The dispersion characteristics of woodpile three-dimensional (3D) function photonic crystals (PCs) composed of plasma and function dielectric elements are theoretically investigated by a modified plane wave expansion method, respectively, and the formulas to obtain the dispersion diagrams are given. Only two cases are considered, which are the presence and absence of the external magnetic field. The external magnetic field is vertical to the wave vector, which means that only the magneto-optic Voiget effect is considered. For the proposed PCs, the function dielectric square columns are inserted into the plasma background with face-centered-tetragonal symmetry according to the woodpile lattices. The relationships between the parameters of such PCs and the features of the photonic band gaps (PBGs) for the extraordinary mode and electromagnetic wave are studied under two different cases. The calculated results show that the dispersion characteristics of the proposed PCs can be tailored by adjusting those parameters. If the extrinsic magnetic field does not exist, larger PBG can be found in the present PCs than 3D dielectric-air PCs, 3D function dielectric PCs and 3D plasma-dielectric PCs with the same lattices. If there is an external magnetic field, the narrower PBG for the extraordinary mode can be obtained than the 3D function dielectric PCs and 3D plasma-dielectric PCs with the same lattices. The computed results also show us a approach to realize the reconfigurable devices based on the PCs.
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