Abstract: We studied the band gap structure of TE (transverse electric) wave and TM (transverse magnetic) wave in twodimensional function photonic crystals by plane wave expansion method, and compared them with the band gap structure of twodimensional conventional photonic crystals. We studied the change of band gap structures of twodimensional function photonic crystals by giving the functional forms of dielectric constants of different dielectric columns. The results show that there exist absolute band gaps and Diraclike points in the twodimensional function photonic crystals.

Key words: band gap structure, two-dimensional function photonic crystal, Dirac-like point, absolute band gap