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Highly sensitive vector curvature sensor based on a triple-core fiber interferometer

Shaoxian Zhang, Ai Zhou, Huiyong Guo, Yujia Zhao, and Libo Yuan

Open Access Open Access

Abstract

A highly sensitive vector curvature sensor based on a triple-core fiber (TCF) interferometer is proposed and demonstrated. The TCF interferometer is composed of a piece of TCF that is fusion spliced to a standard single mode fiber (SMF). A taper is fabricated at the TCF near the TCF-SMF junction to couple the light from the input SMF into the three cores of the TCF and recouple the reflected light from the end of the TCF back to the SMF, which forms a three-beam Michelson interferometer in the TCF. Such a three-beam interferometer has the unique characteristic that its sensitivity is greatly affected by the optical path differences (OPD) and light intensities of the light transmitted in the cores of the TCF. As a result, choosing a TCF with proper refractive index differences between three cores or designing a proper splitting ratio of the TCF taper can effectively enhance the sensitivity of the TCF interferometer. The bending responses of the TCF interferometer were tested in the curvature range of 0-1.305 m−1. Experimental results show that the curvature sensitivities at the opposite bending directions along the cores’ connection are about 91.61 nm/m−1 and -95.22 nm/m−1, respectively.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

The optical fiber sensors based on various principles and structures have attracted the attention of researchers [1–4]. In particular, the optical fiber vector curvature sensors have been widely used in the fields of structural health monitoring, robotics, astronautics, and automotive industry due to the advantages such as compact size, remote monitoring ability and immunity to electromagnetic interference [5,6]. Various configurations based on optical fibers were developed for vector curvature sensing, and the most frequently employed configurations are fiber grating structures [6–17] and inline fiber interferometers [18–23]. For the grating-based sensors, the identification to the bending direction was generally achieved by inscribing gratings in asymmetrical fibers such as eccentric core fibers (ECF) [6,7], multi-core fibers [8–11], D-shaped cladding fiber [12], holey fibers [13] and photonic crystal fibers [14,15] or by introducing asymmetrical refractive index (RI) distribution caused by CO2 laser [16] or femtosecond laser [17] in general fibers. These grating-based curvature sensors have merits of compact size and high production repeatability. However, the sensitivities of the structures based on fiber Bragg gratings are relatively low, and those based on long period gratings have the problem of mode conversion which limits the measurement range of the sensor during bending measurement. In-fiber interferometers, due to the features of easy fabrication and high sensitivity, were favored by researchers for curvature sensing. The most common structures are the core-cladding mode interferometers [18,19], the dual-core fiber (DCF) based interferometers [20–25] and multi-core fiber (MCF) based interferometers [26,27]. Generally, the interferometers based on the core-cladding interference are sensitive to external refractive index due to the cladding-modes involved in the interference. The DCF based interferometers have better bending responses because the interference takes place between modes in different cores where at least one core is offset from the fiber axis. The curvature sensitivity of the DCF based interferometers are determined by the distance between the cores and the axis of the fiber. The larger the core offset, the higher the curvature sensitivity. For some other DCF or MCF interferometers, the light cannot be transmitted independently in their respective core and energy coupling would happen between the adjacent cores [20–22,24,25–27].

In this paper, we propose a three-beam Michelson interferometer (MI) based on a triple-core fiber (TCF) whose core transmits the light independently for vector curvature measurement. Different from the DCF-based interferometer, the curvature sensitivity of the TCF based MI depends not only on the distance of the core from the fiber axis, but also on the optical path differences (OPD) and the light intensity ratios of the three cores. Therefore the sensitivity of the TCF based MI can be adjusted in a large range by changing the RI of the TCF and the splitting ratio of the TCF taper. For the TCF employed in the present work, the three cores of the TCF were distributed in a straight line with one core just in the axis of the fiber. The RI of the centric core was designed lower than those of the other cores to obtain proper OPDs between the three interference beams. The RIs of the two eccentric cores were designed to be nearly the same in order to get a uniform interference spectrum similar to that of a two-beam interferometer.

2. Sensor fabrication and principle

The schematic configuration of the TCF based MI is shown in Fig. 1(a) and the cross-section image of the TCF is displayed in Fig. 1(b). The TCF consists of three cores with diameter of ∼8 µm and a cladding with a diameter of 125 µm. The three cores of the TCF are distributed in a straight line. One core (centric core) is located along the axis of the fiber and the other two ones (eccentric cores) are 24 µm away from the centric core. The RI distribution of the TCF was measured by a RI profiler (S14, Photon Kinetics, Inc). The RI difference between the two eccentric cores is very small, which cannot be detected by the profiler. The RI difference between the centric core and the two eccentric cores is approximately 0.00016. The difference between refractive indices of the centric core and cladding is about 0.004.

 figure: Fig. 1.

Fig. 1. (a) The schematic configuration of the TCF based MI interferometer. (b) The cross-section image of the triple-core fiber.

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The TCF-based MI was fabricated as follows. First, a segment of TCF was fusion spliced to a conventional SMF where the core of the SMF was aligned with centric core of the TCF by using a commercial fiber fusion splicer (Fujikura, FSM-60S). Then the other end of the TCF was cut by using a fiber cleaver to form a reflective surface. Later, the TCF near the SMF-TCF splice junction (about 0.5 cm away from the junction) was tapered by heating and stretching in a flame to couple part of the light from the centric core into the two eccentric cores. The light in the three cores were reflected by the end surface of the TCF and recoupled back into the centric core through the taper, forming a three-beam Michelson interferometer. During the tapering process, the reflected light was monitored in real time with an optical spectrum analyzer (OSA). The tapering was finished when the contrast of the interference spectrum reached to about 10 dB. At last, the fiber was cut again to obtain an interferometer with design length.

When a bend was applied on the TCF in any direction that is not perpendicular to the connection of the three cores, each core has quite different response to the bend: the two cores on the opposite sides are stretched and compressed respectively, while the core in the middle keeps unchanged.

MI with a TCF length of 2 m was fabricated to measure the RI difference between every two cores. Figure 2(a) shows the interference spectrum from the central core of the TCF. For comparison, the spectrum before tapering is also presented in the figure. From the figure, it is apparent that there is no coupling between the three cores before tapering (blue line). Because the cutting surface of the TCF is not fully perpendicular to the axis of the fiber, the energy difference between spectra is generated. The Fourier transformation of the spectrum in the frequency domain is presented in Fig. 2(b). From Fig. 2(b) we can see that there are three frequency components, which are 0.021 nm−1, 0.261 nm−1 and 0.279 nm−1, respectively. The frequency of 0.021 nm−1 corresponds to the RI difference of the two eccentric cores, and 0.261 nm−1 and 0.279 nm−1 are generated from the RI differences between the centric core and the two eccentric cores, respectively. In addition, there exists a difference between the two peak values in intensity, which is because of the energy difference of the light transmitting in the two eccentric cores.

 figure: Fig. 2.

Fig. 2. (a) Transmission spectrum of the MI based on TCF with no taper (blue line) and with taper (black line) (b) is spatial spectrum with taper.

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Generally, the spatial frequency of the interferometer can be expressed as

$${\boldsymbol{f}} = \frac{{2\varDelta n_{eff}^{i,j}L}}{{{\lambda ^2}}}$$
where $\varDelta n_{eff}^{i,j}$ is the effective RI difference between two core modes. L is the distance from the taper to the reflective surface. $\lambda $ is the operation wavelength. The effective RI differences of the three core modes can be calculated with the formula.

The light from the lead-in SMF enters the middle core of TCF, and is divided into three beams after passing through the TCF taper. The beams transmitting along the three cores are then reflected by the end surface of the TCF and recoupled back to the lead-in SMF through the TCF taper. As a result, a three-beam in-line fiber MI is realized.

According to the interference theory, the total intensity of the output of the TCF-based MI can be expressed as

$$I = {|{\widetilde a} |^2} + {|{\widetilde b} |^2} + {|{\widetilde c} |^2} + 2\widetilde a\widetilde b\, cos\,{\phi _{12}} + 2\widetilde b\widetilde c\, cos\,{\phi _{23}} + 2\widetilde a\widetilde c\, cos\,{\phi _{31}}$$
where $\tilde{a}$, $\tilde{b}$ and $\tilde{c}\; $are the amplitude of the core 1, core 2 and core 3, respectively, and ${\phi _{12}}$, ${\phi _{23\; }}$and ${\phi _{13}}$ are the phase differences between core 1 and core 2, core 2 and core 3, core 3 and core 1, respectively. The phase differences are
$${\phi _{ij}} = \frac{{2\pi {L_b}\varDelta n_{eff}^{i,j}}}{\lambda } + \frac{{2\pi (L - {L_b})\varDelta n_{eff}^{i,j}}}{\lambda }$$
where λ is the operating wavelength, $\varDelta n_{eff}^{i,j}$ the effective RI difference between two core modes, L is the distance from the taper to the reflective surface, Lb is the length of the fiber that involved in bending. When a bend is applied to the TCF, the effective RI of the two eccentric core modes changes due to the elastic-optical effect. At the bending direction of 0° or 180° as shown in Fig. 3(b), the effective RIs of two eccentric core increase and decrease with the curvature increase, respectively. The effective RI of the eccentric cores at bending state can be described as [28]
$$n_{eff}^i = {n_i}(1 + Ch\, cos\,\theta )$$
where i = 1, 2, 3, C is the curvature, h is the distance between the core and the fiber central axis, θ is the rotation angle of the TCF relative to the neutral plane as shown in Fig. 3(a).

 figure: Fig. 3.

Fig. 3. The schematic diagram of (a) the cross-section of triple-core fiber and (b) lateral curvature.

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Because the centric core exists in the neutral plane of the bending, the effective RI of the centric core mode does not change with bending. The two eccentric cores are at the opposite sides of the centric core. Therefore the effective RIs of the two eccentric core modes will respectively increase and decrease with bending. The effective RI differences between any two core modes at the bending direction can be describe as

$$\left\{ \begin{array}{l} \varDelta n_{eff}^{1,2} = {n_1}(1 + Ch\, cos\,\theta ) - {n_2}\\ \varDelta n_{eff}^{2,3} = {n_2} - {n_3}(1 - Ch\, cos\,\theta )\\ \varDelta n_{eff}^{3,1} = {n_3}(1 - Ch\, cos\,\theta ) - {n_1}(1 + Ch\, cos\,\theta ) \end{array} \right.$$
From Eq. (2) to Eq. (5), it can be deduced that the interference spectrum will shift with bending due to the variation of the effective RIs of the eccentric core modes. For the three-beam interference, it is difficult to obtain the specific expression of the wavelength of the interference peak, just like in the case of two-beam interference. The curvature sensitivity of the TCF-based MI can be approximately expressed as
$$\begin{aligned}{S_1} &= \left|{\frac{{d\lambda }}{{dC}}} \right|\approx \left|{\frac{{{{\partial I} \mathord{\left/ {\vphantom {{\partial I} {\partial C}}} \right.} {\partial C}}}}{{{{\partial I} \mathord{\left/ {\vphantom {{\partial I} {\partial \lambda }}} \right.} {\partial \lambda }}}}} \right|\\ &= \left|{\frac{{ - \lambda {L_b}{n_1}h}}{{L({n_1} - {n_2}) + {L_b}Ch}} \bullet \frac{{\widetilde a\widetilde b\, sin\,{k_1} + \widetilde b\widetilde c\, sin\,{k_2} + 2\widetilde a\widetilde c\, sin\,{k_3}}}{{\widetilde a\widetilde b\, sin\,({A_1} + {k_1}) + \frac{{{A_2} + {k_2}}}{{{A_1} + {k_1}}}\widetilde b\widetilde c\, sin\,({A_2} + {k_2}) + \frac{{{k_3}}}{{{A_1} + {k_1}}}2\widetilde a\widetilde c\, sin\,{k_3}}}} \right|\end{aligned}$$
where
$$\left\{ \begin{array}{l} {A_1} = \frac{{2\pi (L - {L_b})({n_1} - {n_2})}}{\lambda }\\ {A_2} = \frac{{2\pi (L - {L_b})({n_2} - {n_3})}}{\lambda } \end{array} \right.$$
$$\left\{ \begin{array}{l} {k_1} = \frac{{2\pi {L_b}}}{\lambda }({n_1} + {n_1}Ch - {n_2})\\ {k_2} = \frac{{2\pi {L_b}}}{\lambda }({n_2} - {n_1} + {n_1}Ch)\\ {k_3} = \frac{{2\pi {L_b}}}{\lambda }(2{n_1}Ch) \end{array} \right.$$
From Eqs. (6)– (8), both the first and second term in Eq. (6) contain L and Lb. The effect of L and Lb on the sensitivity is mainly determined by the first term because the two parameters in the second term are in the trigonometric function. Therefore, we deduce that the sensitivity of the sensor increases with the increase of Lb and decrease of L.

In order to compare with the sensitivity of the two-beam interferometer, we also calculated the bending sensitivity of the two-beam interferometer. The two-beam interference model is based on a twin-core fiber that contains a centric core and an eccentric core. The parameters of the twin-core fiber are same as those of the TCF used in the present work. The same calculation method was employed and the calculated sensitivity of the DCF- based interferometer is

$${S_2} = \left|{\frac{{ - \lambda {L_b}{n_1}h}}{{L({n_1} - {n_2}) + {L_b}Ch}}} \right|$$
Comparing Eq. (6) and Eq. (9), it is found that the curvature sensitivity of the TCF-based MI can be modulated by that of the DCF- based interferometer. The modulation parameter F is
$$F = \frac{{{S_1}}}{{{S_2}}} = \left|{\frac{{\widetilde a\widetilde b\, sin\,{k_1} + \widetilde b\widetilde c\, sin\,{k_2} + 2\widetilde a\widetilde c\, sin\,{k_3}}}{{\widetilde a\widetilde b\, sin\,({A_1} + {k_1}) + \frac{{{A_2} + {k_2}}}{{{A_1} + {k_1}}}\widetilde b\widetilde c({A_2} + {k_2}) + \frac{{{k_3}}}{{{A_1} + {k_1}}}2\widetilde a\widetilde c\, sin\,{k_3}}}} \right|$$

3. Experiments and results

The schematic of the experimental setup for the vector curvature measurement is shown in Fig. 4. A MI sensor with TCF length of 17 cm was employed in the experiment. The purpose of choosing such a length is to accumulate sufficient optical path difference (OPD) to obtain an interference spectrum with a suitable wavelength separation. From the perspective of fiber length, the sensor is not compact. Using fiber with larger RI difference between cores (can be reduced to 4 cm length with RI difference of 0.00068) or employing broader band light source can reduce the size of the sensor. At the tapered coupling zone, the diameter of the cores is about 5.5 µm, the distance between adjacent cores is 19 µm and the length of the taper is about 4000 µm.

 figure: Fig. 4.

Fig. 4. The schematic of the experimental setup for vector curvature sensing.

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Because the length of the TCF-based MI is beyond the length of the bending device, only part of the MI was bended in the experiment. The TCF was held by a rotatable fiber holder and the TCF length of about 3.5 cm was suspended, which determined by the distance between the rotatable clamp and the metal sheet. The metal sheet was clamped on a transmission stage to press the end of the suspended TCF. The suspended TCF was bended by moving the metal sheet down. The rotatable clamp with rotation range of 0°-360° and division value of 5° was employed for adjusting the bending direction of the sensing MI through rotating the fiber. The curvature of the bended TCF can be calculated by the formula $C = {{2d} \mathord{\left/ {\vphantom {{2d} {({d^2} + L_b^2}}} \right.} {({d^2} + L_b^2}})$, where d is the displacement of the center of the curved fiber, and Lb is the distance between the rotatable clamp and the metal sheet. In this experiment, Lb was about 3.5 cm and the displacement of d was increased by 0.02 mm per step. The light source used in the experiment had a spectral range of 1480 nm-1640 nm and the interference spectrum of the MI sensor was monitored by an optical spectrum analyzer (OSA Yokogawa AQ6370C).

The vector curvature characteristics of the sensor based on the TCF were tested at four bending directions (0°, 90°, 180° and 270°) in the curvature range of 0-1.305 m−1. Two dips at wavelengths of 1490 nm and 1618 nm were monitored during the bending process. In order to clearly visualize the spectral shift of the raw measurements, only representative spectra corresponding to the small curvatures of 0-0.163 m−1 and the large curvatures of 1.142-1.305 m−1 are displayed. Figure 5 shows the spectrum shift with the increase of the curvature at bending directions of 0°, 90°, 180° and 270°. From the figure, we can see that the interference spectrum proceeds a red shift at the direction of 0° and a blue shift at the direction of 180°. The red- or blue- shift of the transmission spectra is due to the increase or decrease of the optical path length of the eccentric cores. For the bending directions of 90° and 270°, the transmission spectrum of the core was nearly unchanged. This is because the three cores of the MI are just in the neutral plane of the bending in the two directions, which means that there is no change in the optical path difference between any two cores.

 figure: Fig. 5.

Fig. 5. The interference spectrum shift of the MI based on the TCF with different curvature at (a)-(b) 0°, (c)-(d) 90°, (e)-(f) 180° and (g)-(h) 270°.

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The wavelength shifts versus curvature at bending directions of 0°, 90°, 180° and 270° are plotted in Fig. 6. It can be seen apparently that the curvature sensitivity is directly related to the curvature direction and the wavelength shifts of the two dips are linearly dependent on the curvature. At the bending directions of 0° and 180°, the spectrum respectively suffers a red and blue shift with the increase of the curvature, and the corresponding curvature sensitivities are 91.61 nm/m−1 and -95.22 nm/m−1, respectively. While at the bending directions of 90° and 270°, the wavelengths of the dips are nearly unchanged. The insensitive phenomenon at the bending directions of 90° and 270° is because of the existence of three cores in the neutral plane of the bending and the length of the cores is unchanged with the bend. The sensitivity reaches the maximum at the bending directions of 0° and 180° (the connected direction of the three cores), and the signs of the sensitivities are opposite, which is due to the lengthened and compressed of the opposite eccentric cores. The small difference between the absolute values of the two sensitivities is mainly due to the small deviation of the manually adjusted rotatable clamp. In Fig. 6 the curves are linear and have the advantages of easy calibration of sensing relation and high precision of measurement.

 figure: Fig. 6.

Fig. 6. The wavelengths shift of dip with different curvature at (a) 0° and 90°, (b) 180° and 270°. (c) The wavelength shift with the different curvature at 0°, 90°, 180° and 270°.

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The effect of the length of the TCF on the sensitivity of the structure was also experimentally investigated. A sample with a 30 cm long TCF was fabricated and tested. First, the bending response of the structure was measured with a bending length of 3.5 cm. Then the TCF was cut to 26.5 cm, 23.5 cm and 19 cm in sequence and the bending responses at these lengths were measured separately with the same bended length of 3.5 cm. The obtained sensitivities referring to the length of the TCF are presented in Fig. 7. From the figure, it can be seen that the sensitivity of the TCF interferometer decreases with the increase of the TCF length. This agrees well with the theoretical prediction deduced from Eq. (5).

 figure: Fig. 7.

Fig. 7. Effect of the total length of the TCF on the sensitivity of the TCF interferometer with a fixed bended length.

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Then the effect of the bended length of the TCF on the sensitivity of the structure was studied. An interferometer with a 19 cm long TCF was employed for the test. The bending response of the TCF-based MI was measured under the bended lengths of 2.5 cm, 3.5 cm, 4.5 cm and 5.5 cm, respectively. Experimental results are shown in Fig. 8. It is apparent that the sensitivity of the TCF interferometer increases with the increase of the bended length. This is also consistent with the previous derivation.

 figure: Fig. 8.

Fig. 8. Effect of the bended length of the TCF on the sensitivity of the TCF interferometer with a fixed TCF length.

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Afterwards, the influence of the splitting ratio of the TCF on the curvature sensitivity of the TCF-based interferometer was researched. Five samples with different splitting ratio were fabricated for the research. The results are shown in Table 1, in which Pe1, Pc and Pe2 denote the power in the eccentric core 1, the centric core and the eccentric core 2, respectively. Because the two eccentric cores have the nearly same RI and are symmetrically distributed in the TCF, the power in the two cores is very close. In order to present a more intuitive expression, the splitting ratio in the TCF was replaced by the ratio of the power in the centric core to the total power in the two eccentric cores. From the data in Table 1, it can be seen that the lowest sensitivity arises when the splitting ratio is close to 1:1:1. The sensitivity increases either in the case of Pe>Pc or Pc>Pe.

Tables Icon

Table 1. Effect of Splitting Ratio of the TCF on the Curvature Sensitivity of the TCF-Based MI

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Table 2 lists comparisons among the fiber-based curvature sensing. Compared with the vector curvature sensor based on fiber grating and inline fiber interferometer, the proposed sensor is characterized by multi-directional bending sensitivity measurement and a higher curvature sensitivity.

Tables Icon

Table 2. Comparisons Between the Sensors for Curvature Measurement

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Finally, the temperature characteristics of the TCF- based MI was monitored in the temperature range of 30℃-100℃ with a step of 10℃. The wavelength of the two dips at different temperature is plotted in Fig. 9. The wavelengths of the two dips move toward the shorter wavelength as the temperature increases and the temperature sensitivities of the two dips are 85.71 pm/℃ and 77.86 pm/℃, respectively.

 figure: Fig. 9.

Fig. 9. (a) The interference spectrum shift of the MI based on the TCF with different from at 30 °C to100 ℃. (b) The wavelength shift of two dips with different temperatures from 30 °C to 100℃.

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In order to eliminate the influence of temperature, the sensor can be connected to a fiber Bragg grating (FBG) for temperature compensation. The temperature of the experiment was determined by detecting the wavelength change of the peak of FBG. The bending sensing after adding temperature compensation is

$$\varDelta C = \frac{{\varDelta \lambda - \frac{{\varDelta {\lambda _{TC}}}}{{{S_{TC}}}}{S_T}}}{{{S_C}}}$$
where $\varDelta C$ is the change of curvature, ST and STC are the temperature sensitivities of sensor and FBG, respectively. SC is the curvature sensitivity of sensor. $\varDelta \lambda$ and $\varDelta {\lambda _{TC}}$ are wavelength variations of the sensor and the FBG transmission spectrum, respectively.

4. Conclusion

In this paper, we discussed and verified a vector curvature sensor based on TCF MI with a high sensitivity. The feature of the TCF- based MI is that the sensitivity of the structure can be adjusted by the optical path lengths of the cores of the TCF. The direction of curvature can be determined by detecting the wavelength shift direction. The experimental results show that the maximum curvature sensitivities of the TCF- based MI can reach 91.61 nm/m−1 at curvature direction of 0° and -95.22 nm/m−1 at the direction of 180°, and both values are higher than that of some DCF- based interferometers [22,23,25]; With the increase of the total length and bending length of the sensor, the sensitivity decreases and increases, respectively. In addition, the temperature sensitivities of the two dips are 85.71 pm/℃ and 77.86 pm/℃. This sensor has advantages such as high sensitivity, simple structure and easy fabrication, which makes it widely used in various fields.

Funding

National Natural Science Foundation of China (NSFC) (61535004, 61735009, 61827819); Guangxi project (AD17195074); National Defense Pre-Research Foundation of China (6140414030102).

References

1. Q. Wang and W. M. Zhao, “A comprehensive review of lossy mode resonance-based fiber optic sensors,” Opt. Laser Eng. 100, 47–60 (2018). [CrossRef]  

2. Y. Zhao, Q. L. Wu, and Y. N. Zhang, “Theoretical analysis of high-sensitive seawater temperature and salinity measurement based on C-type micro-structured fiber,” Sens. Actuators, B 258, 822–828 (2018). [CrossRef]  

3. N. Paliwal and Joseph John, “Design and modeling of highly sensitive lossy mode resonance-based fiber-optic pressure sensor,” IEEE Sens. J. 18(1), 209–215 (2018). [CrossRef]  

4. Q. Wang and W. M. Zhao, “Optical methods of antibiotic residues detections: A comprehensive review,” Sens. Actuators, B 269, 238–256 (2018). [CrossRef]  

5. A. V. Newkirk, J. E. A. Lopez, A. V. Benitez, J. Albert, R. A. Correa, and A. Schulzgen, “Bending sensor combining multicore fiber with a mode-selective photonic lantern,” Opt. Lett. 40(22), 5188–5191 (2015). [CrossRef]  

6. 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]  

7. J. Kong, A. Zhou, C. Cheng, J. Yang, and L. B. Yuan, “Two-Axis Bending Sensor Based on Cascaded Eccentric Core Fiber Bragg Gratings,” IEEE Photonics Technol. Lett. 28(11), 1237–1240 (2016). [CrossRef]  

8. G. M. H. Flockhart, W. N. MacPherson, J. S. Barton, J. D. C. Jones, L. Zhang, and I. Bennion, “Two-axis bend measurement with Bragg gratings in multicore optical fiber,” Opt. Lett. 28(6), 387–389 (2003). [CrossRef]  

9. 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 fibre,” Electron. Lett. 36(2), 120–121 (2000). [CrossRef]  

10. S. Wang, W. G. Zhang, L. Chen, Y. X. Zhang, P. C. Geng, Y. S. Zhang, T. Y. Yan, L. Yu, W. Hu, and Y. P. Li, “Two-dimensional microbend sensor based on long-period fiber gratings in an isosceles triangle arrangement three-core fiber,” Opt. Lett. 42(23), 4938–4941 (2017). [CrossRef]  

11. D. Barrera, I. Gasulla, and S. Sales, “Multipoint Two-Dimensional Curvature Optical Fiber Sensor Based on a Nontwisted Homogeneous Four-Core Fiber,” J. Lightwave Technol. 33(12), 2445–2450 (2015). [CrossRef]  

12. 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]  

13. Y. G. Han, G. Kim, K. Lee, S. B. Lee, C. H. Jeong, C. H. Oh, and H. J. Kang, “Bending sensitivity of long-period fiber gratings inscribed in holey fibers depending on an axial rotation angle,” Opt. Express 15(20), 12866–12871 (2007). [CrossRef]  

14. Z. H. He, Y. N. Zhu, and H. Du, “Effect of macro-bending on resonant wavelength and intensity of long-period gratings in photonic crystal fiber,” Opt. Express 15(4), 1804–1810 (2007). [CrossRef]  

15. 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]  

16. 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]  

17. Q. Zhou, W. G. Zhang, L. Chen, Z. Y. Bai, L. Y. Zhang, L. Wang, B. Wang, and T. Y. Yan, “Bending Vector Sensor Based on a Sector-Shaped Long-Period Grating,” IEEE Photonics Technol. Lett. 27(7), 713–716 (2015). [CrossRef]  

18. L. Y. Zhang, W. G. Zhang, L. Chen, T. Y. Yan, L. Wang, B. Wang, and Q. Zhou, “A fiber bending vector sensor based on M–Z interferometer exploiting two hump-shaped tapers,” IEEE Photonics Technol. Lett. 27(11), 1173–1176 (2015). [CrossRef]  

19. 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]  

20. S. Wang, W. Zhang, L. Chen, Y. Zhang, P. Geng, B. Wang, T. Yan, Y. Li, S. Wang, G. Zhang W, and L. Chen, “Bending vector sensor based on the multimode-2-core-multimode fiber structure,” IEEE Photonics Technol. Lett. 28(19), 2066–2069 (2016). [CrossRef]  

21. H. Qu, G. F. Yan, and M. Skorobogatiy, “Interferometric fiber-optic bending/nano-displacement sensor using plastic dual-core fiber,” Opt. Lett. 39(16), 4835–4838 (2014). [CrossRef]  

22. G. L. Yin, S. Q. Lou, W. L. Lu, and X. Wang, “A high-sensitive fiber curvature sensor using twin core fiber-based filter,” Appl. Phys. B 115(1), 99–104 (2014). [CrossRef]  

23. Y. Zhao, A. Zhou, H. Guo, Z. Zheng, Y. Xu, C. Zhou, and L. Yuan, “An Integrated fiber Michelson interferometer based on twin-core and side-hole fibers for multi-parameter sensing,” J. Lightwave Technol. 36(23), C1 (2018). [CrossRef]  

24. Y. Wu, L. Pei, W. X. Jin, Y. C. Jiang, Y. G. Yang, Y. Shen, and S. S. Jian, “Highly sensitive curvature sensor based on asymmetrical twin core fiber and multimode fiber,” Opt. Laser Technol. 92, 74–79 (2017). [CrossRef]  

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

26. G. Salceda-Delgado, A. Van Newkirk, J. E. Antonio-Lopez, A. Martinez-Rios, A. Schülzgen, and R. Amezcua Correa, “Compact fiber-optic curvature sensor based on super-mode interference in a seven-core fiber,” Opt. Lett. 40(7), 1468–1471 (2015). [CrossRef]  

27. J. Villatoro, A. V. Newkirk, E. A. Lopez, J. Zubia, A. Schülzgen, and R. A. Correa, “Ultrasensitive vector bending sensor based on multicore optical fiber,” Opt. Lett. 41(4), 832–835 (2016). [CrossRef]  

28. D. Marcuse, “Field deformation and loss caused by curvature of optical fibers,” J. Opt. Soc. Am. 66(4), 311–320 (1976). [CrossRef]  

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Figures (9)
Fig. 1.
Fig. 1. (a) The schematic configuration of the TCF based MI interferometer. (b) The cross-section image of the triple-core fiber.

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Fig. 2.
Fig. 2. (a) Transmission spectrum of the MI based on TCF with no taper (blue line) and with taper (black line) (b) is spatial spectrum with taper.

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Fig. 3.
Fig. 3. The schematic diagram of (a) the cross-section of triple-core fiber and (b) lateral curvature.

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Fig. 4.
Fig. 4. The schematic of the experimental setup for vector curvature sensing.

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Fig. 5.
Fig. 5. The interference spectrum shift of the MI based on the TCF with different curvature at (a)-(b) 0°, (c)-(d) 90°, (e)-(f) 180° and (g)-(h) 270°.

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Fig. 6.
Fig. 6. The wavelengths shift of dip with different curvature at (a) 0° and 90°, (b) 180° and 270°. (c) The wavelength shift with the different curvature at 0°, 90°, 180° and 270°.

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Fig. 7.
Fig. 7. Effect of the total length of the TCF on the sensitivity of the TCF interferometer with a fixed bended length.

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Fig. 8.
Fig. 8. Effect of the bended length of the TCF on the sensitivity of the TCF interferometer with a fixed TCF length.

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Fig. 9.
Fig. 9. (a) The interference spectrum shift of the MI based on the TCF with different from at 30 °C to100 ℃. (b) The wavelength shift of two dips with different temperatures from 30 °C to 100℃.

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Tables (2)

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Table 1. Effect of Splitting Ratio of the TCF on the Curvature Sensitivity of the TCF-Based MI

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Table 2. Comparisons Between the Sensors for Curvature Measurement

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Equations (11)

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f = 2 Δ n e f f i , j L λ 2
I = | a ~ | 2 + | b ~ | 2 + | c ~ | 2 + 2 a ~ b ~ c o s ϕ 12 + 2 b ~ c ~ c o s ϕ 23 + 2 a ~ c ~ c o s ϕ 31
ϕ i j = 2 π L b Δ n e f f i , j λ + 2 π ( L − L b ) Δ n e f f i , j λ
n e f f i = n i ( 1 + C h c o s θ )
{ Δ n e f f 1 , 2 = n 1 ( 1 + C h c o s θ ) − n 2 Δ n e f f 2 , 3 = n 2 − n 3 ( 1 − C h c o s θ ) Δ n e f f 3 , 1 = n 3 ( 1 − C h c o s θ ) − n 1 ( 1 + C h c o s θ )
S 1 = | d λ d C | ≈ | ∂ I / ∂ I ∂ C ∂ C ∂ I / ∂ I ∂ λ ∂ λ | = | − λ L b n 1 h L ( n 1 − n 2 ) + L b C h ∙ a ~ b ~ s i n k 1 + b ~ c ~ s i n k 2 + 2 a ~ c ~ s i n k 3 a ~ b ~ s i n ( A 1 + k 1 ) + A 2 + k 2 A 1 + k 1 b ~ c ~ s i n ( A 2 + k 2 ) + k 3 A 1 + k 1 2 a ~ c ~ s i n k 3 |
{ A 1 = 2 π ( L − L b ) ( n 1 − n 2 ) λ A 2 = 2 π ( L − L b ) ( n 2 − n 3 ) λ
{ k 1 = 2 π L b λ ( n 1 + n 1 C h − n 2 ) k 2 = 2 π L b λ ( n 2 − n 1 + n 1 C h ) k 3 = 2 π L b λ ( 2 n 1 C h )
S 2 = | − λ L b n 1 h L ( n 1 − n 2 ) + L b C h |
F = S 1 S 2 = | a ~ b ~ s i n k 1 + b ~ c ~ s i n k 2 + 2 a ~ c ~ s i n k 3 a ~ b ~ s i n ( A 1 + k 1 ) + A 2 + k 2 A 1 + k 1 b ~ c ~ ( A 2 + k 2 ) + k 3 A 1 + k 1 2 a ~ c ~ s i n k 3 |
Δ C = Δ λ − Δ λ T C S T C S T S C
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