Pseudo volume plasmon in arrays of doped and un-doped semiconductors

We present a theoretical work which shows that for a metamaterial consisting of a periodic array of doped and un-doped semiconductors it is possible to define a frequency ?? _t corresponding to a pseudo volume plasmon. ?? _t?depends on the thicknesses and on the dielectric constants of the components of the metamaterial and on the plasma frequency of the doped semiconductor. As its homologue in noble metal, the pseudo volume plasmon is the collective oscillation of charges present in the metallic part of the metamaterial leading to a pure longitudinal electric wave. We show that ?? _t is the degeneracy frequency between the anti-symmetric mode in a transverse magnetic field and the mode in a transverse electric field. We demonstrate that this degeneracy is due to the periodicity of the structure, which transforms the imaginary solution of a metal?Cdielectric interface into a real solution in the case of the periodic metamaterial.