Multicore fibers （MCFs）， containing more than one core within the same cladding， have attracted increasing attention in recent years. They are initially proposed to overcome the capacity limitation of current optical communication system based on single-core single-mode fibers by providing multiple physical channels^［1］. By combining with spatial division multiplexing （SDM） technology， significant strides in large-capacity long-distance transmission based on MCFs have been reported^［2-4］. They are even expected to play key roles for quantum communications^［5-6］. Meanwhile， MCFs provide excellent platforms for developing versatile fiber sensors， especially for multi-dimensional measurements^［7-9］. For example， MCF-based curvature sensors usually not only offer relatively high bending sensitivity but also the capability to identify the bending orientation^［10］. Some of them are even demonstrated for three-dimensional （3D） shape reconstruction of curved objects^［11-13］.

As regards device configuration， MCF-based curvature sensors can be roughly categorized into two groups. The first group is related to various interferometers such as Fabry-Pérot^［14-15］， Michelson^［16-17］， and Mach-Zehnder interferometers^［18-19］. Most of them are constructed with in-fiber （or in-line） schemes， in which a section of MCF is employed to generate the optical phase difference via different physical paths or guiding modes， and connected with an in-fiber beam splitter and combiner. The splitter or combiner can be realized by several approaches such as offset splicing^［20］， insertion with a short section of multimode or no-core fiber^［21-22］， nonadiabatic tapering^［23］， waist-enlarged splicing^［24］， and so on. These interferometric configurations are well known as easy fabrication， high sensitivity， and good applicability. So far， they have been reported in many uncoupled-core and coupled-core MCFs with different structures and core numbers^［25-27］.

The second category of MCF curvature sensors is based on fiber gratings， including fiber Bragg gratings （FBGs）^［28-29］， long-period gratings （LPGs）^［30-31］， and tilted fiber Bragg gratings （TFBGs）^［32］. The pioneer works about grating fabrication in MCFs were reported by the researchers from Heriot-Watt University and Aston University. They used ultraviolet （UV） laser lateral exposure method to fabricate Bragg gratings in four-core fibers and then applied the gratings for bending measurement^{［28，33］}. Since then， piles of curvature sensors have been successively demonstrated by using UV laser lateral exposure method in various MCFs. For example， Dochow et al.^［34］ demonstrated an FBG in a 19-core fiber bundle by using an excimer UV laser in 2012， and Wu et al.^［29］ inscribed an FBG in a 91-core-array fiber and applied the grating for simultaneous measurement of curvature and strain. Due to the spatial difference and the lensing effect from fiber circular cladding， the gratings in different cores of MCF are hardly uniform in both resonant wavelength and reflectivity^［35］. To overcome this problem， a possible solution is to put an MCF into a sleeve silica tube or a ferrule with a side-polished flat surface， and then irradiate it using the inscribing laser from the flat side. Since both the sleeve tube and the fiber cladding are made of pure silica and attached closely， the lensing effect is effectively eliminated^［35-36］. In terms of the laser source for grating inscription， more and more interest has been devoted to fabricate fiber gratings by femtosecond laser micromachining method. Because it is much more flexible and compatible than those based on UV laser radiation. Firstly， it has no limitation on fiber photosensitivity and is suitable to write gratings in various germanium-free fibers， including pure silica glass^［37］， chalcogenide glass^［38］， phosphate glass^［39］， tellurite glass^［40］， polymer^［41］， and sapphire fibers^［42］. Secondly， the femtosecond laser method can flexibly fabricate gratings in any individual core by different schemes， including point-by-point^{［11，36］}， line-by-line^［43］， and plane-by-plane^［44］. It can even fabricate ultralong grating array in MCFs assisted with a winding system^{［11，36］}. Last but not least， the gratings fabricated by femtosecond laser method usually feature with ultrahigh thermal stability. Some of them can work normally with the ambient temperature as high as 1000 ℃^［45］.

For grating-based MCF sensors， however， simultaneous interrogation of all gratings in different cores is still a challenge. Usually， an additional fan-in/out device is necessary. It will not only undermine the flexibility， efficiency， compactness， and robustness of MCF sensors， but also escalate costs. To address this problem， some researchers proposed to insert a short section of large-core-diameter multimode fiber （MMF） between a seven-core fiber and lead-in single-mode fiber （SMF）， which served as a beam-size adapter to couple the incident light into the central core and one outer core and then collect their Bragg reflection signals^［46］. But it only realizes the interrogation for the central core and one outer core.

In this article， we propose and demonstrate the integration of bridged waveguides and Bragg gratings in a three-core fiber （TCF） by using femtosecond laser micromachining technique， followed with the application for directional curvature sensing. In each core of the TCF， an FBG is inscribed but with different pitch. And， two slant waveguides， acting as in-fiber couplers， are fabricated to link the TCF’s outer cores up with the lead-in SMF core to interrogate all three FBGs simultaneously. The outer-core FBGs not only respond to curvature with high sensitivity but also have the capability to discern the curvature orientation. Particularly， since the outer-core FBGs respond always oppositely to curvature， the wavelength interval between these two FBGs is employed as an indicator for sensing curvature as well. The corresponding maximum sensitivity to curvature is as high as 191.89 pm/m^-1， which is much more sensitive than any individual outer-core FBG. Meanwhile， the central-core FBG is not sensitive to fiber bending but responds to ambient temperature and axial strain with almost the same sensitivities as the outer-core FBGs. Thus， the crosstalks from thermal fluctuation or axial strain can be compensated when this device is applied for curvature sensing. These cross impacts will be further inhibited by taking the wavelength interval between the outer-core FBGs as the indicator. The corresponding sensitivities to temperature and strain are only 0.3 pm/℃ and 0.0218 pm/µε， respectively.

The specialty fiber used in the proposed device is a TCF， whose cross section is illustrated in Fig. 1. The TCF has three identical single-mode cores made from standard G.652 preform. Three cores are located in the same meridional plane and separated with the center-to-center distance of 28 µm. The core diameters are all about 8.4 µm， and the cladding diameter of this TCF is about 125 µm^［22］.

The configuration of the proposed device consists of a section of TCF connected coaxially with SMFs at both ends， as shown in Fig. 2（a）. Each core contains an FBG but with different grating pitch. Two straight waveguides link the outer cores to the lead-in SMF’s core， coupling incident light directly from the SMF’s core to the TCF outer cores and collecting the Bragg reflection signals back to the SMF.

The waveguides and FBGs were successively fabricated by a femtosecond laser micromachining system which comprised a Coherent Ti∶sapphire femtosecond laser and a Newport femtoFBG machine^{［45，47］}. Firstly， a section of TCF was spliced to a standard SMF at one end， and then it was loaded on the translation stages of the micromachining system. By means of the microscope and the charge-coupled device （CCD） camera of this system， the TCF was carefully aligned and rotated so that all three cores could be simultaneously observed with the same clarity. Secondly， the femtosecond laser beam was attenuated and then focused into one of the TCF’s core through a microscope object ［magnification 40×， numerical aperture （NA） 0.75］. The bridged waveguides were fabricated by using a line-by-line scheme， in which 9 parallel lines were inscribed one by one with the span of 1 µm to form a 3×3 square array^［47］. The waveguides started about 2 µm away from the SMF central axis and ended up at the TCF outer cores. Their lengths were about 1520 µm， corresponding to a tilt angle of ~1.0°relative to the fiber central axis. The side-view images of the inscribed waveguides were monitored in real time by using the CCD camera， as the examples of different sections shown in Figs. 2（b）‒（d）. They were basically smooth and uniform. In order to verify the mode coupling by the inscribed waveguides， the TCF output end was mounted on a three-axis translation stage and followed by a collimating objective. The output light distribution was captured by using an infrared （IR） camera （Ophir SP928）. As seen from the picture shown in Fig. 2（e）， light can be observed in all three cores. It indicated that the input light from the SMF core has been effectively coupled into the TCF outer cores by the inscribed waveguides. Thirdly， the femtosecond laser beam was moved to the TCF to fabricate FBGs in all three cores by using a point-by-point writing method^［45］. The FBGs were designed to be about 7 mm in length and resonate in the second order diffraction. Their grating pitches were set at 1.05 µm， 1.07 µm， and 1.09 µm， respectively. It helped to identify directly the FBG signals from different cores via resonant wavelengths. The image of the fabricated FBGs was captured and displayed in Fig. 2（f）. Finally， after the grating fabrication， the TCF with the coupling waveguides and FBGs was cleaved at the other end and spliced to a lead-out SMF for device handling. The length of the TCF was measured to be about 2 cm.

The fabricated device was connected to a 3-port circulator and then linked to a broadband light source （BBS， UBLS-1250-1650-FA-B） and an optical spectrum analyzer （OSA， Yokogawa AQ6370D） to monitor its reflective spectrum. As illustrated in Fig. 3， three distinct peaks appear at specific wavelengths： 1519.63 nm （labeled as peak 1）， 1548.13 nm （labeled as peak 2）， and 1576.38 nm （labeled as peak 3）. They are respectively corresponding to the resonances of FBGs in the three cores numbered in Fig. 2（f）. Their resonant wavelengths basically match the theoretical expectation， following the Bragg grating phase-matching condition λres=2neff⋅Λ/M. Here， λres represents the FBG resonant wavelength， neff denotes the effective refractive index of the fiber core mode， Λ signifies the grating pitch， and M equals 2 for the second order diffraction. The insertion loss of the whole device was about 10 dB， which was measured from the transmitted spectrum.

Taking a fiber as a cylindrical silica rod， the inner side of the rod is compressed and the outer side is stretched when the rod is curved towards a center. The interface between the compressed and stretched sides is considered as a neutral surface， on which there is neither extension nor compression. Different from standard SMFs， as the diagram shown in Fig. 4（a）， the TCF is not an axisymmetric shape any more. It means that transmission property of the TCF will be affected by not only the magnitude but also the orientation of fiber bending. The orientation of the bent TCF is described by the angle θ between the three-cores meridional plane and the X-Y plane of the laboratory coordinate system， as the diagram illustrated in Fig. 4（b）. When these two planes coincide and the core 1 is located on the left side of the central core， the TCF’s orientation equals 0°.

Three FBGs are designed with the same length but different pitches， so that they can not only respond accurately to fiber deformation but also identify the signals from different cores. When the TCF is bent， the effective refractive indices of the modes of three cores change differently. It results that their grating resonant wavelengths shift in different manners. Except for the orientation angle of 0° and 180°， the FBGs in core 1 and core 3 respond always reversely to the fiber bending. Thus， the proposed device can provide a higher sensitivity to curvature by monitoring the variation of the relative wavelengths （i.e.， wavelength interval） between two FBGs^［31］.

Different from fiber bending， the impact of axial strain or ambient temperature on the TCF is almost uniform in the cross section. It means that the fundamental modes in all three cores will be affected with a similar manner by the axial strain or temperature variation. Since three cores in this TCF are made with the same refractive index profile， the FBGs in these three cores will respond to axial strain or temperature with almost the same sensitivities. Based on this property， two approaches can be adopted to compensate the cross-sensitive issue of axial strain or ambient temperature when the proposed device is employed for curvature sensing. The first one is using the FBG in the central core as an indicator to monitor the impact of axial strain or temperature fluctuation， because it is not sensitive to fiber bending but responds to axial strain and temperature as sensitively as the FBGs in outer cores. The second approach relies on the relative variation （wavelength interval） between two outer-core FBGs. These two FBGs always respond oppositely to fiber bending， but have almost the same sensitivity to axial strain or ambient temperature. It indicates that this wavelength interval is actually immune to the variation of axial strain and temperature^［31］.

Regarding to the sensing performance， the responses of the proposed device to curvature， temperature， and axial strain were successively characterized. The experimental setups for these characterizations are shown in Figs. 5（a）‒（c）， respectively.

For directional curvature characterization， the fabricated TCF device was clamped on two high-precision rotators installed on two translation stages. The sensor head was then rotated to the 0° orientation with a marker made in the fabrication process. It is noteworthy that this rotation alignment may not be precise enough to localize the true “0° orientation” of the TCF， as the curvature characterization was conducted without microscopy. However， this minor deviation can be calibrated by analyzing the sensor’s curvature responses in all orientations. The initial length of the straight fiber between two rotators was defined as L0. One stage was fixed， as shown in Fig. 5（a）， while the other one was driven by a differential micrometer to move along the fiber axial direction. The moving distance of the stage was denoted as ΔL. When the stage moved towards the fixed one， the initially straight fiber was naturally curved due to gravity^［48］. It was approximately treated as an arc， which was defined by the circle center O and radius R. The corresponding curvature C of the curved fiber was defined by 1/R. Based on the diagram shown in Fig. 5（a）， the relationship of the curvature C against the fiber initial length L0 and the stage movement ΔL was expressed as follows^［46］：

In this setup， the initial length L0 was set at ~150 mm， and the stage was moved with a step of 1.0 mm. It caused the applied curvature varying within the range from 0 to ~8.4317 m^-1. The reflective spectrum of the device was monitored and recorded using the BBS and OSA for each step. After the reflection spectra were recorded， the movable stage was returned to its starting position and the curvature measurement was repeated for three times for repeatability characterization. Subsequently， both rotators were simultaneously rotated by 15° in a clockwise direction to change the orientation angle of the device. These aforementioned procedures were then repeated to measure the curvature responses of the device at each 15°orientation angle.

Through analyzing all the collected spectra in each orientation angle， the resonant peak of the FBG in core 1 （peak 1） was found to shift towards shorter wavelengths for the curvature increased from 0 to 8.4317 m^-1， when the device orientation ranged within 0°‒180°. Meanwhile， the resonant peak of the FBG in core 3 （peak 3） responded to the curvature with red shifts. For example， Fig. 6 illustrates the spectral variation of the device for increased curvature when its orientation equals 90°. On the contrary， when the device was bent in the orientation of 180°‒360° with the same increments of curvature， peak 1 shifted to the longer wavelengths whereas peak 3 moved toward shorter wavelengths. Besides， the resonant peak of the FBG in the central core （peak 2） remained almost insensitive to the applied curvature at each orientation angle.

Figures 7 and 8 provide a more comprehensive view of the curvature responses of the proposed device across all orientations. As shown， peak 1 and peak 3 respond linearly to the applied curvature with the very similar sensitivity but opposite directions in each orientation. Their sensitivities to curvature are calculated to be of 7.95 pm/m^-1 （peak 1） and -9.86 pm/m^-1 （peak 3） for 0°orientation， and 2.8 pm/m^-1 （peak 1） and 0.075 pm/m^-1 （peak 3） for 180° orientation. As the orientation angle increases， their sensitivities vary sinusoidally and reach maximums around 90° and 270°. The maximum values are respectively -95.41 pm/m^-1 （peak 1， R2=0.9998） and 96.48 pm/m^-1 （peak 3， R2=0.9997） for 90°， and 93.55 pm/m^-1 （peak 1， R2=0.9994） and -93.66 pm/m^-1 （peak 3， R2=0.9997） for 270°. According to the repeatability characterization， the wavelength deviations of each orientation angle are derived， as the error bars shown in Fig. 7. The maximum deviation is about ±0.046 nm， and the corresponding accuracy for curvature sensing is around 0.47 m^{-1［49-50］}.

Furthermore， since the FBGs in core 1 and core 3 responded always oppositely to curvature， the wavelength interval between these two FBG peaks was also employed as an indicator for curvature sensing. As can be seen from the results shown in Fig. 9（a）， the wavelength interval responds linearly to the curvature applied in different orientations. The sensitivity varies sinusoidally as increasing the orientation angle from 0° to 360°， as shown in Fig. 9（b）， in which the maximum sensitivities are about 191.89 pm/m^-1 （R²=0.9998） around 90°and -186.91 pm/m^-1 （R2=0.9998） around 270°. Basically， they are the sum of the maximum curvature sensitivities of peak 1 or peak 3. It is also several times higher than previously reported curvature sensors based on FBGs in MCFs^{［11，29，46，51］}.

It iss noteworthy that there is a very small horizontal offset （~2.86°） in the sinusoidally fitted curve in Fig. 9（b）. It indicates that the TCF initial position deflects slightly from the true “0° orientation”.

For temperature characterization， the proposed device was put inside a customized thermostat， which can stabilize temperature within the range of 20‒110 ℃ with the precision of 0.01 ℃^［22］. In order to keep the sensor head straight during measurements， as the diagram depicted in Fig. 5（b）， the lead-in and lead-out fibers were fixed on two holders with a tiny tension. Then， the device was connected to the BBS and OSA via a circulator for monitoring the reflective spectrum in real time. This characterization experiment was repeated three times to evaluate the repeatability and accuracy of the thermal response.

From the results shown in Fig. 10， it can be seen that all three resonant peaks shift to longer wavelengths in a consistent manner when the device is heated from 25 to 95 ℃ with a step of 10 ℃. Their sensitivities to ambient temperature are calculated to be about 9.15， 9.13 and 9.47 pm/℃， respectively， according to the linear fittings illustrated in Fig. 11. The corresponding R2 values are about 0.9984， 0.9995， and 0.9996， respectively. Their thermal performance resembles those of conventional FBGs in SMFs^［52-53］. The error bars shown in Fig. 11 are derived from the repeat measurements， in which the wavelength deviations of three FBG peaks are less than ±0.016 nm. It indicates that the accuracy of the proposed device is about 1.7 ℃ for temperature sensing.

Remarkably， the wavelength interval between peak 1 and peak 3 exhibited negligible variation with increasing temperature， since these two peaks responded almost synchronously to temperature. The corresponding thermal sensitivity is about 0.32 pm/℃， which is only ~3% compared with peak 1 or peak 3. It performs much better than previous “temperature insensitive” curvature sensors^{［27，31］}.

Finally， the proposed TCF device was mounted on two translation stages with the distance of 20.0 cm for axial stain measurement， as the diagram shown in Fig. 5（c）. Similarly， the BBS and OSA were connected to the device via a circulator for monitoring the reflective spectra in real time. One stage was fixed， while the other one was driven by a micrometer to move along the fiber axial direction for changing the strain inside the device. Since both the TCF and the lead-in/out SMFs were all-solid silica-based fibers and had the same diameter， the axial strain should be uniformly distributed along the stretched section. It is usually calculated by the equation ε=ΔL/L0^［54］， where L0 is the initial length of the fiber between two stages， and ΔL denotes the fiber length variation as changing the applied strain. This strain measurement was also repeated three times to characterize the repeatability and accuracy of the proposed sensor.

When the axial strain increased from 0 to 2000 µε with the step of 200 µε， the whole spectrum underwent a red shift slightly， as shown by the curves in Fig. 12. The corresponding strain sensitivities of peak 1， peak 2 and peak 3 are 0.7534 pm/µε （R2=0.9981）， 0.7693 pm/µε （R2=0.9987） and 0.7752 pm/µε （R2=0.9995）， respectively， as illustrated in Fig. 13. They are comparable with the previously reported FBGs by using femtosecond laser method^［45］. The error bars shown in Fig. 13 reflects that the repeatability of this device is good for axial strain sensing. The maximum peak wavelength deviation is about ±0.026 nm. Thus， the corresponding accuracy in strain measurement is about 33 µε.

Furthermore， the impact of axial strain can be significantly depressed， if the wavelength interval between peak 1 and peak 3 is taken as the indicator. The corresponding sensitivity of the wavelength interval to axial strain is only about 0.0218 pm/µε. It is even lower than those of previously reported strain-insensitive devices^［31］.

In conclusion， we have successfully demonstrated the fabrication and sensing performance of a directional curvature fiber sensor that incorporates two bridged waveguides and three FBGs within a TCF. Both the waveguides and FBGs were fabricated using femtosecond laser micromachining method. The waveguides serve as a beam splitter/combiner， coupling the incident light into all three cores of the TCF and collecting the FBGs’ reflective signals back to the lead-in SMF for interrogation. The outer-core FBGs exhibit directional-dependent sensitivity to applied curvature， while the central-core FBG shows negligible curvature sensitivity but temperature and strain responses consistent with the outer-core FBGs. Consequently， the cross impact of thermal or axial-strain variation can be compensated with the assistance of the central-core FBG， when the outer-core FBGs are used for curvature sensing. More interestingly， we found that the wavelength interval between two outer-core FBG peaks can be used for directional curvature measurement as well， since these two outer-core FBGs respond oppositely to curvature in each orientation. The maximum curvature sensitivity achieved is about 191.89 pm/m^-1， which is about twice as high as that of each individual outer-core FBG. Moreover， the temperature and strain sensitivities of this wavelength interval are only 0.3 pm/℃ and 0.0218 pm/µε， respectively. It means that the impact of thermal or strain fluctuation is depressed by almost two orders of magnitude. Thus， the proposed device provides an additional advantage for self-neutralizing the cross sensitivity to temperature or axial strain when the wavelength interval between two outer-core FBG peaks is adopted as the indicator for measuring directional curvature.