The study of Lamb shift plays a unique role in quantum electrodynamics because it provides an excellent test of the theory on photonic crystals (PCs). In this Letter, we present the first observation of large Lamb shift in the YBO(3):Eu(3+) inverse opals fabricated by the polystyrene templating method. In addition, it is very interesting to observe that the luminescent dynamics of Eu(3+) decayed with a faster power law (t(-3)), followed by a slower exponential process due to the coexistence of the diffusion field and the propagating field in the PCs.
The study of Lamb shift plays a unique role in quantum electrodynamics because it provides an excellent test of the theory on photonic crystals (PCs). In this Letter, we present the first observation of large Lamb shift in the YBO(3):Eu(3+) inverse opals fabricated by the polystyrene templating method. In addition, it is very interesting to observe that the luminescent dynamics of Eu(3+) decayed with a faster power law (t(-3)), followed by a slower exponential process due to the coexistence of the diffusion field and the propagating field in the PCs.
Here, we present strong modification of photonic crystals on the spontaneous emissions of Eu3+ ions in YVO4:Eu3+ inverse opal. It is interesting that due to the effect of local field, the 5D0-7FJ radiative lifetimes of Eu3+ ions in the PCs are all prolonged ∼2.5 times in contrast to the grinded reference (REF) in air, consistent with the empty cavity model. The photonic stop band and the radiative lifetime are both highly sensitive to the refractive index of the infiltrated solutions, in accordance with the real cavity model.
Engineering spontaneous emission by means of photonic crystals (PHC) is under extensive study. However PHC modification of line emissions of rare earth (RE) ions has not been thoroughly understood, especially in cases of weak opal PHCs and while emitters are well dispersed into dielectric media. In this study, poly-methyl methacrylate (PMMA) opal PHCs containing uniformly dispersed europium chelate were fabricated with finely controlled photonic stop band (PSB) positions. Measurements of luminescent dynamics and angle resolved/integrated emission spectra as well as numerical calculations of total densities of states (DOS) were performed. We determined that in weak opals, the total spontaneous emission rate (SER) of Σ(5)D(0)-(7)F(J) for Eu(3+) was independent of PSB positions but was higher than that of the disordered powder sample, which was attributed to higher effective refractive indices in the PHC rather than PSB effect. Branch SER of (5)D(0)-(7)F(2) for Eu(3+) in the PHCs, on the other hand, was spatially redistributed, suppressed or enhanced in directions of elevated or reduced optical modes, keeping the angle-integrated total unchanged. All the results are in agreement with total DOS approximation. Our paper addressed two unstudied issues regarding modified narrow line emission in weak opal PHCs: firstly whether PSB could change the SER of emitters and whether there exist, apart from PSB, other reasons to change SERs; secondly, while directional enhancement and suppression by PSB has been confirmed, whether the angle-integrated overall effect is enhancing or suppressing.
Motivated by the significant controversy between the two dispersion models and Weisskopf-Wigner approximation (WWA), for the first time to our knowledge, we introduce the position-dependent photon-atom interaction into the Green function method of the evolution operator and develop a universal theoretical treatment on spontaneous emission of atoms in photonic crystals (PCs). A position-sensitive generalized Lorentzian formulism (non-Lorentzian shape) for the decay of an excited atom in PCs is derived, an exact numerical method for calculating the local coupling strength, proportional to the photonic local density of state (LDOS), is presented. For weak interaction PCs with pseudo gaps, the generalized Lorentzian formulism may be reduced to the famous Lorentzian spectrum. In this case, we introduced a lifetime distribution function for an assembly of atoms and found that the lifetime distribution strongly depend on the spread configuration of these atoms in space, which clarifies successfully the tremendous discrepancy between different experiments. For the PCs with large full gaps, we found that the atomic position can fundamentally change the decay behavior of an excited atom: in strong interaction positions, the atomic decay is non-classical or exhibits an envelope-damped Rabi oscillation, while in weak interaction positions the WWA is valid. Recently, we also predicted giant Lamb shifts for hydrogen atoms in PCs, and revealed that in inhomogeneous electromagnetic environment, the dominant contribution to the Lamb shift comes from real photon emission, while the contribution from emission and reabsorption of virtual photon is negligible, in vast contrast with the case of free space where the virtual photon processes play a key role.
We present the first experiments that demonstrate strong angle-independent modification of spontaneous emission spectra from laser dyes in photonic crystals, made of inverse opals in titania. We show that both the fluorescence quantum efficiency and weak disorder play a key role in interpreting the experimental data. We compare the angle-independent emission spectra of dye in photonic crystals with spectra from such crystals with much smaller lattice spacings, for which emission is in the long wavelength limit. The ratio of emission power spectra shows inhibition of emission up to a factor ∼ 5 over a large bandwidth of 13% of the first order Bragg resonance frequency. The inhibition shifts to increasing wavelength with the lattice parameter, confirming the photonic nature of the phenomenon. The center frequency and bandwidth of the inhibition agree with the calculated total density of states, but the measured inhibition of the vacuum fluctuations is much larger. This result is confirmed by experiments using different dyes. We likely probe the strongly modulated local photonic density of states, due to the spatially nonuniform distribution of dye molecules over the unit cell.
Being motivated by the controversial results based on two dispersion models and Weisskopf–Wigner approximation (WWA), we introduce, for the first time to our knowledge, the position-dependent photon-atom interaction into the Green function method of the evolution operator and develop a universal theoretical approach to study spontaneous emission of atoms in photonic crystals (PCs). A position-sensitive generalized Lorentzian formalism (non-Lorentzian shape) for the decay of an excited atom in PCs is derived, and an exact numerical method for calculating the local coupling strength, proportional to the photonic local density of state (LDOS), is presented. For weak interaction PCs with pseudo gaps, the generalized Lorentzian formalism may be reduced to the famous Lorentzian spectrum. In this case, we introduce a lifetime distribution function for an assembly of atoms and find that it depends strongly on the atomic configuration in space, which clarifies successfully the tremendous discrepancy between different experiments. For the PCs with large full gaps, we find that the atomic position can fundamentally change the decay behavior of an excited atom: in strong interaction positions, the atomic decay is non-classical or exhibits an envelope-damped Rabi oscillation, while in weak interaction positions the WWA is valid. Recently, we also predicted giant Lamb shifts for hydrogen atoms in PCs, and revealed that in inhomogeneous electromagnetic environment, the dominant contribution to the Lamb shift comes from real photon emission, while the contribution from emission and reabsorption of virtual photon is negligible, in vast contrast with the case of free space where the virtual photon processes play a key role.
Spontaneous emission in photonic crystals with anisotropic three-dimensional dispersion relation is studied. If the upper level is below a characteristic 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 frquency in the band, or a diffusion field, respectively. 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 states.