  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 excitations hosted in natural materials at the atomistic level
is far less explored. Here, we develop a Maxwell Hamiltonian theory of matter
combined with the quantum theory of atomistic polarization to obtain the
electrodynamic dispersion of natural materials interacting with the photon
field. We apply this theory to silicon and discover the existence of anomalous
atomistic waves. These waves occur in the spectral region where propagating
waves are conventionally forbidden in a macroscopic theory. Our findings
demonstrate that natural media can host a variety of yet to be discovered waves
with sub-nano-meter effective wavelengths in the pico-photonics regime.
