Enhancement and suppression of the spontaneous emission of a two-level atom in a photonic crystal with a state-conservative photonic pseudogap

It is shown that there exist a conservation rule of the number of states in a photonic crystal with pseudogaps in the whole frequency regime, and a local conservation rule of the number of states in a photonic crystal with completely photonic band gaps in every band regime. These conservation rules state that, relative to the photonic density of states (DOS) in the effective medium of a photonic crystal, if a valley of the DOS in the photonic crystal appears in some range of frequencies, it must be compensated for by the increases over some other ranges. In this paper, using a model DOS with a state-conservative photonic pseudogap, we obtain naturally the enhancement and suppression of spontaneous emission of a two-level atom in a photonic crystal, and a DOS-induced suppression, enhancement, narrowing and redshift or blueshift of spontaneous emission spectra. Our theory will be especially appropriate in the problem of the spontaneous emission of a collection of dependently emitting atoms or molecules with essentially random dipole orientations in a photonic crystal with a photonic pseudogap.