## 4 Radiation Pressure-Driven PhC Cavity Sensors
### Sensing Applications Based on Radiation Pressure
#### 4.2.2 Force Sensing  
Displacement of the mechanical resonator is closely related with applied force by the mechanical susceptibility \(\chi_{xx}\) as defined in Fourier transformation of \(x(\omega)=\chi_{xx}(\omega)[F_{ex}(\omega)+F_{L}(\omega)]\), where \(F_{ex}(\omega)\) and \(F_{L}(\omega)\) are applied external force and noise force. A combination of large optomechanical coupling \(g_{om}\), large mechanical susceptibility (low mass \(m_{eff}\) and high \(Q_{m}\)) and sharp optical resonance (large \(Q_{opt}\)) contributes to sensitivity-enhanced radiation pressure-driven devices. Miniature mechanical structures on the sub-\(\upmu\)m scale with high mechanical frequency and low stiffness are highly preferred on account of their good immunity to environmental vibration and sensitivity. Therefore, PCN cavities are more attractive in these sensing applications due to their ultralow mass, flexural mechanics and high optical Q-factors. Currently, force sensors based on PhC cavities are widely studied [124; 125; 126]. As shown in Figure 19a, a split PCN cavity had two cantilever nanomechanical resonators serving as optical mirrors [124]. Mechanical resonances of the suspended mirror could be efficiently excited by several sources (indicated by red arrows in Figure 19a). High optomechanical coupling in the nanocavities was realized when mechanical motion of suspended mirror controlled the splitting gap. As the nanocavity length effectively modified, resulting in a dispersive coupling to optical resonance. Mechanical resonances of the suspended mirror were optically coupled through radiation pressure, thereby allowing sensitive torque measurements. It was demonstrated that 500 MHz/nm dissipative coupling rate and 2 GHz/nm dispersive coupling rate were capable to detect mechanical resonances with the torque sensitivity of \(1.2\times 10^{-20}\) Nm/\(\sqrt{\text{Hz}}\) in ambient condition and \(1.3\times 10^{-21}\) Nm/\(\sqrt{\text{Hz}}\) in low vacuum. Likewise, a suspended paddle-like nanocavity [126] in the middle of the split PCN cavity modified the gap between two optical mirrors due to the torsional and feasible mechanical mode of paddle cavity, as shown in Figure 19b. The floating motions of suspended paddle nanocavity were supported by two nanotethers, and the mechanical resonances excited by applied torsion could be modulated and detected through optomechanical coupling. Figure 18: A tunable slotted-waveguide PhC electro-optomechanical cavity [82; 122]. These optomechanical nanocavity systems provide a unique platform for studying optomechanical couplings and their impacts on magneto-mechanical sensing. When combining with magnetostrictive materials, this split PCN cavity can be used as an external magnetic field sensor. As presented in Figure 20, a magnetometer was proposed by integrating a ferromagnetic thin-film permalloy island onto a rectangular pad at the end of the moving nanobeam [70]. In the presence of an in-plane magnetic field \(H_{x}\), the permalloy came to be magnetized with a net moment along the field \(x\)-direction. When a magnetic field \(H_{z}\) directed along the \(z\)-direction, a magnetic torque was generated along the torsion rod that supported the moving nanobeam. Due to its torque sensitivity of 1.3 \(\times 10^{-21}\) Nm/\(\sqrt{\mathrm{Hz}}\), the optomechanical nanocavity could detect nanoscale magnetic phenomena at the field strengths on the order of the earth's field (44-60 \(\upmu\)T), corresponds to a magnetic moment sensitivity of \((2.4\pm 0.4)\times 10^{7}\)\(\upmu\)B. Another novel multi-cavity optomechanical torque sensor [127] using a nanobeam composed of two PCN cavities on each side was demonstrated as depicted in Figure 21a. The nanobeam was suspended on two axial spokes that were anchored to the substrate. In the architecture, the nanobeam could oscillate as a torsion driven by optical force excited in the side PCN cavity.