A new and explicit method for obtaining the band structure of a dielectric or conducting photonic crystal

An averaged field approach is presented for obtaining the band structure of a photonic crystal when the dimension of the inclusions (dielectric or conducting) is small compared with the longest period of the rectangular lattice of the photonic crystal. The method is illustrated for the 2-dimensional case but can be easily generalised to the three-dimensional case. The band structure is obtained in an explicit and simple way. The method is verified numerically by comparing with the conventional plane-wave expansion method (for the dielectric case) and a FDTD method (for the conducting case)