## 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
Split nanobeam in PCN cavity is a typical example, and it can be structurally classified into longitudinally split and transversely split cavities. The longitudinally split PCN cavity consisted of an air gap in the middle of nanocavity and a pair of Bragg mirrors patterned on side cantilever beams. By altering the axial separation gap of two aligned cantilevers, the Q-factor of the cavity was largely tuned and yet, the resonant frequency was barely affected [65]. Longitudinally split PCN cavities could also be mechanically controlled by varying the offset laterally in-plane [66] and out-of-plane [67] while maintaining the constant separation gap. The transversely split PCN cavity was split by an air-slot into two symmetric parts. By controlling both movable structures by the comb-drive actuators, the width of air-slot affected the performance of cavity resonance. In the reported experiments [68, 69], the second-order mode resonance shift of up to 17 nm was achieved with an air-slot \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Classification**} & **Single PCN** & **Coupled PCNs** & **Zipper** & **Split PCN Cavity** & **Slot** \\  & **Cavity** & **Cavity** & **Longitudinally** & **Transversely** & **Embedded-PCN** \\  & & & **Split PCN** & **Split PCN** & **Cavity** \\ \hline Structure & & & & & \\ Optical Q & \(9.06\times 10^{5}\) & \(-3.8\times 10^{3}\) & \(-10^{4}\)\(-10^{5}\) & \(5.2\times 10^{3}\) & 400 & \(-1.2\times 10^{5}\) \\ Mechanical Q & \(6.8\times 10^{5}\) & \(5.9\times 10^{3}\) & 50–150 (air) & \(<\)100 (air) & N/A & 417 (air) \\ Mechanical frequency & \(5.1\) GHz & \(-1.18\) MHz & \(-8\) MHz & 10.5 MHz & \(-3\) MHz & 2.69 GHz \\ Optomechanical & \(1.1\) MHz & \(-6.43\) kHz & \(123\) GHz/mm & \(3\) GHz/mm & \(11.5\) MHz & \(310\) kHz \\ coupling rate & (g/2\(\pi\)) & (g/2\(\pi\)) & (g/2\(\pi\)) & (g/2\(\pi\)) & (g/2\(\pi\)) \\ Mode volume & N/A & N/A & \(0.2\) (\(\lambda/m\))\({}^{3}\) & \(0.35\) (\(\lambda/m\))\({}^{3}\) & N/A & \(0.017\) (\(\lambda/m\))\({}^{3}\) \\ Mass & \(127\) fg & \(-10\) pg & \(-3\) pg & \(-1\) pg & \(-24\) pg & \(103\) fg \\ Reference & [43] & [44] & [45] & [46] & [47] & [48] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Typical configurations of 1D PhC cavities for opto-mechanical interactions. gap increment of 26 nm while the Q-factor could be maintained. In the radiation pressure-driven systems, the dynamics of suspended structure in the longitudinally split PCN cavities [46; 70] were applied for detecting mechanical motions. Likewise, the transversely split PCN cavity mechanically resembled a pair of double clamped beams [47], and the half beam with an ultra-small mass (\(\sim\)2.4 pg) and small spring constant contributed to a large mechanical motion with an ultra-high optomechanical coupling rate \(g_{o}/2\pi\approx 11.5\) MHz. To further enhance optomechanical coupling, a central nano-slot was added in the middle of the PCN cavity [48; 71]. In Ref. [48], the slotted PCN optomechanical cavity with an ultrasmall mode volume 0.017 \((\lambda/n)^{3}\) and an optical Q-factor up to \(1.2\times 10^{5}\) was demonstrated, which enabled the device to work in the resolved sideband with an optomechanical coupling rate of 310 kHz and a measured mechanical mode of 2.69 GHz. In such a configuration, the maximum electric field in the small mode volume was localized out of dielectric material. It provided an attractive platform to explore an additional coupling to the mechanical resonator (e.g., carbon nanotubes and nanowires).