## 3 Mechanically Tunable PhC Cavity Sensors
### Sensing Applications of Mechanically Tunable PhC Cavities
#### 3.2.3 Mode-Splitting Based Coupled PhC Sensors  
Mechanically tunable configuration can also be obtained via multi-coupled cavities by controlling the coupling strength between them. Taking a pair of PCN cavities coupled configuration in Figure 10a as an example, their coupling strength can be tuned by controlling the in-plane coupling gap to cause  
Figure 8: Schematics of the tunable PhC cavities based on near-field probe perturbation: (**a**) moveable probe-based single PCN cavity (inset: close-up view on two probe tips) [42]; (**b**) PhC side-coupled piston-rod microcavity (inset: depth variation \(\Delta h\) due to the strain displacement) [89]. Figure 9: (**a**) Schematic of PCN cavity with polydimethylsiloxane (PDMS) coating; (**b**) cross-sectional view of gas cell and membrane deformation caused by pressure difference [101]. resonance shifts of even and odd modes. Such a configuration has attracted a lot of interests due to its potential for strong opto-mechanical interaction. Mechanically tunable coupled-PCN cavities could be modulated by the in-plane gap between two nanobeams (see Figure 10b) [49; 50; 51; 52], in-plane laterally center offset (see Figure 10c) [53; 54], out-of-plane rotation of suspended cavity (see Figure 10d) [55] as well as out-of-plane bending nanobeams (see Figure 10e) [56]. [PERSON] et al. [53] proposed a coupled PCN cavity by laterally driving a center-to-center offset to control the coupling strength dynamically, resulting in that optical mode splitting width decreased with the increment of lateral offset. [PERSON] et al. [55] designed a torsion-induced coupled PCN cavity using a NEMS comb drive to demonstrate an optical spring effect with a maximum 77.1 Hz mechanical frequency drop by laser detuning. Besides, the out-of-plane coupled PCN cavity motion was presented using a vertical electrostatic force generated by tuning the potential difference between isolated layers [56]. With an applied voltage of 12 V, an out-of-plane displacement could cause a redshift of 40.5 pm in the second-order odd resonance mode and a blueshift of 63.5 pm in the second-order even resonance mode. For sensing applications, a mechanically tunable coupled PCN cavity can also get its application in magnetic field sensing based on MEMS-actuated Lorentz force. As demonstrated in Figure 11a, a magnetometer was presented based on the resonance wavelength shift of a target supermode of the coupled PCN cavities. With the presence of magnetic field, the interaction between magnetic field and electric current in gold nano-wires could generate a Lorenz force to actuate a vertical offset variation between two coupled cavities. The resonance shift was caused by the Lorentz force-induced relative out-of-plane motion of movable nanobeam, thereby affecting the optical transmission [14]. The sensitivity and resolution were experimentally demonstrated as 22.9 mV/T and 48.1 \(\mu\)T/Hz\({}^{1/2}\), respectively. Compared with other MEMS magnetometers, the proposed coupled PCN cavity sensor had a much smaller footprint. Thus, it could potentially achieve higher spatial sensing resolution of magnetic field. With an on-chip integrated NEMS actuator, another coupled PCN cavity was mechanically reconfigured in the lateral direction while keeping a constant separation gap [54], as shown in Figure 11b. By measuring the variation of resonance wavelength split width, the shearing optical force was detected at the scale sub-nano Newton (-0.29 nN). Such a lateral shearing optical force detection could be further studied in the applications of optomechanics and might be developed for optically driven tunable filters and optical switches. Similarly, 2D PhC cavities can also be vertically coupled [79] by electrostatically actuating the out-of-motion controlled separation gap between two cavities. As a result, a resonant wavelength split can be obtained with the variation of vertical coupling gap.