  Nanophotonics, which deals with the study of light-matter interaction at
scales smaller than the wavelength of radiation, has widespread applications
from plasmonic waveguiding, topological photonic crystals, super-lensing, solar
absorbers, and infrared imaging. The physical phenomena governing these effects
can be captured by using a macroscopic homogenized quantity called the
refractive index. However, the lattice-level description of optical waves in a
crystalline material using a quantum theory has long been unresolved. Inspired
by the dynamics of electron waves and their corresponding band structure, here,
we put forth a pico-optical band theory of solids which reveals waves hidden
deep within a crystal lattice. We show that these hidden waves arise from
optical pico-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 pico-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 is readily applicable to a wide range of emerging 2D and 3D
materials. In stark contrast to the macroscopic refractive index of these
materials used widely today, this picophotonic framework shows that hidden
waves exist throughout the crystal lattice and have unique pico-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 Moire materials. Our work establishes a
foundational crystallographic feature to discover novel pico-optical waves in
light-matter interaction.
