  We propose a new method to compute band structures of dispersive photonic
crystals. It can treat arbitrarily frequency-dependent, lossy or lossless
materials. The band structure problem is first formulated as the eigenvalue
problem of an operator function. Finite elements are then used for
discretization. Finally, the spectral indicator method is employed to compute
the eigenvalues. Numerical examples in both the TE and TM cases are presented
to show the effectiveness. There exist very few examples in literature for the
TM case and three examples in this paper can serve as benchmarks.
