## 4 Radiation Pressure-Driven PhC Cavity Sensors
### Sensing Applications Based on Radiation Pressure
#### 4.2.4 Inertial Sensing  
Inertial sensors are generally used to detect and measure acceleration, tilt, and vibration. In principle, the MEMS-based accelerometer works to measure the displacement of a mechanical mass, known as a proof mass [139; 140]. In MEMS devices, displacement detection is electrically measured through the capacitance between proof mass and electrode. However, currently available MEMS accelerometers still lack the sensitivity and bandwidth required for precise navigation, and the sensitivity is limited by thermal-electronic noise in the readout circuits. To eliminate the electronic noise effect, optical fiber sensing methods can reach the fundamental thermal-mechanical limit. In this critical limit, Brownian-motion of mechanical resonator limits the detection sensitivity. This thermal-mechanical noise imposes a trade-off between the sensitivity (\(a_{th}\)) and bandwidth (\(\Omega_{m}\)) of the accelerometer given as \(a_{th}=\sqrt{4\Omega_{m}k_{B}T/m\Omega_{m}}\). To achieve high sensitivity for a given bandwidth, the denominator term \(mQ_{m}\) needs to be maximized. For instance, a sensitivity of 1 ng/Hz\({}^{1/2}\) over a bandwidth of 10 kHz requires \(m\Omega_{m}>1\) kg. However, for high bandwidth devices, a high-resolution displacement measurement \(x(w)\sim a_{th}/\Omega_{m}^{2}\) at the fundamental mechanical frequency is required to approach the thermal limit. This technical task is difficult for electrical circuit readout, for example, MEMS accelerometers have kHz scale bandwidths, but their sensitivities are limited to a few mg/Hz\({}^{1/2}\)  
Figure 23: A femtogram scale nanomechanical resonator embedded in a double-slot PCN cavity, and the right inset is zoom-in view of central nanomechanical resonator [138]. Figure 22: (a) Analytical model of PCN cavity for nanoparticle trapping [134; 135; 136]; (b) optomechanical PhC cavity operation in water for mass sensing (the colored box indicates that the optomechanical device is immersed in water) [137]. A comparison of sensitivity and bandwidth of three types of accelerator above has been summarized in Table 4.  
As mentioned above, acceleration sensing is based on displacement sensing, and it prefers low mechanical frequency to achieve high sensitivity. Besides, its sensitivity is proportional to \(g_{om}\) because optomechanical coupling transduces mechanical motions to optical signals. As a result, many efforts in the optomechanical PhC cavities have been done to improve these two aspects. The first optomechanical accelerator was defined using an on-chip zipper PCN cavity to measure the motion of a large suspended Si\({}_{3}\)N\({}_{4}\) proof mass [130], as indicated in Figure 24. Two parallel suspended Si\({}_{3}\)N\({}_{4}\) doubly clamped PCNs (10-\(\upmu\)m-long and less than 1-\(\upmu\)m-wide), and a separation gap of around 100 nm formed the zipper cavity. Due to the high confinement of optical mode between the coupled nanobeams, the optical resonance frequency was extremely sensitive to the mechanical motion of moveable nanobeam cavity. To work as an accelerometer, a large proof mass was attached to the movable beams to realize the motion sensing. The detection could reach up to the standard quantum limit experimentally. Using the highly tensioned tethers supporting the proof-mass, a large proof mass can be realized without sacrificing mechanical \(Q_{m}\), and hence reduce the effect of thermal noise. The proposed optomechanical accelerator exhibited a sensitivity of \(\sim\)0.1 \(\upmu\)g/Hz\({}^{1/2}\) near the mechanical resonance frequency around 20 kHz. In a similar manner, another optomechanical inertial sensor based on a slot-type 2D photonic crystal cavity [143] was demonstrated in Figure 25a. One side of the slot cavity was anchored on the silicon top layer and the other suspended side was attached to a large proof mass of 5.6 ng for acceleration detection.