Waveguide Bragg grating-enhanced microcantilever-based force sensor

We present an integrated optomechanical force sensor that employs waveguide Bragg gratings (WBGs) embedded in microcantilevers, offering a compact, fully passive optical readout suitable for atomic force microscopy (AFM) applications. Using a fully coupled three-dimensional (3D) finite element framework, we simultaneously model cantilever deformation, stress-induced refractive index changes, and optical mode evolution, offering improved accuracy and efficiency over decoupled approaches. Our analysis shows that the Bragg resonance shift arises primarily from the photoelastic effect and the resulting inhomogeneous refractive index distribution, with negligible contribution from cantilever bending-induced grating period changes, clarifying a mechanism often oversimplified in previous studies. By examining both the magnitude and direction of the resonance shift at a fixed interrogation wavelength or across the full reflection spectrum, we demonstrate that both compressive and tensile forces can be detected, enabling directional, all-optical force sensing. Simulations indicate that nanoscale forces applied at the cantilever tip produce detectable Bragg wavelength shifts, achieving a maximum force resolution of approximately 0.62 nm and a minimum detectable force of 1.6 nN (for a 1 pm wavelength resolution). Beyond AFM, these findings establish clear design rules for the development of highly sensitive, fabrication-tolerant, and fully integrated photonic force transducers with potential applications in biosensing, lab-on-chip applications, and scalable MEMS/NEMS sensor arrays.