  Rare-earth ions doped crystals are of great significance for micro-sensing
and quantum information, whilst the ions in the crystals emit light with
spontaneous partial polarization, which is, though believed to be originated
from the crystal lattice structure, still lacking a deterministic explanation
that can be tested with quantitative accuracy. We report the experimental
evidence showing the profound physical relation between the polarization degree
of light emitted by the doped ion and the lattice symmetry, by demonstrating,
with unprecedented precision, that the lattice constant ratio c/a directly
quantifies the macroscopic effective polar angle of the electric and magnetic
dipoles, which essentially determines the linear polarization degree of the
emission. Based on this discovery, we further propose a pure optical technology
to identify the three-dimensional orientation of a rod-shaped single
microcrystal using the polarization-resolved micro-spectroscopy. Our results,
revealing the physical origin of light polarization in ion-doped crystals, open
the way towards on-demand polarization control with crystallography, and
provide a versatile platform for polarization-based microscale sensing in
dynamical systems.
