Unraveling Optical Pico-polarization of Zinc-Blend Materials*

The dynamics of electron waves and their corresponding dispersion in crystalline materials have shaped our understanding of materials science and condensed matter physics. On the contrary, the lattice-level description of optical waves has long been unresolved. Here, we put forth a pico-optical band theory of solids which completely characterizes the dynamics of optical polarization waves within a crystal lattice. We unravel the optical pico-polarization of 14 distinct Group IV, III-V, and II-VI materials. We show that our optical pico-polarization indices generalize the concept of the refractive index of the medium to determine the polarization texture and crowding throughout the crystal lattice. The optical pico-polarization indices serve as symmetry indicators and provide a signature for identifying optical topological phases in natural materials. Our work establishes a foundational crystallographic feature to discover novel pico-optical phases of matter.