Angle-multiplexed metasurface-grating for ultra-compact spectrometers

Miniaturizing optical spectrometers is constrained by the trade-off between spectral resolution and optical path length. We present an ultra-compact architecture leveraging angular dispersion of guided-mode resonances (GMR) for spectral encoding. Exploiting phase-matching at oblique incidence yields deterministic mapping, where incidence angle linearly tunes resonant wavelength. Our symmetric multi-layer architecture, a low-index metasurface-grating sandwiched between high-index guiding layers, achieves high-Q resonances (Q>10³). Tailored for 550-1700 nm, we theoretically demonstrate 23.1 nm/° sensitivity with 0.75 nm resolution (≈12 cm^-1), enabling Raman fingerprinting of bacterial isolates with strain-level differentiation. This compact (≈1 nm) solid-state solution advances consumer-grade chemical sensing, lab-on-chip diagnostics, and smartphone spectroscopy.