Integral and integradifferential equations for photonic crystal

In resent years, in connection with big development of nanotechnology, there is a grate interest to one-dimensional (ID), two-dimensional (ZD), and three-dimensional (3D) artificial periodic structures, which usually obtained by implantation of different bodies (metallic, dielectric, semiconductive etc.) into the based homogeneous dielectric (see, for example, special issue [1]). Such structures in optics were named as photonic crystals (PCs). Often they have unique properties such as cyrality, anisotropy and bianisotropy [2-4], both negative permittivity and permiability in any frequency range [5-7] with corresponding effects [8], including the unusual refraction and reflection lows. Also they may have the bandgap [5-7]. Such structures well known for a long time and were named earlier as artificial dielectrics (AD) [9-11],but the most papers used the approximate or model approaches to analyze AD or PC. Moreover, the PCs usually are analyzed in the resonance or high frequency range where the rigorous electromagnetic modeling is necessary.