## 2 Photonic Crystal Cavities for Opto-Mechanical Interaction
### Experimental Opto-Mechanical PhC Cavities
#### 2.2.1 One-Dimensional Photonic Crystal Nanobeam in Opto-Mechanical System  
For 1D photonic crystal nanobeam (PCN) cavities, their opto-mechanical configurations and metrics are illustrated and summarized in Table 1. 1D PCN cavities attract great attention for their ultra-compact size, ultra-small mode volume, and high integrability with PICs in the ultra-sensitive optical sensing. A single PCN cavity in the mechanically tunable method was mainly developed to detect an external nanoscale probe driven by a NEMS comb-drive actuator [8; 42]. However, mechanical tuning of a probe perturbation inevitably caused a significant drop in Q-factor and transmission of cavity. In the radiation pressure-driven applications, single PCN cavities have been extensively developed for optomechanical systems. To enhance the mechanical quality factor in the suspended PCN cavity, an attached phononic shield-a lattice around the resonator [43] was proposed. The lattice phononic shield enhanced the arbitrary mechanical modes of a nanobeam by adjusting the frequency of phononic band gap, which reduced mechanical loss while maintaining the optical properties of cavity mode. Figure 1: Schematics of (**a**) 1D, (**b**) 2D, and (**c**) 3D photonic crystal (PhC) cavities [37; 38]. When two PCN cavities are placed close to each other and their mode fields are coupled together, resonant frequencies of coupled supermodes can be adjusted by controlling the coupling strength between two cavities. In mechanically tunable coupled PCN configurations, under the applied electrostatic force of N/MEMS actuation, physical displacement of moveable PCN cavity could be modulated in-plane gap between two nanobeams [49, 50, 51, 52], in-plane laterally center offset [53, 54], out-of-plane rotation of suspended cavity [55] as well as out-of-plane bending nanobeams [56]. In a similar method, a vertically coupled PCN cavity [57] was electrostatically controlled. With two PCNs etched on two vertically coupled GaAs flexible nanobeams, a large wavelength tuning range over 12 nm was achieved through a bias voltage 15V. Moreover, triple-coupled PCN cavities [58, 59] with a Q-factor reaching up to \(8\times 10^{4}\) have been reported. By precisely controlling the position of cavity vertically and horizontally, a 41.69-pm wavelength tuning of resonance and small degradation of Q-factor were obtained [59]. Coupled resonant system with high Q-factor and high transmission opened interesting perspectives in nonlinear optics and signal processing. In the radiation pressure-driven systems, two laterally coupled PCN cavities [44, 60] could support propagating waveguide modes and achieve a large coupling strength to GHz mechanical resonators in the Si\({}_{3}\)N\({}_{4}\) PCN cavity. More importantly, a flexible design of mechanical resonator could greatly vary mechanical stiffness and frequency, in turn, resulting in stronger optomechanical coupling strength. Another laterally coupled PCNs [61, 62, 45, 63] also called zipper cavity, were designed and fabricated with resonator mass of pg order of magnitude. Consequently, a combination of decreasing mechanical loss at the mechanical frequency and reduced effective motion mass (10 pg to 50 fg) resulted in a dramatically enhanced force sensitivity of optomechanical system. In the zipper nanobeams, an optical force-induced spring effect was observed through mechanical frequency shift and linewidth variation. From the perspectives of engineering applications, zipper nanobeam paved the way for wide-bandwidth optical frequency conversion and filtering induced by optical forces. Besides, a vertically coupled PCN cavity [64] was demonstrated with a lower motion mass, and a comparable optical Q-factor and mode volume, resulting in larger zero-point fluctuations of mechanical modes and larger photon-phonon coupling rates. Except for the tunable mechanisms of coupled PCN cavities, another effective approach to tune a cavity is to reshape the resonator itself.