## 4 Radiation Pressure-Driven PhC Cavity Sensors
### Sensing Applications Based on Radiation Pressure
#### 4.2.3 Mass Sensing  
Mass sensors play a significant role in the nanotechnological measurements. Traditionally, the mass spectrometer is used for nanoparticle sensing, but the particle should be ionized before extraction. In recent years, nanomechanical cavities are widely applied in mass detection with a high-mass sensitivity of as small as 1 \(\times 10^{-21}\) g in vacuum and 1 \(\times 10^{-15}\) g in liquid condition. With the mass variation \(\Delta m\) deposited onto the surface of a nanomechanical cavity, this can lead to the resonant frequency shift given by \(\Delta m=\frac{2m_{eff}}{\Omega_{m}}\Omega_{m}\). To realize high mass sensitivity, it can be clearly seen that resonator mass \(m_{eff}\) should be small but both mechanical frequency \(\Omega_{m}\) and Q-factor \(Q_{m}\) should be large to obtain a small minimum detectable frequency. Some efforts [108; 131; 132] using cavity optomechanics for mass sensing have been reported. However, thermo-optical noise caused by the instability of coupling methods, for example tapered fiber coupling, limits their sensing resolution to the level of picograms. To reduce this noise, the integrated bus waveguide [133] coupling may be an alternative and effective scheme. For PhC cavities based optomechanical mass sensors, most research has focused on the numerical analysis [134; 135; 136], as shown in Figure 22a. Theoretically, any mass change in the sensing oscillator could cause a certain amount of mechanical frequency shift. When a nanoparticle deviated from the center of the crystal hole, the optical trapping force and optical potential on the manipulated nanoparticle were analyzed. As the radius of particle varied from 100 to 500 nm, the mechanical frequency of particle decreased from 4.6 to 0.9 GHz. Significantly, the corresponding changing percent of the mechanical frequency of the cavity, \(\Delta\Omega_{m}/\Omega_{m}\) reached up to approximately 400%. Compared with the optical frequency shift of \(\pm 0.06\%\), monitoring the mechanical frequency was demonstrated as the better performance for particle sensing. However, the experimental demonstration of these sensing concepts was limited by the fiber taper coupling configuration and the quantification of nanoparticles. As a result, an alternative coupling method [137] in a PCN resonator was experimentally proposed as shown in Figure 22b. An on-chip femtogram-scale optomechanical crystal nanobeam with a coupled bus waveguide was operated in air and water environments. With a drop in mechanical quality factor from 2285 in the air to 6.6 in the water, the mechanical frequency was reduced to 5.251 from 5.3 GHz in air. Finally, the mass sensitivity of this proposed device could be estimated to be at the level of 1.33 ag/\(\sqrt{\text{Hz}}\). To be noted, these femtogram-scale nano-optomechanical resonators in liquid were promising in chemical analysis and biomedical applications. Meanwhile, nanomechanical resonators have extremely high sensitivities due to their ultrasmall mass and large mechanical Q-factor. For nanomechanical cavity mass sensing, the minimum detectable mass resolution is determined by the effective mass of a mechanical resonator. Therefore, another solution to further enhance mass sensitivity is to introduce a nanomechanical resonator into the on-chip integrated optomechanical systems [83; 86; 138]. As shown in Figure 23, a femtogram scale nanomechanical resonator with an ultralow effective mass of 6.42 fg was embedded in a double-slot PCN cavity [138] with a measured optical Q-factor up to \(2.25\times 10^{4}\). A displacement sensitivity of 0.13 fm/Hz\({}^{1/2}\) was demonstrated, which was 22 times beyond SQL. Similarly, a flexural nanomechanical  
Figure 21: Optomechanical torsion sensor: (**a**) a suspended nanobeam inscribed with PhC cavities at each side; (**b**) laser detuning of mechanical twisting of nanobeam [127]. resonator was also demonstrated in a 2D PhC nanocavity [83].