## Abstract

We demonstrated a two-dimensional vector-bending sensor by use of fiber Bragg gratings (FBGs) inscribed in a homogeneous seven-core fiber. Seven FBGs were simultaneously inscribed in each of all seven cores using a modified Talbot interferometer and a lens scanning method. The vector bending response of six outer-core FBGs was investigated at all 360° directions with a step size of 15°. The bending sensitivities of the six outer-core FBGs display six perfect '8'-shaped patterns in a polar-coordinate system. That is, they exhibit strong bending-direction dependence with a maximum sensitivity of 59.47 pm/m^{−1}. The orientation and amplitude of the vector bending can be reconstructed using measured Bragg wavelength shifts of any two off-diagonal outer-core FBGs. So, the six outer-core FBGs have 12 combinations for bend reconstruction, which can be averaged across multiple reconstructions to develop an accurate two-dimensional vector bending sensor. The average relative error was lower than 4.5% for reconstructed amplitude and less than 2.8% for reconstructed orientation angle *θ*. Moreover, the seven-core FBGs offer several advantages such as a compact structure, fabrication flexibility, and the temperature compensating ability of central-core FBG.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

## 1. Introduction

Vector bending sensors developed from optical fibers have been extensively investigated in recent years and have been implemented for a variety of applications, such as structural deformation, intelligent artificial limbs and mechanical engineering [1,2]. Vector bending sensors are usually divided into one- [3–10] and two-dimensional [11–14] sensors with different directional discrimination capabilities. One-dimensional bending sensors can only identify positive and negative directions by breaking cylindrical symmetry of the fiber. These include off-axis fiber Bragg gratings (FBGs) [3], eccentric FBGs [4,5], tilted FBGs [6], asymmetric long period fiber gratings (LPGs) [7–9], and lateral-offset Mach–Zehnder interferometers [1,10]. Two-dimensional bending sensors are usual constructed by combining two or more one-dimensional sensors in a particular alignment [11], such as two orthogonal LPGs [12] or orthogonal tilted FBGs [13]. However, orthogonal cascaded sensors require high precision alignment operations and can only identify limited axial directions. Additionally, two-dimensional bending sensors can also be produced by nesting multiple fibers grating together, which presents a significant packaging challenge [2,15,16].

Multicore fibers (MCFs) have developed rapidly in recent years due to exponential growth in data transmission requirements [17–19]. The use of vector bending sensors based on fiber gratings (FBGs or LPGs) in various MCFs has also been increasing, as the well-defined spatial distribution of different cores produces differential responses to fiber bend [20–27]. For instance, a one-dimensional bending sensor was produced by inscribing an FBG in one core of a twin-core few-mode fiber [22]. A two-dimensional bending sensor based on LPGs has also been proposed in three-core fibers [23]. There have been reports of vector bending sensors based on seven-core FBGs [25], tilted FBGs [26] and LPGs [27]. However, conventional method for inscribing MCF-based gratings requires focusing a laser beam on one core for inscribing the first grating and then rotating the MCF by a certain angle for inscribing another grating on next core [27]. This method is always inefficient and destructive to the quality of gratings. Furthermore, it should be noted that not all cores in a MCF have been utilized for bend sensing in previous studies [25,26]. Hence, the approaches which can utilize all sensing channel and improve the vector bending measurement accuracy are still in demand.

In this study, we demonstrate the use of FBGs in seven-core fiber for two-dimensional vector bend sensing. These FBGs were inscribed in a homogeneous seven-core fiber using a modified Talbot interferometer [28] with a perpendicular lens scanning method. This makes it convenient for inscribed high quality FBGs in all cores without multiple-exposure. Each FBG exhibited a different response to vector bending due to the regular hexagon distribution of each core. The vector bending response of six-outer-core FBGs was investigated experimentally. Bending sensitivities at varying orientations were measured radially for display in a polar-coordinate system, achieving a maximum sensitivity of 59.47 pm/m^{−1}. The bending sensitivities of outer-core FBGs along a same diagonal line were almost equivalent with opposite directions, for a given bending orientation. Bend orientation and curvature amplitude could then be reconstructed based on the spectral shifts of any two off-diagonal outer-core FBGs. There are 12 combinations which can be used to reconstruct curvature for seven-core fiber (6 outer cores). These can be averaged across multiple reconstructions to acquire a more accurate value. The average relative error is lower than 4.5% for reconstructed amplitudes and less than 2.8% for the orientation angle *θ*. Seven-core FBGs offer several advantages such as a robust structure, fabrication flexibility, and the ability of two-dimensional vector bend sensing.

## 2. FBGs inscription in a seven-core fiber

The homogeneous seven-core fiber used in our experiments was fabricated by YOFC (Wuhan, China). Figure 1(a) shows a microscope image of the cross-section of a seven-core fiber which composed six outer cores and a central core. These six outer cores are distributed in a regular hexagon. Each fiber core consists of two layers: an inner core and an intermediate layer. The intermediate layer has a lower refractive index and is used as a depressed cladding trench to ensure mode isolation between adjacent fiber cores. The diameters of the inner core and fiber cladding are 8 and 150 μm, respectively. The distance between adjacent fiber cores is ~42 μm. Prior to FBGs inscription, the seven-core fiber was H_{2}-loaded at 100 bar and 80 °C for 7 days to enhance its photosensitivity.

Figure 1(b) and 1(c) show the experimental configuration used for inscribing seven-core FBGs. The experimental setup is composed of a modified Talbot interferometer with a scanning lens. A uniform phase mask (Ibsen Photonics) with a period of 1069 nm, was designed for zero order suppression at 266 nm wavelength and used as a beam splitter. The ± 1th beams are then redirected to interfere in the fiber core by two rotation mirrors, and used for FBGs inscription. A short-focal-length cylindrical lens was positioned in front of the interference area and was used to increase the power density in this area. The period of the interference pattern (the grating period) can be determined by [28]:

where*λ*is the laser wavelength,

_{laser}*φ*is the rotation angle of the mirrors, and

*α*is the ray deviation angle for the + 1 and 0-order diffraction peaks located after the phase mask. In this study,

*α*is 14.408°. This approach is stable and allows for the inscription of FBGs with variable Bragg wavelengths applied in WDM system.

A CW laser source (Coherent, Verdi G-5W 532 nm) with a second harmonic generator (SHG, Coherent, model MBD) is used to produce an ultraviolet (UV) laser for FBG inscription. The laser beam has a 1/e^{2} Gaussian diameter of 4 mm, a power of 100 mW, and a wavelength of 266 nm. As shown in Fig. 1(b), the laser beam was focused onto the seven-core fiber using a cylindrical lens with a focal length of 25 mm. The focal width and Rayleigh length of the laser beam were calculated (using Gaussian beam optics) to be 2.11 and 13.23 μm, respectively. A perpendicular scanning was implemented for the cylindrical lens (i.e. along *z* axis shown in Fig. 1(b)), with a speed of 0.002 mm/s and and a scanning length of 0.2 mm, to ensure that FBG can be inscribed in all seven cores without multiple-exposure.

After FBGs inscription, the transmission and reflection spectra of the seven-core FBGs were measured using a broadband light source (BBS) together with an optical spectrum analyzer (OSA, Yokagawa AQ6370C) and two fan-in/out devices (YOFC). As shown in Fig. 2(a) and 2(b), seven FBGs were successfully inscribed into the seven cores of the MCF with similar Bragg wavelengths of λ_{B} = 1550.04, 1550.48, 1550.65, 1550.15, 1549.41, 1549.77, and 1550.2 nm, and resonance loss at λ_{B} of −7.18, −2.86, −9.58, −8.61, −4.87, −4.77, and −5.65 dB, respectively. It is worth noting that, the Bragg wavelengths of these FBGs are slightly different from each other. This should result from the uneven UV exposure formed by the focusing effect of the circular fiber cladding layer [29,30].

## 3. Two-dimensional vector bending experiments

We investigated two-dimensional bending response of the seven-core FBGs via the experimental setup shown in Fig. 3(a). Firstly, the seven-core fiber, which contained the seven-core FBGs, was spliced with a fan-in/out device and then connected with a multi-channel demodulator (B&A FT210-08) to measure its reflection spectra. The seven-core FBGs were then mounted on a pair of 3D translation stages by two rotary fiber holders (Newport model 466A-718). The bending curvature could be changed by moving the translation stages. In addition, the bending orientation could be changed by simultaneous rotating the two rotary fiber holders. As shown in Fig. 3(b) and 3(c), the bend orientation angle *θ* was defined as the included angle between the bending plane and the axis connecting core_{1} and core_{4} in the seven-core fiber. In case *θ* equals 0° or 360°, the bending orientation coincided with the core_{1} and core_{4} axis, and core_{1} was located on the outer side of the bent seven-core fiber. It is important to point out that the initial angle (*θ* = 0°) alignment of the MCF was performed simply by detecting its near-mode field patterns through a CCD camera. Finally, the FBG reflection spectra were recorded as bend measurements were conducted.

First, the curvature of the seven-core FBGs was set by adjusting the distance between two translation stages. Subsequently, the bending orientation of the seven-core FBGs was set by simultaneously adjusting the rotary fiber holders with a step of 15°. It should also be noted that fiber twisting should be avoided during bending measurements. The wavelength shifts in the reflection spectra were recorded for each FBG at various orientation angles.

When locates at the outer side of the bending seven-core fiber, the outer-core FBG will be stretched which results a shift to longer wavelengths (i.e. ‘red’ shift). On the contrary, when locates at the inner side, the outer-core FBG will be compressed which results in a shift to shorter wavelengths (i.e. ‘blue’ shift). However, tiny bend-induced strain applied to the central-core FBG (i.e. core_{7}) when the seven-core fiber is bend, which makes its insensitive to bending [19]. Thus, the central-core FBG can be used to compensate temperature-induced wavelength shift, which overcomes the cross-sensitivity problem between bend and temperature in the bend sensing applications [25].

Results for two FBGs along the same diagonal line (i.e. FBG_{1} and FBG_{4}) are shown in Figs. 4(a) and 4(b) for increasing curvature. A linear fit was applied to all shifts in the Bragg wavelength at given angles *θ*, with the slope representing bend sensitivity. Figures 4(c) and 4(d) show Bragg wavelength shifts for FBG_{1} and FBG_{4} with increasing orientation angles. All shifts for a given curvature show good agreement with sinusoidal behavior [22]. As shown in Fig. 4(a), FBG_{1} had the highest positive sensitivity (59.47 pm/m^{−1}) at 0° and the highest negative sensitivity (−55.49 pm/m^{−1}) at 180°. However, FBG_{1} had the lowest sensitivity approaching to zero at 90° and 270°. In contrast, as shown in Fig. 4(b), FBG4 had the highest negative sensitivity (−56.34 pm/m^{−1}) at 0° and the highest positive sensitivity (55.49 pm/m^{−1}) at 180°. The bend sensitivity of FBG_{4} reached a minimum and approached zero for *θ* equal to 90° and 270°. Above all, the results reveal that the bend sensitivities of two outer-core FBGs along a same diagonal line have a similar amplitude and opposite directionality.

Bend sensitivities were obtained from the linear fits for FBG_{1} and FBG_{4} at different orientations and are displayed in polar coordinates in Fig. 5. Strong angular dependence of the bending response was achieved and two perfect '8'-shaped patterns are clearly visible. The sensitivity of FBG_{1} was positive during stretching when the bending orientation angle was in the range of 270°–0°–90°. In contrast, the sensitivity was negative during compression while in the range of 90°–180°–270°. The bend sensitivity of FBG_{1} achieved its maximum value for angles equal to 0° and 180° (i.e., the bend direction along the diagonal line of core_{1} and core_{4}), while reached a minimum and approached zero in the case of *θ* equal to 90° and 270° (i.e., the bend direction perpendicular to the diagonal of core_{1} and core_{4}). Moreover, at a same bend orientation, the sensitivity amplitude of FBG_{4} is very close to that of FBG_{1} and the direction is completely opposite. There are slight differences in sensitivity amplitudes of these two FBGs, which may be due to fine measurement errors. The two substantially coincident '8'-shaped patterns suggest the seven-core fiber maintains good circular symmetry during bending. The angular-dependent bending sensitivity of these seven-core FBGs supports their potential for use in vector bend sensing.

Furthermore, the bending responses of the other four outer-core FBGs (i.e. FBG_{2}, FBG_{3}, FBG_{5} and FBG_{6}) were analyzed. As shown in Fig. 6, there are six '8'-shaped patterns corresponding to the six outer-core FBGs. Each '8'-shaped pattern includes two maxima and two minima. Maximum sensitivities were achieved when the bending axis was coincides with the FBG plates, while minimum sensitivities occurred with the bending axis in the orthogonal direction. Similarly, the two FBGs along a same diagonal line have almost the same bending sensitivities and opposite directions. The maximum positive sensitivity for each outer-core FBG was 59.47, 57.35, 57.08, 55.49, 56.28, and 57.13 pm/m^{−1} (K_{1}, K_{2}, K_{3}, K_{4}, K_{5}, and K_{6}), with corresponding azimuths of 0°, 60°, 120°, 180°, 240°, and 300°, respectively. This sensitivity of each FBG varied slightly due to the differences in fabrication processes and embedded sensor depths. Two-dimensional curvature reconstruction could then be achieved during vector bend solving using the maximum sensitivity of each FBG (K_{1}, K_{2}, K_{3}, K_{4}, K_{5}, and K_{6}) and the regular hexagon geometric relationship between individual cores.

## 4. Curvature reconstruction

In order to reconstruct the orientation and amplitude of the bending vector $\stackrel{\u20d7}{R}$, we assumed the cross section of the seven-core fiber maintained a circular shape. The Bragg wavelength shift Δ*λ* of each FBG is the first-hand data that can be measured during bending measurements. From the relationship *R = Δλ/S* (*S* is the bend sensitivity come from Fig. 6) [2], the vector components $\overrightarrow{{r}_{n}}$ of the bending vector $\stackrel{\u20d7}{R}$ projected on the six outer-core FBGs can be expressed as:

*n =*1, 2, …, 6. Subsequently, the bending vector $\stackrel{\u20d7}{R}$ could be reconstructed from these vector components $\overrightarrow{{r}_{n}}$ using geometric positional relationship between these FBGs in the seven-core fiber. As shown in Figs. 7, the bending vector $\stackrel{\u20d7}{R}$ was projected on three diagonal lines, in four different quadrants. Note that, in theory, the bending components of two outer-core FBGs along a same diagonal line are equal in amplitude but in opposite directions ($\stackrel{\u20d7}{{r}_{1}}=-\stackrel{\u20d7}{{r}_{4}},\stackrel{\u20d7}{{r}_{2}}=-\stackrel{\u20d7}{{r}_{5}},$ $\stackrel{\u20d7}{{r}_{3}}=-\stackrel{\u20d7}{{r}_{6}}$). Actually, their obtained amplitudes vary slightly due to some fine measurement errors. It is also worth noting that the orientation and amplitude of the bending vector $\stackrel{\u20d7}{R}$ could be reconstructed based on the spectra shifts of any two off-diagonal outer-core FBGs. This theoretical analysis can be extended to different core combinations using the corresponding regular hexagon geometric relationships between the positions of each core. So, there are 12 combinations which can be used to reconstruct curvature for seven-core fibers (6 outer cores). They can be averaged across multiple reconstructions to achieve a more accurate value.

For example, in quadrant I, as shown in Fig. 7(a), $\stackrel{\u20d7}{{r}_{1}}$, $\stackrel{\u20d7}{{r}_{2}}$, and $\stackrel{\u20d7}{{r}_{3}}$ were the components of the bending vector $\stackrel{\u20d7}{R}$ projected onto three diagonal lines, respectively. According to Eq. (2), $\stackrel{\u20d7}{{r}_{1}}$, $\stackrel{\u20d7}{{r}_{2}}$, and $\stackrel{\u20d7}{{r}_{3}}$ could be calculated from the specific Bragg wavelength shifts $\stackrel{\u20d7}{{\text{\Delta \lambda}}_{\text{n}}}$. And then, using the regular hexagon geometric relationship between these FBGs, the orientation and amplitude of bending vector $\stackrel{\u20d7}{R}$ can be calculated using any two of the three components. So that, there are 3 combinations (i.e. ($\stackrel{\u20d7}{{r}_{1}}$, $\stackrel{\u20d7}{{r}_{2}}$), ($\stackrel{\u20d7}{{r}_{1}}$, $\stackrel{\u20d7}{{r}_{3}}$) and ($\stackrel{\u20d7}{{r}_{2}}$, $\stackrel{\u20d7}{{r}_{3}}$)) for reconstruct $\stackrel{\u20d7}{R}$ which can be expressed as follows:

*y*

_{1},

*y*

_{2}, and

*y*

_{3}can be expressed as: The corresponding orientation angle

*θ*can be determined by:

We tested the reconstruction performance of seven-core FBGs using a set of sampled data. For a set of given conditions ($\left|\stackrel{\u20d7}{R}\right|=6.095,\text{}\theta =30\xb0$), the measured Bragg wavelength shifts (Δλ_{n}) of the six outer-core FBGs were −0.324, −0.325, −0.005, 0.302, 0.311, and 0.002 nm, respectively. The curvature components $\stackrel{\u20d7}{{\text{r}}_{\text{n}}}$ for these FBGs are calculated by using Eq. (2) as −5.446, −5.661, −0.088, 5.430, 5.525 and 0.034 m^{−1}, respectively. The curvature $\left|\stackrel{\u20d7}{R}\right|$ can be reconstructed using Eq. (3) to Eq. (7), as shown in Table 1.

The averaged reconstruction results of 12 different combinations (6.373 m^{−1}, 30.84°) was very close to the actual curvature and bend direction (6.095 m^{−1}, 30°). The average relative error was lower than 4.5% for reconstructed amplitudes and less than 2.8% for the orientation angle *θ*. These relative errors were lower than prior studies based on seven-core fiber [25,31]. Moreover, it should be noted that the averaged values obtained by multiple reconstructions can counteract measurement errors and provide more accurate results. Subsequently, we used this method to perform three sets of curvature reconstruction in different quadrants.

It could be seen clearly from Table 2 that the seven-core FBGs can be used as a two-dimensional vector bending sensor to reconstruct the orientation and curvature of bending vectors, with accurate accordance values. For a given orientation angle *θ*, larger curvatures will result in smaller relative reconstruction errors. However, reconstructions of the orientation angle did not show a specific tendency.

## 5. Conclusion

We have proposed and demonstrated a two-dimensional bend sensor utilizing FBGs which were inscribed in a homogeneous seven-core fiber using a modified Talbot interferometer with a perpendicular lens scanning method. The bending responses of six outer-core FBGs were investigated in all 360° directions with a step size of 15°. Strong angular dependences were observed in the bend sensitivities of outer-core FBGs, with a maximum sensitivity of 59.47 pm/m^{−1}. The orientation and amplitude of curvature could be reconstructed using the acquired Bragg wavelength shifts and the regular hexagon geometric relationship between each core. For seven-core fibers, there are 12 combinations that can be used to reconstruct curvature. For a specific set of conditions curvature ($\left|\stackrel{\u20d7}{R}\right|=6.095,\text{}\theta =30\xb0$), the reconstructed average value of 12 different combinations was (6.373 m^{−1}, 30.84°), with a relative error of 4.5% for amplitudes and 2.8% for the orientation angle *θ*. These seven-core fiber-based FBGs are capable of two-dimensional vector bend sensing and have significant potential for intelligent artificial limb applications.

## Funding

National Natural Science Foundation of China (NSFC) (61875128, 61505120, 61425007, 61635007); Natural Science Foundation of Guangdong Province (2017A010102015, 2015B010105007, 2014A030308007); Science and Technology Innovation Commission of Shenzhen (JCYJ20170302154614941, JCYJ20170302143105991, JCYJ20170412105604705, JCYJ20160427104925452, JCYJ20160307143716576); China Postdoctoral Science Foundation (2017M612720, 2016M600669), Research Funding from Shenzhen University (2017019, 2016030), and Development and Reform Commission of Shenzhen Municipality Foundation.

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