Unraveling Optical Polarization at Deep Microscopic Scales in Crystalline Materials

Nanophotonics, the study of light-matter interaction at scales smaller than the wavelength of radiation, has widespread applications in plasmonic waveguiding, topological photonic crystals, superlensing, solar absorbers, and infrared imaging. The physical phenomena governing these effects can be described using a macroscopic homogenized refractive index. However, the lattice-level description of optical polarization in a crystalline material using a quantum theory has been unresolved. Inspired by the dynamics of electron waves and their corresponding band structure, we propose a microscopic optical band theory of solids specifically applicable to optical polarization. This framework reveals propagating waves hidden deep within a crystal lattice. These hidden waves arise from crystal-optical indices, a family of quantum functions obeying crystal symmetries, and cannot be described by the conventional concept of refractive index. We present for the first time the hidden waves and deep microscopic optical band structure of 14 distinct materials. We choose Si, Ge, InAs, GaAs, CdTe, and others from Group IV, III–V, and II–VI due to their technological relevance, but our framework can be extended to a wide range of emerging 2D and 3D materials. In contrast to the macroscopic refractive index of these materials used widely today, this framework shows that hidden waves exist throughout the crystal lattice and have unique optical polarization texture and crowding. We also present an open-source software package, Purdue-Picomax, for the research community to discover hidden waves in new materials like hBN, graphene, and Moiré materials. Our work establishes a foundational crystallographic feature to discover novel deep microscopic optical waves in light-matter interaction.