Picoelectrodynamics: Atomistic Nonlocal Electrodynamic Waves in Silicon*

The concept of photonic frequency $(omega)$ - momentum $(q)$ dispersion has been extensively studied in artificial dielectric structures such as photonic crystals and metamaterials. However, the $omega-q$ dispersion of electrodynamic waves hosted in natural materials at the atomistic level is far less explored. Here, we develop an atomistic nonlocal electrodynamic theory of matter by combining the Maxwell Hamiltonian theory of matter with a quantum theory of atomistic polarization. We apply this theory to silicon and discover the existence of atomistic electrodynamic waves. Atomistic electrodynamic waves have sub-nano-meter effective wavelengths in the picoelectrodynamics regime. Further, we show that the atomistic optical conductivity in silicon is highly anisotropic along different momentum directions due to atomistic electronic correlations. Our findings demonstrate that the natural media host variety of yet to be discovered electromagnetic phases of matter and provide a pathway towards the discovery of rich atomic scale light-matter interaction phenomena.