Domain integral representation vs. homogenization methods for the analysis of photonic band gaps and absorbers

The reflectivity of two-dimensional pyramidal absorbers and the transmittance of photonic crystals made of dielectric fibers is analyzed by means of two approaches. In the first one an integral representation of the scattered field is used and the absorbers are modeled by a stack of gratings of infinite extent. In the second approach, the absorbers and the crystal are replaced by an equivalent multilayered medium obtained by means of two homogenization methods. We assess the efficiency of these methods with respect to parameters such as the density of the gratings, their relative permittivity and the polarization of the incident wave.