## 3 Mechanically Tunable PhC Cavity Sensors
### Sensing Applications of Mechanically Tunable PhC Cavities
#### 3.2.1 Deformable Cavity-Based PhC Sensors
Later  
Figure 4: Nanobender cavity for displacement sensing: (**a**) nanobender cavity with waveguide-zipper PhC cavities coupling and electrical actuations; (**b**) close-up view on the zipper PhC cavities and waveguide coupling structure [96]. Figure 3: (**a**) Schematic of tunable longitudinally split PCN cavity; (**b**) longitudinal motion of side nanobeam [65], (**c**) lateral motion of side nanobeam [66]; (**d**) bending of both sides of nanobeam [67]; (**e**) schematic of a tunable transversely split PCN cavity [68]. All red arrows indicate the motion direction. in 2011 [72], they further investigated the sensing schematics of dual ring PhCs with various positions close to the junction of cantilever and substrate. The detection limit of force reached up to 7.58 nN. Besides, they also proposed a silicon device integrated with triple ring PhCs as a mechanical sensor [11], wherein a minimum detectable force of 0.847 nN with a force ranging from 10 to 20 nN was obtained. Similar to [PERSON]'s measurement system, [PERSON] et al. [98, 99] proposed a strain sensor using a silicon 2D PhC cavity by loading standard weights to the planar cantilever so that longitudinal strains were created in the PhC structure, as shown in Figure 5c. A linear relationship between applied strain and resonance shift was identified with a sensitivity of 0.95 pm/u-strain. Additionally, an electric field sensor based on reversible strain-tuning of a quantum dot strongly coupled to a PhC cavity [15] was demonstrated in Figure 5d. By mounting PhC cavity sample and piezo-electric actuator in parallel on the holder, the applied stress in the y-axis direction was exerted to deform defect of PhC cavities. The in-plane strain induced by applied electric field could lead to expansion or contraction of the PhC defect areas, thereafter the shift of resonant wavelength. Therefore, a redshift of 0.45 nm was experimentally achieved with an electric field of 15 kV/cm applied to a piezo-electric actuator. Mechanically tunable 2D PhC cavities could also be achieved by varying the air-slot distance, which has been developed for displacement sensing. [PERSON] et al. [9] theoretically demonstrated a micro-displacement sensor with a fixed and moving hole-array based slot PhC cavity, as shown in Figure 6a. The tuning of high-Q cavity was formed by laterally shifting two adjacent holes outwards in the opposite direction. It demonstrated a quasi-linear measurement of displacement with a sensitivity of 1.0 \(a^{-1}\) in simulation results. In a similar manner, Figure 6b demonstrated a magnetometer based on an on-chip scale slot PhC cavity with movable and fixed sections [13]. An air-slot was inserted in a planar photonic crystal slab and high Q factors were attained by designing the dimensions of the air holes near the cavity center. As the movable mass of optical cavity assembly was affected by the magnetic field to displace the movable mass and change the width of air-slot, the alteration of the  
Figure 5: (**a**) Schematic of the pressure detection system based on PhC cavity (inset: layout of PhC using a hexagonal array of holes with the lattice constants \(a\), \(\mathrm{A_{d}}\) and \(r\) are the distance between the center two holes and radius of hole) [97]; (**b**) 3D illustration of 2D PhC slab strain sensors using PhC resonator structure (inset: deformed single ring PhC cavity driven by stress) [73]; (**c**) schematic of PhC cavity for strain sensing (inset: sectional view of strain applied on PhC) [98, 99]; (**d**) schematic of electric field sensor with strain tuning of defect with PhC cavity [15]. width of air-slot can be detect through the optical resonance. With an in-plane displacement sensitivity of 1.0 pm/Hz\({}^{1/2}\), the enhanced magnetic sensitivity of 11.4 nT/Hz\({}^{1/2}\) was achieved. Out-of-plane deformation of 2D PhC cavity was also adopted for mechanical sensing applications. As shown in Figure 7a, a Si\({}_{3}\)N\({}_{4}\) cantilever was embedded in the center defect of 2D PhC cavity [77].