Decay Distribution of Spontaneous Emission from an Assembly of Atoms in Photonic Crystals with Pseudogaps

Since the pioneering work of Yablonovitch [1] and John [2], the spontaneous emission properties of atoms or molecules in the three-dimensional (3D) photonic crystals (PC’s) are extensively investigated. Because of the difficulty in the fabrication of samples, the experimental studies in this topic have been achieved only in the 3D PC’s with pseudo-photonic-band gaps (pseudo-PBG’s). The inhibition effect of radiative decay in PC’s was first reported ten years ago [3]. However, a later comprehensive experiment showed that the non-PC effects can account for a major fraction of the change in the radiative lifetime [4]. Recently, the wide lifetime distribution containing both inhibited and accelerated decay components was reported in the artificial opal sample [5], in which dye molecules homogeneously spread over the background solution. However, when the dye molecules are homogeneously embedded on a spherical layer inside silica globules in a similar system [6], only a single decay lifetime was found and very little change in the decay lifetime was observed. Evidently, there exist substantial discrepancies in these experimental observations. Up to now, the clearly theoretical clarification for these experiments still remains an open question [7]. Theoretically, isotropic and anisotropic dispersion models near band edges have been extensively employed to study the spontaneous emission problems in the 3D PC’s with absolute-PBG’s [8–15]. Obviously, the dispersion models are not applicable to the 3D PC’s with pseudoPBG’s, because the propagating modes in some directions overlap with pseudo-PBG’s. Moreover, the position dependence of interaction between atoms and photons is omitted in these models, while it has been well known in the 1D inhomogeneous system [16–18]. To understand different experimental results, the conventional averaged lifetime over a few positions of atom was evaluated [19]. But, this attempt was a failure. Furthermore, it is assumed in the numerical calculations that the magnitudes jEn,krj of the field modes are invariant under the operation of the lattice point group operator [19–21]. Recently, this assumption has been proven to be invalid and a new calculation method is presented [22]. In this Letter, we study the decay kinetics of the atoms (or molecules) in the PC’s with pseudo-PBG’s by considering the position-dependent interaction. Theoretically, a lifetime distribution function for an assembly of atoms or molecules is defined and numerically evaluated to reveal the dynamic decay processes. This can provide a theoretical clarification for the recent reported experiments. For a two-level atom at r point in a PC, the Hamiltonian of the system reads as