  In this paper, we have firstly proposed two-dimensional function photonic
crystals, which the dielectric constants of medium columns are the functions of
space coordinates $\vec{r}$, it is different from the two-dimensional
conventional photonic crystals constituting by the medium columns of dielectric
constants are constants. We find the band gaps of two-dimensional function
photonic crystals are different from the two-dimensional conventional photonic
crystals, and when the functions form of dielectric constants are different,
the band gaps structure should be changed, which can be designed into the
appropriate band gaps structures by the two-dimensional function photonic
crystals.
