Pico-photonics: Anomalous Atomistic Electrodynamic Dispersion in Silicon

The concept of photonic frequency and momentum dispersion has been extensively studied in artificial dielectric materials such as photonic crystals and metamaterials. However, atomistic dispersion of electrodynamic excitations in natural media is an unexplored frontier. Here, we propose the concept of atomistic electrodynamic dispersion as a solution to the Maxwell Hamiltonian of matter. The atomistic electrodynamic dispersion determines the functional frequency and momentum dependency of the transverse electrodynamic excitations. We introduce the microscopic transverse dielectric tensor derived from the electronic bandstructure to the Maxwell Hamiltonian. Using this theory, we show the existence of anomalous electromagnetic waves in the forbidden spectral region in silicon. The anomalous waves have sub-nano meter wavelengths in the pico-photonics regime. The recognition of anomalous waves in silicon is a direct consequence of including short-range local-field effects in the transverse dielectric response of the material. Moreover, at a given frequency, the anomalous waves are found to generate previously undisclosed electromagnetic energy contributions. Our findings demonstrate the evidence for existence of new electromagnetic phases of matter in natural media such as silicon.