This indicates that the temperature compensation is not needed when the temperature variation is less than a few degrees.

 figure: Fig. 8

Fig. 8 Temperature response of the proposed sensor.

Download Full Size | PPT Slide | PDF

5. Conclusion

A micro-fabricated fiber MZI is demonstrated for directional curvature sensing. A hollow ellipsoid in a fiber is fabricated by femtosecond laser micromachining system, which forms a MZI. When the fiber is bent in different directions, the spectra of the MZI show different responses to the bending orientations. The sensitivities of 0.42dB/m−1, 0.186dB/m−1, −0.41dB/m−1, −0.265dB/m−1 are obtained in the bending directions of 0°, 90°, 180°, and 270°, respectively. The temperature-induced curvature error is only ~0.012 m−1/°C in the bending directions of 0° and 180°. Such a device is compact, robust and efficient in operation and has a good linear response to curvature in a logarithmic unit, within a large range from 0 to 9 m−1.

Funding

National Natural Science Foundation of China (No. 61661166009, 61377094); and Zhejiang Provincial Open Foundation of the Most Important Subjects (No. JL150537 and JL150545).

References and links

1. M. J. Gander, W. N. Macpherson, R. Mcbride, J. D. C. Jones, L. Zhang, I. Bennion, P. M. Blanchard, J. G. Burnett, and A. H. Greenaway, “Bend measurement using Bragg gratings in multicore fiber,” Electron. Lett. 36(2), 120–121 (2000). [CrossRef]  

2. X. Chen, C. Zhang, D. J. Webb, K. Kalli, and G. D. Peng, “Highly sensitive bend sensor based on Bragg grating in eccentric core polymer fiber,” IEEE Photonics Technol. Lett. 22(11), 850–852 (2010). [CrossRef]  

3. Y. Jin, C. C. Chan, X. Dong, and Y. Zhang, “Temperature-independent bending sensor with tilted fiber Bragg grating interacting with multimode fiber,” Opt. Commun. 282(19), 3905–3907 (2009). [CrossRef]  

4. L. Shao, L. Xiong, C. Chen, A. Laronche, and J. Albert, “Directional Bend Sensor Based on Re-Grown Tilted Fiber Bragg Grating,” J. Lightwave Technol. 28(18), 2681–2687 (2010). [CrossRef]  

5. H. J. Patrick, C. Chang, and S. T. Vohra, “Long period fiber gratings for structural bending sensing,” Electron. Lett. 34(18), 1773–1775 (1998). [CrossRef]  

6. C. C. Ye, S. W. James, and R. P. Tatam, “Simultaneous temperature and bend sensing with long-period fiber gratings,” Opt. Lett. 25(14), 1007–1009 (2000). [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. Y. Gong, T. Zhao, Y. J. Rao, and Y. Wu, “All-fiber curvature sensor based on multimode interference,” IEEE Photonics Technol. Lett. 23(11), 679–681 (2011). [CrossRef]  

9. D. Monzon-Hernandez, A. Martinez-Rios, I. Torres-Gomez, and G. Salceda-Delgado, “Compact optical fiber curvature sensor based on concatenating two tapers,” Opt. Lett. 36(22), 4380–4382 (2011). [CrossRef]   [PubMed]  

10. H. Gong, X. Yang, K. Ni, C. L. Zhao, and X. Dong, “An optical fiber curvature sensor based on two peanut-shape structures modal interferometer,” IEEE Photonics Technol. Lett. 26(1), 22–24 (2014). [CrossRef]  

11. L. Niu, C. L. Zhao, H. Gong, Y. Li, and S. Jin, “Curvature sensor based on two cascading abrupt-tapers modal interferometer in single mode fiber,” Opt. Commun. 333(15), 11–15 (2014). [CrossRef]  

12. 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]  

13. 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]  

14. H. F. Chen, Y. Wang, and D. N. Wang, “Selectively infiltrated PCF for directional bend sensing with large bending range,” IEEE Photonics Technol. Lett. 27(5), 502–505 (2015). [CrossRef]  

15. J. Kong, X. Ouyang, A. Zhou, H. Yu, and L. Yuan, “Pure directional bending measurement with a fiber Bragg grating at the connection joint of eccentric-core and single-mode fibers,” J. Lightwave Technol. 34(14), 3288–3292 (2016). [CrossRef]  

16. 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]  

17. H. Gong, D. N. Wang, B. Xu, K. Ni, H. Liu, and C. L. Zhao, “Miniature and robust optical fiber in-line Mach-Zehnder interferometer based on a hollow ellipsoid,” Opt. Lett. 40(15), 3516–3519 (2015). [CrossRef]   [PubMed]  

References

  • View by:

  1. M. J. Gander, W. N. Macpherson, R. Mcbride, J. D. C. Jones, L. Zhang, I. Bennion, P. M. Blanchard, J. G. Burnett, and A. H. Greenaway, “Bend measurement using Bragg gratings in multicore fiber,” Electron. Lett. 36(2), 120–121 (2000).
    [Crossref]
  2. X. Chen, C. Zhang, D. J. Webb, K. Kalli, and G. D. Peng, “Highly sensitive bend sensor based on Bragg grating in eccentric core polymer fiber,” IEEE Photonics Technol. Lett. 22(11), 850–852 (2010).
    [Crossref]
  3. Y. Jin, C. C. Chan, X. Dong, and Y. Zhang, “Temperature-independent bending sensor with tilted fiber Bragg grating interacting with multimode fiber,” Opt. Commun. 282(19), 3905–3907 (2009).
    [Crossref]
  4. L. Shao, L. Xiong, C. Chen, A. Laronche, and J. Albert, “Directional Bend Sensor Based on Re-Grown Tilted Fiber Bragg Grating,” J. Lightwave Technol. 28(18), 2681–2687 (2010).
    [Crossref]
  5. H. J. Patrick, C. Chang, and S. T. Vohra, “Long period fiber gratings for structural bending sensing,” Electron. Lett. 34(18), 1773–1775 (1998).
    [Crossref]
  6. C. C. Ye, S. W. James, and R. P. Tatam, “Simultaneous temperature and bend sensing with long-period fiber gratings,” Opt. Lett. 25(14), 1007–1009 (2000).
    [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. Y. Gong, T. Zhao, Y. J. Rao, and Y. Wu, “All-fiber curvature sensor based on multimode interference,” IEEE Photonics Technol. Lett. 23(11), 679–681 (2011).
    [Crossref]
  9. D. Monzon-Hernandez, A. Martinez-Rios, I. Torres-Gomez, and G. Salceda-Delgado, “Compact optical fiber curvature sensor based on concatenating two tapers,” Opt. Lett. 36(22), 4380–4382 (2011).
    [Crossref] [PubMed]
  10. H. Gong, X. Yang, K. Ni, C. L. Zhao, and X. Dong, “An optical fiber curvature sensor based on two peanut-shape structures modal interferometer,” IEEE Photonics Technol. Lett. 26(1), 22–24 (2014).
    [Crossref]
  11. L. Niu, C. L. Zhao, H. Gong, Y. Li, and S. Jin, “Curvature sensor based on two cascading abrupt-tapers modal interferometer in single mode fiber,” Opt. Commun. 333(15), 11–15 (2014).
    [Crossref]
  12. 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]
  13. 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]
  14. H. F. Chen, Y. Wang, and D. N. Wang, “Selectively infiltrated PCF for directional bend sensing with large bending range,” IEEE Photonics Technol. Lett. 27(5), 502–505 (2015).
    [Crossref]
  15. J. Kong, X. Ouyang, A. Zhou, H. Yu, and L. Yuan, “Pure directional bending measurement with a fiber Bragg grating at the connection joint of eccentric-core and single-mode fibers,” J. Lightwave Technol. 34(14), 3288–3292 (2016).
    [Crossref]
  16. 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]
  17. H. Gong, D. N. Wang, B. Xu, K. Ni, H. Liu, and C. L. Zhao, “Miniature and robust optical fiber in-line Mach-Zehnder interferometer based on a hollow ellipsoid,” Opt. Lett. 40(15), 3516–3519 (2015).
    [Crossref] [PubMed]

2016 (2)

2015 (2)

H. Gong, D. N. Wang, B. Xu, K. Ni, H. Liu, and C. L. Zhao, “Miniature and robust optical fiber in-line Mach-Zehnder interferometer based on a hollow ellipsoid,” Opt. Lett. 40(15), 3516–3519 (2015).
[Crossref] [PubMed]

H. F. Chen, Y. Wang, and D. N. Wang, “Selectively infiltrated PCF for directional bend sensing with large bending range,” IEEE Photonics Technol. Lett. 27(5), 502–505 (2015).
[Crossref]

2014 (2)

H. Gong, X. Yang, K. Ni, C. L. Zhao, and X. Dong, “An optical fiber curvature sensor based on two peanut-shape structures modal interferometer,” IEEE Photonics Technol. Lett. 26(1), 22–24 (2014).
[Crossref]

L. Niu, C. L. Zhao, H. Gong, Y. Li, and S. Jin, “Curvature sensor based on two cascading abrupt-tapers modal interferometer in single mode fiber,” Opt. Commun. 333(15), 11–15 (2014).
[Crossref]

2013 (1)

2012 (2)

2011 (2)

Y. Gong, T. Zhao, Y. J. Rao, and Y. Wu, “All-fiber curvature sensor based on multimode interference,” IEEE Photonics Technol. Lett. 23(11), 679–681 (2011).
[Crossref]

D. Monzon-Hernandez, A. Martinez-Rios, I. Torres-Gomez, and G. Salceda-Delgado, “Compact optical fiber curvature sensor based on concatenating two tapers,” Opt. Lett. 36(22), 4380–4382 (2011).
[Crossref] [PubMed]

2010 (2)

X. Chen, C. Zhang, D. J. Webb, K. Kalli, and G. D. Peng, “Highly sensitive bend sensor based on Bragg grating in eccentric core polymer fiber,” IEEE Photonics Technol. Lett. 22(11), 850–852 (2010).
[Crossref]

L. Shao, L. Xiong, C. Chen, A. Laronche, and J. Albert, “Directional Bend Sensor Based on Re-Grown Tilted Fiber Bragg Grating,” J. Lightwave Technol. 28(18), 2681–2687 (2010).
[Crossref]

2009 (1)

Y. Jin, C. C. Chan, X. Dong, and Y. Zhang, “Temperature-independent bending sensor with tilted fiber Bragg grating interacting with multimode fiber,” Opt. Commun. 282(19), 3905–3907 (2009).
[Crossref]

2000 (2)

M. J. Gander, W. N. Macpherson, R. Mcbride, J. D. C. Jones, L. Zhang, I. Bennion, P. M. Blanchard, J. G. Burnett, and A. H. Greenaway, “Bend measurement using Bragg gratings in multicore fiber,” Electron. Lett. 36(2), 120–121 (2000).
[Crossref]

C. C. Ye, S. W. James, and R. P. Tatam, “Simultaneous temperature and bend sensing with long-period fiber gratings,” Opt. Lett. 25(14), 1007–1009 (2000).
[Crossref] [PubMed]

1998 (1)

H. J. Patrick, C. Chang, and S. T. Vohra, “Long period fiber gratings for structural bending sensing,” Electron. Lett. 34(18), 1773–1775 (1998).
[Crossref]

Albert, J.

Bai, Z.

Bennion, I.

M. J. Gander, W. N. Macpherson, R. Mcbride, J. D. C. Jones, L. Zhang, I. Bennion, P. M. Blanchard, J. G. Burnett, and A. H. Greenaway, “Bend measurement using Bragg gratings in multicore fiber,” Electron. Lett. 36(2), 120–121 (2000).
[Crossref]

Blanchard, P. M.

M. J. Gander, W. N. Macpherson, R. Mcbride, J. D. C. Jones, L. Zhang, I. Bennion, P. M. Blanchard, J. G. Burnett, and A. H. Greenaway, “Bend measurement using Bragg gratings in multicore fiber,” Electron. Lett. 36(2), 120–121 (2000).
[Crossref]

Burnett, J. G.

M. J. Gander, W. N. Macpherson, R. Mcbride, J. D. C. Jones, L. Zhang, I. Bennion, P. M. Blanchard, J. G. Burnett, and A. H. Greenaway, “Bend measurement using Bragg gratings in multicore fiber,” Electron. Lett. 36(2), 120–121 (2000).
[Crossref]

Chan, C. C.

Y. Jin, C. C. Chan, X. Dong, and Y. Zhang, “Temperature-independent bending sensor with tilted fiber Bragg grating interacting with multimode fiber,” Opt. Commun. 282(19), 3905–3907 (2009).
[Crossref]

Chang, C.

H. J. Patrick, C. Chang, and S. T. Vohra, “Long period fiber gratings for structural bending sensing,” Electron. Lett. 34(18), 1773–1775 (1998).
[Crossref]

Chen, C.

Chen, H. F.

H. F. Chen, Y. Wang, and D. N. Wang, “Selectively infiltrated PCF for directional bend sensing with large bending range,” IEEE Photonics Technol. Lett. 27(5), 502–505 (2015).
[Crossref]

Chen, X.

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]

X. Chen, C. Zhang, D. J. Webb, K. Kalli, and G. D. Peng, “Highly sensitive bend sensor based on Bragg grating in eccentric core polymer fiber,” IEEE Photonics Technol. Lett. 22(11), 850–852 (2010).
[Crossref]

Dong, X.

H. Gong, X. Yang, K. Ni, C. L. Zhao, and X. Dong, “An optical fiber curvature sensor based on two peanut-shape structures modal interferometer,” IEEE Photonics Technol. Lett. 26(1), 22–24 (2014).
[Crossref]

Y. Jin, C. C. Chan, X. Dong, and Y. Zhang, “Temperature-independent bending sensor with tilted fiber Bragg grating interacting with multimode fiber,” Opt. Commun. 282(19), 3905–3907 (2009).
[Crossref]

Du, C.

Feng, D.

Gander, M. J.

M. J. Gander, W. N. Macpherson, R. Mcbride, J. D. C. Jones, L. Zhang, I. Bennion, P. M. Blanchard, J. G. Burnett, and A. H. Greenaway, “Bend measurement using Bragg gratings in multicore fiber,” Electron. Lett. 36(2), 120–121 (2000).
[Crossref]

Gao, S.

Geng, P.

Gong, H.

H. Gong, D. N. Wang, B. Xu, K. Ni, H. Liu, and C. L. Zhao, “Miniature and robust optical fiber in-line Mach-Zehnder interferometer based on a hollow ellipsoid,” Opt. Lett. 40(15), 3516–3519 (2015).
[Crossref] [PubMed]

L. Niu, C. L. Zhao, H. Gong, Y. Li, and S. Jin, “Curvature sensor based on two cascading abrupt-tapers modal interferometer in single mode fiber,” Opt. Commun. 333(15), 11–15 (2014).
[Crossref]

H. Gong, X. Yang, K. Ni, C. L. Zhao, and X. Dong, “An optical fiber curvature sensor based on two peanut-shape structures modal interferometer,” IEEE Photonics Technol. Lett. 26(1), 22–24 (2014).
[Crossref]

Gong, Y.

Y. Gong, T. Zhao, Y. J. Rao, and Y. Wu, “All-fiber curvature sensor based on multimode interference,” IEEE Photonics Technol. Lett. 23(11), 679–681 (2011).
[Crossref]

Greenaway, A. H.

M. J. Gander, W. N. Macpherson, R. Mcbride, J. D. C. Jones, L. Zhang, I. Bennion, P. M. Blanchard, J. G. Burnett, and A. H. Greenaway, “Bend measurement using Bragg gratings in multicore fiber,” Electron. Lett. 36(2), 120–121 (2000).
[Crossref]

Huang, Q.

James, S. W.

Jin, S.

L. Niu, C. L. Zhao, H. Gong, Y. Li, and S. Jin, “Curvature sensor based on two cascading abrupt-tapers modal interferometer in single mode fiber,” Opt. Commun. 333(15), 11–15 (2014).
[Crossref]

Jin, Y.

Y. Jin, C. C. Chan, X. Dong, and Y. Zhang, “Temperature-independent bending sensor with tilted fiber Bragg grating interacting with multimode fiber,” Opt. Commun. 282(19), 3905–3907 (2009).
[Crossref]

Jones, J. D. C.

M. J. Gander, W. N. Macpherson, R. Mcbride, J. D. C. Jones, L. Zhang, I. Bennion, P. M. Blanchard, J. G. Burnett, and A. H. Greenaway, “Bend measurement using Bragg gratings in multicore fiber,” Electron. Lett. 36(2), 120–121 (2000).
[Crossref]

Kalli, K.

X. Chen, C. Zhang, D. J. Webb, K. Kalli, and G. D. Peng, “Highly sensitive bend sensor based on Bragg grating in eccentric core polymer fiber,” IEEE Photonics Technol. Lett. 22(11), 850–852 (2010).
[Crossref]

Kong, J.

Laronche, A.

Li, J.

Li, Y.

L. Niu, C. L. Zhao, H. Gong, Y. Li, and S. Jin, “Curvature sensor based on two cascading abrupt-tapers modal interferometer in single mode fiber,” Opt. Commun. 333(15), 11–15 (2014).
[Crossref]

Liu, H.

Macpherson, W. N.

M. J. Gander, W. N. Macpherson, R. Mcbride, J. D. C. Jones, L. Zhang, I. Bennion, P. M. Blanchard, J. G. Burnett, and A. H. Greenaway, “Bend measurement using Bragg gratings in multicore fiber,” Electron. Lett. 36(2), 120–121 (2000).
[Crossref]

Martinez-Rios, A.

Mcbride, R.

M. J. Gander, W. N. Macpherson, R. Mcbride, J. D. C. Jones, L. Zhang, I. Bennion, P. M. Blanchard, J. G. Burnett, and A. H. Greenaway, “Bend measurement using Bragg gratings in multicore fiber,” Electron. Lett. 36(2), 120–121 (2000).
[Crossref]

Monzon-Hernandez, D.

Ni, K.

H. Gong, D. N. Wang, B. Xu, K. Ni, H. Liu, and C. L. Zhao, “Miniature and robust optical fiber in-line Mach-Zehnder interferometer based on a hollow ellipsoid,” Opt. Lett. 40(15), 3516–3519 (2015).
[Crossref] [PubMed]

H. Gong, X. Yang, K. Ni, C. L. Zhao, and X. Dong, “An optical fiber curvature sensor based on two peanut-shape structures modal interferometer,” IEEE Photonics Technol. Lett. 26(1), 22–24 (2014).
[Crossref]

Niu, L.

L. Niu, C. L. Zhao, H. Gong, Y. Li, and S. Jin, “Curvature sensor based on two cascading abrupt-tapers modal interferometer in single mode fiber,” Opt. Commun. 333(15), 11–15 (2014).
[Crossref]

Ou, Z.

Ouyang, X.

Patrick, H. J.

H. J. Patrick, C. Chang, and S. T. Vohra, “Long period fiber gratings for structural bending sensing,” Electron. Lett. 34(18), 1773–1775 (1998).
[Crossref]

Peng, G. D.

X. Chen, C. Zhang, D. J. Webb, K. Kalli, and G. D. Peng, “Highly sensitive bend sensor based on Bragg grating in eccentric core polymer fiber,” IEEE Photonics Technol. Lett. 22(11), 850–852 (2010).
[Crossref]

Qiao, X.

Rao, Y. J.

Y. Gong, T. Zhao, Y. J. Rao, and Y. Wu, “All-fiber curvature sensor based on multimode interference,” IEEE Photonics Technol. Lett. 23(11), 679–681 (2011).
[Crossref]

Salceda-Delgado, G.

Shao, L.

Tatam, R. P.

Torres-Gomez, I.

Vohra, S. T.

H. J. Patrick, C. Chang, and S. T. Vohra, “Long period fiber gratings for structural bending sensing,” Electron. Lett. 34(18), 1773–1775 (1998).
[Crossref]

Wang, D. N.

H. F. Chen, Y. Wang, and D. N. Wang, “Selectively infiltrated PCF for directional bend sensing with large bending range,” IEEE Photonics Technol. Lett. 27(5), 502–505 (2015).
[Crossref]

H. Gong, D. N. Wang, B. Xu, K. Ni, H. Liu, and C. L. Zhao, “Miniature and robust optical fiber in-line Mach-Zehnder interferometer based on a hollow ellipsoid,” Opt. Lett. 40(15), 3516–3519 (2015).
[Crossref] [PubMed]

Wang, J.

Wang, L.

Wang, Y.

H. F. Chen, Y. Wang, and D. N. Wang, “Selectively infiltrated PCF for directional bend sensing with large bending range,” IEEE Photonics Technol. Lett. 27(5), 502–505 (2015).
[Crossref]

Webb, D. J.

X. Chen, C. Zhang, D. J. Webb, K. Kalli, and G. D. Peng, “Highly sensitive bend sensor based on Bragg grating in eccentric core polymer fiber,” IEEE Photonics Technol. Lett. 22(11), 850–852 (2010).
[Crossref]

Wei, H.

Wu, Y.

Y. Gong, T. Zhao, Y. J. Rao, and Y. Wu, “All-fiber curvature sensor based on multimode interference,” IEEE Photonics Technol. Lett. 23(11), 679–681 (2011).
[Crossref]

Xiong, L.

Xu, B.

Xue, X.

Yan, P.

Yang, X.

H. Gong, X. Yang, K. Ni, C. L. Zhao, and X. Dong, “An optical fiber curvature sensor based on two peanut-shape structures modal interferometer,” IEEE Photonics Technol. Lett. 26(1), 22–24 (2014).
[Crossref]

Ye, C. C.

Yu, H.

Yu, Y.

Yuan, L.

Zhang, C.

X. Chen, C. Zhang, D. J. Webb, K. Kalli, and G. D. Peng, “Highly sensitive bend sensor based on Bragg grating in eccentric core polymer fiber,” IEEE Photonics Technol. Lett. 22(11), 850–852 (2010).
[Crossref]

Zhang, H.

Zhang, L.

M. J. Gander, W. N. Macpherson, R. Mcbride, J. D. C. Jones, L. Zhang, I. Bennion, P. M. Blanchard, J. G. Burnett, and A. H. Greenaway, “Bend measurement using Bragg gratings in multicore fiber,” Electron. Lett. 36(2), 120–121 (2000).
[Crossref]

Zhang, S.

Zhang, W.

Zhang, Y.

Y. Jin, C. C. Chan, X. Dong, and Y. Zhang, “Temperature-independent bending sensor with tilted fiber Bragg grating interacting with multimode fiber,” Opt. Commun. 282(19), 3905–3907 (2009).
[Crossref]

Zhao, C. L.

H. Gong, D. N. Wang, B. Xu, K. Ni, H. Liu, and C. L. Zhao, “Miniature and robust optical fiber in-line Mach-Zehnder interferometer based on a hollow ellipsoid,” Opt. Lett. 40(15), 3516–3519 (2015).
[Crossref] [PubMed]

L. Niu, C. L. Zhao, H. Gong, Y. Li, and S. Jin, “Curvature sensor based on two cascading abrupt-tapers modal interferometer in single mode fiber,” Opt. Commun. 333(15), 11–15 (2014).
[Crossref]

H. Gong, X. Yang, K. Ni, C. L. Zhao, and X. Dong, “An optical fiber curvature sensor based on two peanut-shape structures modal interferometer,” IEEE Photonics Technol. Lett. 26(1), 22–24 (2014).
[Crossref]

Zhao, T.

Y. Gong, T. Zhao, Y. J. Rao, and Y. Wu, “All-fiber curvature sensor based on multimode interference,” IEEE Photonics Technol. Lett. 23(11), 679–681 (2011).
[Crossref]

Zhou, A.

Electron. Lett. (2)

M. J. Gander, W. N. Macpherson, R. Mcbride, J. D. C. Jones, L. Zhang, I. Bennion, P. M. Blanchard, J. G. Burnett, and A. H. Greenaway, “Bend measurement using Bragg gratings in multicore fiber,” Electron. Lett. 36(2), 120–121 (2000).
[Crossref]

H. J. Patrick, C. Chang, and S. T. Vohra, “Long period fiber gratings for structural bending sensing,” Electron. Lett. 34(18), 1773–1775 (1998).
[Crossref]

IEEE Photonics Technol. Lett. (4)

X. Chen, C. Zhang, D. J. Webb, K. Kalli, and G. D. Peng, “Highly sensitive bend sensor based on Bragg grating in eccentric core polymer fiber,” IEEE Photonics Technol. Lett. 22(11), 850–852 (2010).
[Crossref]

Y. Gong, T. Zhao, Y. J. Rao, and Y. Wu, “All-fiber curvature sensor based on multimode interference,” IEEE Photonics Technol. Lett. 23(11), 679–681 (2011).
[Crossref]

H. F. Chen, Y. Wang, and D. N. Wang, “Selectively infiltrated PCF for directional bend sensing with large bending range,” IEEE Photonics Technol. Lett. 27(5), 502–505 (2015).
[Crossref]

H. Gong, X. Yang, K. Ni, C. L. Zhao, and X. Dong, “An optical fiber curvature sensor based on two peanut-shape structures modal interferometer,” IEEE Photonics Technol. Lett. 26(1), 22–24 (2014).
[Crossref]

J. Lightwave Technol. (2)

Opt. Commun. (2)

Y. Jin, C. C. Chan, X. Dong, and Y. Zhang, “Temperature-independent bending sensor with tilted fiber Bragg grating interacting with multimode fiber,” Opt. Commun. 282(19), 3905–3907 (2009).
[Crossref]

L. Niu, C. L. Zhao, H. Gong, Y. Li, and S. Jin, “Curvature sensor based on two cascading abrupt-tapers modal interferometer in single mode fiber,” Opt. Commun. 333(15), 11–15 (2014).
[Crossref]

Opt. Express (2)

Opt. Lett. (5)

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 (8)

Fig. 1
Fig. 1 Schematic diagram of the fiber in-line MZI (a), and the microscope image (b).
Fig. 2
Fig. 2 Diagrams of the fabrication process.
Fig. 3
Fig. 3 Experimental setup (a), and four bending orientations (b).
Fig. 4
Fig. 4 (a) Spectral variations in 0° bending, (b) in 180° bending, (c) the diagram of concave bending, (d) the diagram of convex bending.
Fig. 5
Fig. 5 Frequency spectra in 0° bending (a), and in 180° bending (b).
Fig. 6
Fig. 6 Spectral variations in 90° bending (a), and in 270° bending (b).
Fig. 7
Fig. 7 Intensity variations in the four bending directions.
Fig. 8
Fig. 8 Temperature response of the proposed sensor.

Equations (4)

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

T= I 1 + I 2 +2 I 1 I 2 cos[2πΔ(nL)/λ]
λ m =2Δ(nL)/(2m+1)
S= λ m 2 /Δ(nL)
C=2d/( d 2 + L 2 )

Metrics