An averaged-field approach for obtaining the band structure of a dielectric photonic crystal

An averaged-field approach is suggested for obtaining the explicit form of the dispersion equation for electromagnetic waves propagating in a three- o r two-dimensional dielectric photonic crystal when the dimension of the inc lusions is small compared with the longest period of the rectangular lattic e of the photonic crystal. The band structure is obtained in an explicit an d simple way. The method is verified numerically by comparing with the conv entional plane-wave expansion method for a special case.