## 4 Radiation Pressure-Driven PhC Cavity Sensors
### Sensing Applications Based on Radiation Pressure
#### 4.2.1 Displacement Sensing
The first optomechanical PhC cavity system was featured with strong nonlinear optomechanical coupling, low mass as well as large optical mode displacing, as illustrated in Figure 16. A suspended paddle-like nanocavity [117; 118; 119] with hundreds of femtograms of mass could support several mechanical resonances (see inset in Figure 16) driven by the radiation pressure at the cavity resonance. This paddle nanocavity was nonlinearly coupled to a PhC nanocavity with a quadratic optomechanical coupling coefficient \(g_{2}>2\pi\times 400\) MHz/nm\({}^{2}\) and an optomechanical coupling rate of \(\Delta\omega_{0}>2\pi\times 16\) Hz. Additionally, thermally driven mechanical movements of the paddle nanocavity were also coupled and translated by observing resonances in the mechanical spectrum. The paddle nanocavity was useful for optomechanical force sensing and nonlinear optomechanics. To enhance the performance of the square of mechanical motion, a large position-squared optomechanical coupling was realized in a planar silicon PhC cavity [120], as presented in Figure 17a. By tuning the coupling rate of mode splitting in PhC cavities, it experimentally demonstrated a position-squared vacuum coupling rate reached up to g/2\(\pi=245\) Hz inferred between the optical supermodes. Under the action of radiation pressure, it excited the fundamental in-plane mechanical motion at the frequency of \(\Omega_{m}\)/2\(\pi=8.7\) MHz, which corresponded to a coupling displacement coefficient of g\({}^{\prime}\)/2\(\pi=1\) THz/nm\({}^{2}\). In comparison to other photonic schemes, due to the strong optomechanics effect and flexible mechanical structure, the position-squared coupling rate was much larger than that reported in the microdisk-cantilever [121] and paddle nanocavity [117] systems. Figure 15: Schematics of squeezed light in optomechanics for displacement sensing: (**a**) waveguide-coupled zipper optomechanical PCN cavity [112]; (**b**) optical fiber tip routed zipper PCN cavity [61]. Another displacement transducer with an imprecision below SQL was demonstrated using a sliced PCN cavity, as shown in Figure 17b[47]. Light in the sliced PCN resonator was highly confined in the nanoscale volume to create a radiation pressure to move the interface of sliced cavity with a low mass of \(\sim\)2.4 pg, which lead to unprecedented optomechanical interaction strength of g/2\(\pi\approx\) 11.5 MHz. The nonlinear transducer with a relatively large cavity bandwidth (0.5 THz) is attractive for system integration and miniature sensor technologies in nano-optomechanical systems. PhC cavities are significantly promising to provide the platform for on-chip integration with MEMS technologies, wherein large radiation pressure can be excited due to the strong optomechanical coupling in the nanoscale mode volume. Therefore, a chip-scale platform for studying the mechanical degree of freedom induced by radiation pressure is achieved by integrating cavity optomechanics with MEMS, where optomechanical system demonstrates near quantum-limited motion read-out and strong radiation pressure backaction. As shown in Figure 18, the electromechanical control of cavity air slot width could tune the optical cavity resonance in the slot 2D PhC membrane cavity [82; 122]. The strong light confinement in the air slot region made the optical mode frequency ultrasensitive to the separation of two PhC membranes. The optical field was localized inside the air-slot nanocavity between two PhC membranes, which gave rise to the radiation pressure due to strong optomechanical coupling. It was demonstrated that a wide-band (\(\sim\)19 nm) electromechanical tuning of the optical resonance near shot-noise limited optical read-out of mechanical motion at the acoustic mode frequency of 3.6 MHz [82]. Likewise, another all-integrated MEMS was developed in an ultrahigh Q-factor slotted PhC microcavity [123]. Both electromechanical and optomechanical interactions yield effective electrical actuation and sensitive optical transduction of mechanical modes of the PhC membrane.