Miniaturized computational dispersion-engineered silicon photonic vernier caliper spectrometer

The development of miniaturized spectrometers for cost-effective mobile applications remains challenging, as small footprints fundamentally degrade bandwidth and resolution. Typically, achieving high resolution necessitates extended and sophisticated optical paths for spectral decorrelation. These restrict bandwidth both physically (through resonant wavelength periodicity constraints) and mathematically (due to resulting ill-conditioned large matrix factorizations). Here, we report a spectrometer using a computational dispersion-engineered silicon photonic Vernier caliper. This deterministic design enables periodicity-suppressed orthogonal measurements by nature, thus overcoming the bandwidth-resolution-footprint limit of current chip-scale spectrometers. Leveraging the dispersion-engineered Vernier subwavelength grating microrings and factorizations-free matrix computation, an average spectral resolution of 1.35 pm is achieved throughout a bandwidth of > 160 nm with a footprint of < 55 × 35 μm 2 in a single detection channel, establishing the highest bandwidth-to-resolution-to-footprint ratio (> 61.5 μm − 2 ) demonstrated to date. Furthermore, broadband densely overlapped molecular absorption spectra of hydrogen cyanide are precisely measured, resolving 49 R- and P-branch lines with linewidths ranging from 15 to 86 pm which is fundamentally challenging for compressive sensing approaches. Our chip-scale spectrometer provides a new path toward precise and real-time multi-species spectral analysis and facilitates their commercialization.