On the Theory of Light Propagation in Crystalline Dielectrics

A synoptic view on the long-established theory of light propagation in crystalline dielectrics is presented, providing a new exact solution for the microscopic local electromagnetic field thus disclosing the role of the divergence-free (transversal) and curl-free (longitudinal) parts of the electromagnetic field inside a material as a function of the density of polarizable atoms. Our results enable fast and efficient calculation of the photonic bandstructure and also the (non-local) dielectric tensor, solely with the crystalline symmetry and atom-individual polarizabilities as input.