On the Homogenization of Maxwell Equations

We discuss the following general problem: given a composite, made from at least two different materials with each its own (scalar, and possibly complex-valued) ε and μ, distributed in space in a regular, crystal-like, pattern, find the equivalent permittivity and permeability (they will, in general, be tensors). This is homogenization. A computation in which such repetitive composites are present can then be done by simply replacing these with their equivalent, homogenized, materials.