# Long-Period Grating with Asymmetrical Modulation for Curvature Sensing
## 3 Experiments and Results
Since the LPFG is fabricated with an asymmetric structure, the grating resonance results from the circularly asymmetric mode coupling, and that asymmetry is in the plane of the 0\({}^{\circ}\) and 180\({}^{\circ}\) directions. That means that bending the fiber in these two directions has a larger influence on the effective index of the cladding mode than bending the fiber in the 90\({}^{\circ}\) and 270\({}^{\circ}\) directions; thus, the curvature sensitivities are higher. The difference of sensitivity in different bending directions means that the sensor is capable of distinguishing the orientation of the curvature. By referring to the sensitivities in different bending directions, the direction of the curvature can be determined. Figure 6: Spectra response of the sample with offset of 3 \(\upmu\)m in bending direction of **(a)** 0\({}^{\circ}\), **(b)** 90\({}^{\circ}\), **(c)** 180\({}^{\circ}\), and **(d)** 270\({}^{\circ}\). For the sample with an offset of 6 \(\upmu\)m, the curvature sensing characteristic is investigated in the same way as the previous sample. The curvature responses in different bending directions are plotted in Figure 8. The results indicate that the sensitivity of this sample is further improved compared to the sample with offset of 3 \(\upmu\)m, and the sensitivities in the bending direction of 0\({}^{\circ}\) and 180\({}^{\circ}\) are also close, which are 28.6 nm/m\({}^{-1}\) and 29.4 nm/m\({}^{-1}\), respectively, while the sensitivities in the other two directions, 90\({}^{\circ}\) and 270\({}^{\circ}\), are 20.4 nm/m\({}^{-1}\) and 20.8 nm/m\({}^{-1}\), respectively, which are much smaller. The higher sensitivity is attributed to the larger separation between the fiber core and the index modulation area. Increasing the separation not only increases the curvature sensitivity, but also leads to much larger differences in sensitivities of the orthogonal bending directions. In this way, it would be much easier to distinguish the orientation of the curvature. It is clear that to achieve higher curvature-sensing performance, the offset of the grating modulation should be large; however, as discussed above, the large offset could lead to a very weak grating resonance. A compromise should be made between the sensing performance and the grating strength, since weak grating resonance will lead to low signal-noise ratios and the line width will also be large, which causes the detection limit of the sensor to be quite poor. Table 1 gives the comparison of the sensing performance of our work and other curvature sensors, from which we can see that our sensor has higher sensitivity in a larger curvature measurement range. Figure 8: Curvature response of the sample with offset of 6 \(\upmu\)m in four bending directions. Figure 7: Curvature response of the sample with offset of 3 \(\upmu\)m in four bending directions. Temperature is another important parameter that should be monitored during certain engineering processes. To investigate the temperature response of the LPFG, a heating treatment with a tube furnace (LCO 102 SINGLE, ECOM Co., Ltd., Ishikari, Japan) is applied to the grating. Temperature is increased from room temperature to 60 \({}^{\circ}\)C with a step of 5 \({}^{\circ}\)C. Each temperature is kept for 10 min before the spectrum is recorded. Figure 9a gives the grating spectrum under different temperature values. From Figure 9a, we can see that temperature does not cause much change in the resonant wavelength. The spectrum shifts slightly towards longer wavelength as temperature rises. The wavelength shift is caused by the thermo-optic effect and the thermal-expansion effect of the fiber material. When temperature changes, the refractive index of the silica material, as well as the length of the fiber, will change, which will lead to the variation of the modes' effective indices and the grating periods. Thus, the resonant wavelength of the grating will experience a shift.