In recent years, multicore fiber Bragg grating (FBG) vector displacement sensors have become a research hotspot in the field of vector displacement sensing because of their multidimensional measurement capability, high sensitivity, high resolution, and high precision. However, in practical applications, multicore FBG vector displacement sensors require a fan-in and fan-out device to realize multichannel signal demodulation. The use of this device not only increases the difficulty of fiber fusion splicing and reduces the compactibility of the sensor but also increases the cost and complexity of the system and reduces modulation efficiency, which poses a challenge to the practical application of the existing multicore FBG vector displacement sensor. In this study, a vector displacement sensing structure based on multicore FBGs and coupled waveguides is proposed, to measure multiple signals in a single channel and avoid the use of fan-in and fan-out device.

First, for preparation, a sensing structure was studied. FBGs were inscribed in the central core (core 1) and two outer cores (core 2 and core 3) with an azimuth difference of 60° for a seven-core fiber, using femtosecond laser direct-writing technology. In addition, straight coupled waveguides for connecting core 1 to core 3 and core 1 to core 2 were prepared, to enable signal light transmission back and forth between the central and outer cores. Figure 2 shows the principle of multiplexing multichannel sensing signals, using a single core based on this structure. Subsequently, the principle of displacement sensing based on multicore FBGs was theoretically analyzed. Finally, based on the self-built displacement testing system (Fig. 7), a displacement-sensing test was performed on the prepared sensing structure, to verify its performance.

Femtosecond laser direct writing technology was used to prepare a reference FBG (FBG1) for auxiliary positioning and temperature compensation in core 1, and a sensing FBG (FBG2 and FBG3) for detecting displacement changes in core 2 and core 3. The lengths of FBG1‒FBG3 were 5 mm. Subsequently, two coupled waveguides for connecting core 1 & core 2 (waveguide 2) and core 1 & core 3 (waveguide 3) were prepared using line-by-line technology. Waveguide 2 was located upstream of the fiber with a width of 5 μm, whereas waveguide 3 was located downstream with a width of 7.5 μm. The reason for the different widths of the two waveguides was to make the reflection intensities of FBG2 and FBG3 closer to facilitate demodulation. Finally, the reflection spectra of FBG1‒FBG3 measured by a single-mode fiber circulator (Fig. 5) show that the reflection intensity of the three FBGs were basically close to being the same. The end-side light distribution (Fig. 6) shows that the prepared coupled waveguides exhibit good light-conduction performance. Subsequently, a displacement sensing test was performed based on the displacement testing system (Fig. 7). First, the directional response of the sensing structure in the direction angle of 0‒360° was tested in 10° increments, verifying that the directional response of this sensing structure approximately follows a sinusoidal distribution [Fig. 8(a)]. The phase difference between FBG2 and FBG3 was 60°, which is consistent with the theoretical analysis results. In addition, the displacement response under the most sensitive direction angle was tested, verifying a maximum displacement sensitivity of approximately 0.28 nm/mm. Subsequently, the directional response was reconstructed to verify the accuracy of the sensing structure in detecting the displacement direction. After three repeated measurements (0‒360°, in increments of 20°), the corresponding relationship between the applied angle and average calculated reconstructed angle was obtained [Fig. 9(a)]. From the linear fitting of the reconstruction angle, the actual applied direction was observed to be in good agreement with the calculated reconstruction result. Moreover, the average reconstruction errors of each angle in three repeated experiments were measured, and the overall error range was within ±5° [Fig. 9 (b)]. Finally, to investigate the performance of the sensor structure in detail, additional groups of the directional and displacement responses of FBG2 and FBG3 were tested. The directional response of FBG2 and FBG3 (0‒360°, in increments of 10°) for a displacement range of 0.5‒3.0 mm [Figs. 10 (a) and (b)] and the displacement response of FBG2 and FBG3 (0‒3 mm, with a step of 0.5 mm) in all directions (0‒360°, in increments of 40°) were tested. The results indicate that the direction and magnitude of any displacement can be determined by monitoring the wavelength shifts of FBG2 and FBG3, using displacement vector synthesis. By setting more groups of displacements and directions and averaging the FBG wavelength shift in each group, more comprehensive and accurate two-dimensional vector displacement sensing can be achieved in the fiber radial direction.

This study demonstrates a novel single-channel measurement multicore FBG vector-displacement sensing structure. Using femtosecond laser direct-writing FBGs and coupled waveguides in multicore fibers, the multiplexing of multichannel signals was realized in a single core. This structure avoids the use of conventional fan-in and fan-out devices, reduces the cost and complexity of multicore FBG vector-displacement sensing systems, and realizes a highly integrated sensing structure. The design and fabrication processes of FBGs and coupled waveguides are discussed. The widths of waveguide 2 and waveguide 3 were determined to be 5.0 μm and 7.5 μm, respectively. The end-side light distribution of the structure verified the satisfactory light conduction performance of the waveguide. Two-dimensional vector displacement sensing in the direction of 0‒360° was subsequently tested based on this structure, and the results of the reconstructed direction indicated the directional accuracy of this sensing structure. Finally, the direction response of the structure under different displacement sizes was tested, verifying a series of stable responses that followed an approximate sinusoidal distribution. The displacement responses at different direction angles were also tested, and the maximum displacement sensitivity of the structure was approximately 0.28 nm/mm. The experimental results show that by monitoring the wavelength shift of FBG2 and FBG3 and by further employing the method of displacement vector synthesis, such a structure can finally determine the direction and magnitude of displacement and realize two-dimensional vector displacement sensing. Such a sensing structure has good compactibility and low preparation difficulty, making it applicable to intelligent machinery, shape monitoring, crack growth monitoring, and other fields in the future.