  A method is introduced to analyze the degeneracy properties of the band
structure of a photonic crystal making use of the super cells. The band
structure associated with a super cell of a photonic crystal has degeneracies
at the edge of the Brillouin zone if the photonic crystal has some kind of
point group symmetry. Both E-polarization and H-polarization cases have the
same degeneracies for a 2-dimensional (2D) photonic crystal. Two theorems are
given and proved. These degeneracies can be lifted to create photonic band gaps
by changing the transform matrix between the super cell and the smallest unit
cell. The existence of the photonic band gaps for many known 2D photonic
crystals is explained through the degeneracy analysis.
