# Long-Period Grating with Asymmetrical Modulation for Curvature Sensing
## 3 Experiments and Results  
In the fabrication process, three LPFGs are written in SMF with different offsets, which will exhibit different bending sensing characteristics. Figure 4a depicts the experimental setup for the bending sensing experiment. A pair of displacement platforms are used to fix the sample during the curvature sensing, the separation of which is tuned to introduce different curvature values. A broadband light source (BBS) and an optical spectrometer analyzer are used to monitor the transmission spectrum during the experiment. The curvature sensing experiments are performed with three samples separately. To introduce curvature to the LPFG, the grating is fixed between the two platforms, one of which is kept still while the other is pushed towards the former one with a certain increment. The curvature could be approximately expressed by the following [23]:  
\[c=\frac{1}{R}\cong\sqrt{\frac{24x}{L^{3}}} \tag{4}\]  
where \(x\) is the feed displacement and \(L\) is the distance between the two stages. In the curvature measurement, the curvature response is tested in four bending directions. Each time after the curvature measurement, the displacement platform is initialized, the sample is rotated 90\({}^{\circ}\), and four directions are tested, as depicted in Figure 4b. The curvature response of the LPFG sample without index modulation offset is firstly investigated. The curvature applied to the grating is increased from 0 to 4.83 m\({}^{-1}\), and transmission spectra of the grating are recorded. Figure 5a shows the transmission spectra at different curvature values, from which we can see that with the curvature increasing, the transmission spectra exhibit an obvious blueshift response. The change of the resonant wavelength is due to the curvature-introduced index variation in the fiber material, which in turn influences the effective indices of the modes involved in the grating resonance. is applied to the LPFG in the same way as described before. The transmission spectrum is found to shift towards shorter wavelength, as shown in Figure 6a. Then, the bending direction is changed to 90\({}^{\circ}\), which is vertical to the grating-fiber core plane. The spectrum response to curvature is shown in Figure 6b. Figure 6c,d show the curvature response of the other two bending directions, 180\({}^{\circ}\) and 270\({}^{\circ}\), respectively. It is obvious that all bending directions have wavelength shift response to increasing curvature; however, the sensitivity may not be the same. The wavelength shifts against curvature in different bending directions are plotted in Figure 7. From Figure 7, we can see that the curvature sensitivities of the bending direction of 0\({}^{\circ}\) and 180\({}^{\circ}\) are close to each other, while the sensitivities of 90\({}^{\circ}\) and 270\({}^{\circ}\) are similar. Compared with other curvature sensors based on asymmetric LPFGs, the curvature responses in directions of 0\({}^{\circ}\) and 180\({}^{\circ}\) are not opposite; this is because even through asymmetric index modulations are introduced to fabricate the LPFG, the excited cladding modes intensity distributions are not too far away from the fiber axis, and bending the fiber to different directions does not have an opposite influence on the effective index of the cladding mode. Linear fittings are applied to the data, and the sensitivities are estimated to be 16.39 nm/m\({}^{-1}\) and 16.38 nm/m\({}^{-1}\) for bending angles of 0\({}^{\circ}\) and 180\({}^{\circ}\), respectively. For bending angles of 90\({}^{\circ}\) and 270\({}^{\circ}\), the sensitivities are 14 nm/m\({}^{-1}\) and 12.93 nm/m\({}^{-1}\). In general, the sensitivities are higher compared to the LPFG without any offset. On the other hand, the curvature sensitivity changes in different bending directions. In the grating-fiber core plane (bending angles of 0\({}^{\circ}\) and 180\({}^{\circ}\)), the sensitivity is higher, while in the other plane (bending angles of 90\({}^{\circ}\) and 270\({}^{\circ}\)), the sensitivity is low.