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 co mpared with the longest period of the rectangular lattice of the photonic c rystal. The method is illustrated for the H-polarization of the 2-dimension al case. The band structure is obtained in an explicit and simple way. The method is verified numerically by comparing with the conventional plane-wav e expansion method.