Chip-scale precision optical displacement readout of fused silica dual-shell resonators

We propose and demonstrate a photonic integrated circuit (PIC) based optical displacement detection readout for characterizing fused silica Dual-Shell hemispherical resonators. The system employs on-chip homodyne interferometry to measure picometer to nanometer-scale displacements of Dual-Shell fused silica resonators operating in their fundamental <i>n</i> = 2 wineglass mode. The PIC implementation leverages silicon photonic components, including custom-designed grating couplers for free-space optical interrogation, integrated germanium photodetectors, and thermo-optic phase shifters for quadrature control. Experimental characterization of a vacuum-packaged dual shell resonator revealed <i>n</i> = 2 mode resonance frequencies of <i>f</i>₁ = 34664.8 Hz and <i>f</i>₂ = 34791.4 Hz, with a frequency split of 126.6 Hz, showing excellent agreement with reference laser Doppler vibrometer (LDV) measurements. The system's dual-channel capability enables simultaneous displacement measurements at multiple rim locations and the ability to distinguish between orthogonal wineglass modes. This integrated optical approach offers a compact, scalable solution for high-precision displacement sensing in MEMS gyroscopes, with potential applications in inertial navigation systems requiring sub-nanometer displacement resolution.