Common-path metasurface interferometry for on-chip transverse-displacement metrology in chip-scale inertial sensors

The resolution of a chip-scale inertial sensor—an accelerometer, gyroscope or micro-vibrometer—is ultimately set by the readout that transduces the motion of its proof mass, and an on-chip readout must combine interferometric sensitivity with a wavelength-thin form factor. We address this need with a fully planar, common-path metasurface interferometer and analyze the conditions under that it could operate. The device cascades two metasurfaces within a sub-110 μm optical path: a Pancharatnam–Berry phase-gradient encoder that deflects the two circular-polarization components by ±15 deg (macro-period Λ≈2.0 μm) and writes a transverse displacement onto their relative phase, and a polarization-multiplexed bifocal metalens that re-collects both spins in-plane and, through a built-in π bias, converts the encoded phase into two complementary, common-mode-rejecting focal channels. A Jones-matrix transfer model and a cascaded full-wave-assisted simulation establish the splitting, recombination and focusing across the 70 μm air gap onto the 105 μm detection plane, and yield a projected displacement sensitivity of about 80 V μm, a Monte Carlo standard deviation of 12.43 pm, and a local resolution below 40 pm under a 1 mV electronic-noise floor. The normalized optical slope of the transducer is 4π/Λ≈6.283 μm−1, set by the encoder period and the coherent recombination; the ∼80 V μm voltage slope refers to a specified readout condition and additionally includes the detector responsivity and electronic gain, whereas under a 1 kHz bandwidth the conditional system resolution is 1.12 pm root sum square. Going beyond a single resolution figure, we add an explicit stability and error-scope analysis—spanning channel imbalance, inter-channel cross-talk, phase-reference drift, the finite quadrature window, and the periodic ambiguity of absolute displacement—to delineate what would be required for these simulated numbers to hold in practice. The results are therefore a model-based benchmark and a design guideline for integrated motion readout, not an experimentally validated sensor specification.