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Rare-earth ions doped crystals are of great significance for micro-sensingand quantum information, whilst the ions in the crystals emit light withspontaneous partial polarization, which is, though believed to be originatedfrom the crystal lattice structure, still lacking a deterministic explanationthat can be tested with quantitative accuracy. We report the experimentalevidence showing the profound physical relation between the polarization degreeof light emitted by the doped ion and the lattice symmetry, by demonstrating,with unprecedented precision, that the lattice constant ratio c/a directlyquantifies the macroscopic effective polar angle of the electric and magneticdipoles, which essentially determines the linear polarization degree of theemission. Based on this discovery, we further propose a pure optical technologyto identify the three-dimensional orientation of a rod-shaped singlemicrocrystal using the polarization-resolved micro-spectroscopy. Our results,revealing the physical origin of light polarization in ion-doped crystals, openthe way towards on-demand polarization control with crystallography, andprovide a versatile platform for polarization-based microscale sensing indynamical systems.

Deterministic relation between optical polarization and lattice symmetry revealed in ion-doped single microcrystals