Doppler-encoded Mie scattering rainbow of flying particles

Light scattering constitutes the most fundamental process in light-matter interactions and serves as the cornerstone of modern particle metrology. Although numerous scattering-based techniques have been established for characterizing particles in constrained motion, the precise analysis of freely flying particles remains largely underdeveloped. This limitation stems primarily from the severe constraints on accessible data acquisition time and the motion-induced image blur inherent in conventional scattering detection schemes. Here, we report the observation of a Doppler-encoded Mie scattering effect using optically propelled microparticles in antiresonant hollow-core fibers and further introduce a transverse Doppler spectrometry for single-particle-level metrology of flying particles. It is found that, when collected in the near field by a high-numerical aperture objective, the scattering fringes of a flying particle with divergent diffraction angles are encoded with distinct Doppler frequency shifts-this forms a broadband "scattering rainbow" in the transverse direction relative to the incident beam axis. This angle-dependent Doppler effect transforms the spatial diffraction pattern of a flying particle into the frequency domain, enabling high-precision determination of diameter and refractive index of airborne particles within a millisecond-scale observation window. Our findings unlock degrees of freedom for resolving flying particle features in the frequency domain, establishing a versatile diagnostic platform for a broad spectrum of applications that demand in situ particle analysis, such as atmospheric aerosol monitoring, hypersonic flow diagnostics, and label-free flow cytometry.