Obtaining the Band Structure of a Two-Dimensional Photonic Crystal by an Averaged Field Approach

An averaged field approach is suggested for obtaining the band structure of a photonic crystal when the dimension of the inclusions is much smaller compared with the longest period of the rectangular lattice of the photonic crystal.The method is illustrated for the H-polarization of the 2-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.