## 3 Experimental Results  
In our experiment, the fiber taper was fabricated by a flame-heated taper-drawing technique. The minimum diameter of the fiber taper was about 3.71 \(\upmu\)m, and the length of the whole taper region was about 1.9 cm. In the chirped F-P interferometer fabrication process, we used a uniformed phase mask with \(\wedge\) equal to 1072 nm to inscribe the Bragg grating. The chirped grating was mounted onto two fiber clamps, and the distance between the two clamps was 19.06 mm. In the sensing experiment, one clamp was fixed while the other moved along the fiber axis. Figure 4 shows the measured reflected spectra of the F-P interferometer with different tension. Figure 3: (**a**) The structure of the two separated fiber Bragg gratings (FBGs)-based F–P interferometer and the reflected spectra of the FBGs; (**b**) The structure of the FBG-based F–P interferometer and the reflected spectra of the FBG. The full bandwidth of the F-P interferometer spectra was more than 35 nm, but there were two valleys in the long wavelength region (at 1527.8 nm and 1536.3 nm for spectra under displacement of 1.05 mm). These valleys may have been caused by the steep decline of the reflectance. Although the scanning speed of the ArF excimer laser beam was constant, the slope of outline shape function changed with the position along the fiber, which means that the FBG at different positions received different laser powers. When the slope of the outlined shape function reached its maximum value, the power absorption efficiency reached its minimum value. The reflective spectra at the wavelengths before the valleys are relative flat and can be used for chirped optical shaping. Thus, the available bandwidth of the F-P interferometer was over than 20 nm. When the displacement was increased by 0.05 mm, the reflected spectra were changed from the blue curve to the red curve, and the wavelength shift marked by the first notch was 1.86 nm. To investigate the chirp characteristics of the sensor, we marked the first 60 notches of the spectra when the displacement was between 0.9 mm and 1.1 mm, as shown in Figure 5.  
It can be seen that when the displacement introduced to the F-P interferometer increases, the notches in the reflected spectra shift to the long wavelength region, and the differential of the notches' wavelength also change slightly. This is because the stiffness along the fiber is not constant,  
Figure 4: The F–P interferometer experimentally reflected spectra under displacements of 1.05 mm (blue dot line) and 1.1 mm (red line). Figure 5: The first 60 notches of the F–P interferometer-reflected spectra under different displacements. and the FBG period changes more slowly when the fiber diameter is larger. The displacement sensing can be achieved by marking the wavelength of the first notch, but the marking step usually needs manual work due to the existence of multiple wavelength spectra. By adding a cross-correlation process to the reflected spectra, only one peak needs to be marked. The principle of the cross-correlation process is discussed in [8]. The wavelength of the notches in the reflected spectra means that the phase difference is an odd multiple of \(\pi\). Thus, we can build a reference function based on this wavelength to the phase and do the cross-correlation process to the reflected spectra. The cross-correlation result under different tensions is shown in Figure 6.  
The cross-correlation curve has one narrow peak and other side lobes. The separation of the peaks between the different displacements is clear enough to recognize the displacement changes below. The sensing curve that was achieved by marking the first notch wavelength and the cross-correlation peak wavelength is shown in in Figure 7.  
It can be seen that the first notch wavelength and the cross-correlation peak wavelength change with the displacement in opposite directions. The shifting curves of the two methods do not change  
Figure 6: The cross-correlation curves under a displacement of 1.05 mm (blue dot line) and 1.1 mm (red line).