Abstract: We used the planewave expansion method to derive the master equation of twodimensional photonic crystal for transverse magnetic mode and transverse electric mode, and obtained the complete photonicbandgap of twodimensional photonic crystal for two modes. We studied the change rule
of filling ratio and dielectric constant of background medium with the complete photonicbandgap width and center frequency location of twodimensional photonic crystal. Thus, the optimal design of the complete photonicbandgap was realized.

Key words: wave expansion method, twodimensional photonic crystal, plane\, complete photonicbandgap