ABSTRACT
The use of homogenization methods in characterizing the interaction of electromagnetic fields with matter has a long history. Lorentz was the first to recognize that to properly describe molecular optics it was necessary to incorporate atomic concepts into Maxwell’s equations, and take into account the electric vibrations of the particles. He obtained a relation between the dielectric constant and the density of the material at optical frequencies, and established the foundations of macroscopic electromagnetism. The homogenization theory is an attempt to describe the interaction of electromagnetic radiation with very complex systems formed by an extremely large number of atoms, or in case of microstructured materials, formed by many inclusions. Electromagnetic fields with Floquet periodicity are of special importance in the characterization of periodic media. For dielectric crystals, the classical boundary conditions can also be derived directly from the expansion of the microscopic fields into Floquet modes using the concept of transverse averaged fields.
