Abnormal phenomena in a one-dimensional periodic structure containing left-handed materials

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).