Spontaneous radiation and lamb shift in three-dimensional photonic crystals

Spontaneous emission in photonic crystals with anisotropic three-dimensiona l dispersion relation is studied. If the upper level is below a characteris tic frequency omega(1), or above omega(2), or between omega(1) and omega(2) , the radiation is a localized field with a frequency in the band gap, or a propagating field with a frequency in the band, or a diffusion field, resp ectively An analytical expression for the Lamb shift Is obtained. The Lamb shift for the current case is small compared to that in an ordinary vacuum or in one- or two-dimensional photonic crystals due to lower density of sta tes.