Spectral properties of optical mediums with transmitting symmetry containing plasma-like layers

The materials with a periodical symmetry (superlattices, layered-periodical structures) are applied in different areas of science. For example, in X-ray techniques they are used as reflectors, in optical and infrared ranges the periodical layered coats are applied for a coated lens etc. The properties of such mediums depend on the physical properties of the materials, from which they are formed and on geometrical sizes of the layers and on the structure period. The electrodynamical properties of the materials formed by the periodical iteration of the layers of a dielectric and substance, the dielectric permeability of which depends on frequency and can be negative, are investigated in the paper. Such a substance is the semiconductor for infrared or optical ranges, gas-discharge plasma for a centimetre wave frequency. We shall show that the specific allowed bands exist in semiconducting lattices that are connected with the plasma properties of the lattice layers.