Symmetry Fingerprints Unlocked: Room-Temperature Single-Particle Polarized Spectroscopy Reveals Complete Symmetry Landscape in Rare-Earth Crystals

Abstract: The point group symmetry of luminescent centers-such as defects, impurities, and dopant ions-fundamentally determines optical transition characteristics, underpinning advances in materials science and optoelectronics. Conventional low-temperature spectroscopy assesses such symmetry through the splitting of optical transitions, yet lacks sensitivity to key vectorial features such as symmetry axis orientations. Here, we introduce a single-particle approach that integrates computational electromagnetism with polarization-resolved microspectroscopy at room temperature, enabling unambiguous mapping of transition dipole orientations from a single magnetic optical transition and thus direct determination of point group symmetry in rare-earth-doped microcrystals. This technique also reveals spontaneous symmetry breaking in chiral space groups during crystallization, giving rise to intrinsic single-particle optical chirality. Leveraging these symmetry insights, we establish a practical protocol for optically polarized sensing of the three-dimensional orientation (3D) of rare-earth-doped single particles in cellular environments. Our method uncovers both the vectorial point group symmetry of rare-earth ions and the chiral nature of the crystal-a level of structural information unattainable by conventional spectroscopic or crystallographic techniques. By bridging microscopic symmetry with macroscopic functionality, this work enables quantitative evaluation of the Forster dipole orientation factor (k2) for rational donor-acceptor design, and lays the foundation for next-generation energy transfer systems, ultra-bright rare-earth nanocrystals, nanophotonic materials, and real-time single-particle sensing in biological contexts.