Bloch wave approach to the optics of crystals - art. no. 021704

The Bloch wave method is used to find the effective permittivity tensor <(< epsilon>)over tilde> of periodic liquid crystals and artificial structures whose period p is short with respect to the light wavelength lambda and who se optical properties are defined by a permittivity field epsilon (r). The main role of the multiple scattering within the periodic medium is evidence d, and very general expressions of <(<epsilon>)over tilde>, based on expans ions in ascending powers of the ratio p/lambda and of the light wave vector k, are found. Such expansions allow to discuss the general properties of < (<epsilon>)over tilde>, to clarify the role of the spatial dispersions, i.e ., to separate the part of <(<epsilon>)over tilde> explicitly depending on k from its k-independent part, and to find some interesting properties of c rystals that are (i) periodic in only one direction, or (ii) locally isotro pic. Finally, the limits of validity of the macroscopic model are discussed . Within these limits only a few terms of the power expansions are required , and their expressions are explicitly given. The obtained results are also useful to better understand the macroscopic optical properties of solid cr ystals.