Photonic band structure of one-dimensional metal/dielectric structures calculated by the plane-wave expansion method

The plane-wave expansion(PWE) method is employed to calculate the photonic band structures of metal/dielectric(M/D) periodic systems. We consider a one-dimensional(1D) M/D superlattice with a metal layer characterized by a frequency-dependent dielectric function. To calculate the photonic band of such a system, we propose a new method and thus avoid solving the nonlinear eigenvalue equations. We obtained the frequency dispersions and the energy distributions of eigen-modes of 1D superlattices. This general method is applicable to calculate the photonic band of a broad class of physical systems, e.g. 2D and 3D M/D photonic crystals. For comparison, we present a simple introduction of the finite-difference(FD) method to calculate the same system, and the agreement turns out to be good. But the FD method cannot be applied to the TM modes of the M/D superlattice.