Unraveling Optical Polarization at Deep Microscopic Scales in Crystalline Materials

Understanding how optical waves propagate through the crystal structure of materials is crucial for designing optical materials and advancing the frontier of optical technologies. A long-standing challenge has been to fully understand how atomic arrangements and their symmetries influence the propagation of optical waves throughout the crystal lattice. To address this, here we develop a deep microscopic optical band theory of solids specifically applicable to optical polarization. We show that much like electrons have a band structure defining their allowed states within a crystal, optical waves within a crystal exhibit a deep microscopic optical band structure. In contrast to the macroscopic refractive index of materials used widely today, the deep microscopic optical band structure unveils that hidden waves exist throughout the crystal lattice and have a unique optical polarization texture and crowding. Further, we demonstrate that in non-centrosymmetric materials with screw symmetry, our framework reveals hidden optical spin polarization texture and accurately predicts the super-dispersive nature of optical gyrotropy. Our work establishes a foundational crystallographic feature to discover novel deep microscopic optical waves in light-matter interaction.