# Optical accelerometers for Detecting Low-Frequency Micro-Vibrations
## 6 Optical Wavelength Modulation
One-dimensional PHCs are periodic stacks of materials with different refractive indices. When the periodicity or material properties of the bandgap material will be changed, the central wavelength of its output light will be changed. [PERSON] et al. used alternating silicon and air to form a bandgap PHC accelerometer with a mass connected to a silicon finger in the middle. When acceleration is applied to the accelerometer, the silicon finger in the middle moves in the sensing direction, thus changing the periodic condition of the bandgap, and the acceleration value can be obtained from the amount of change in the central wavelength of the output light [91]. A similar study was conducted by [PERSON] et al. [92]. [PERSON] et al. proposed a two-dimensional PHC-based accelerometer consisting of two waveguides and a ring resonator with a two-dimensional rod-like PHC microstructure, and a holder connecting the central rod and mass of the nanocavity. When there is an acceleration acting on this accelerometer, the displacement of the mass causes the radius of the ring resonator to become larger, which results in a wavelength red-shift of the output resonant mode. By detecting the wavelength shift in the readout system, the magnitude and direction of the acceleration can be interpreted [93]. A similar study was conducted by [PERSON] et al. [94]. FBG accelerometers exhibit the advantages of anti-electromagnetic interference, low loss, good scalability, small size, and light weight. They can be applied in complex environments. In addition, FBG-based optical accelerometers provide an effective solution for realizing the multipoint monitoring of the health of the large infrastructure. However, as can be seen from Equation (14), the output signal of the FBG can be modulated by temperature compared to other types of optical modulation methods. Therefore, compared to other types of optically modulated accelerometers, FBG accelerometers have the highest sensitivity to ambient temperature and require temperature compensation when used. PHC accelerometers have the advantage of large bandwidth and compact size. However, their  
Figure 19: Improved cantilever FBG accelerometer: (**a**) polyimide patch and (**b**) double semicircular flexible hinge. Figures are reprinted with permission from: (**a**) Ref. [84]. Copyright 2012 Elsevier; (**b**) Ref. [88]. Copyright 2014 Elsevier. application and development are limited by manufacturing technology, and high-quality processing and material technology are prerequisites for achieving high sensitivity and high resolution in PHC [95]. In addition, the low-frequency response characteristics of PHC accelerometers have not been reported despite their large bandwidth. Moreover, the detection of optical wavelengths relies on specialized high-precision instruments, and the readout output signal is complex and difficult to integrate and process. The parameters of the structures and the optical accelerometer based on optical wavelength modulation (i.e., resonant frequency, working frequency band, and sensitivity) are provided in Table 4.