  The explicit dispersion equation for a one-dimensional periodic structure
with alternative layers of left-handed material (LHM) and right-handed material
(RHM) is given and analyzed. Some abnormal phenomena such as spurious modes
with complex frequencies, discrete modes and photon tunnelling modes are
observed in the band structure. The existence of spurious modes with complex
frequencies is a common problem in the calculation of the band structure for
such a photonic crystal. Physical explanation and significance are given for
the discrete modes (with real values of wave number) and photon tunnelling
propagation modes (with imaginary wave numbers in a limited region).
