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Physical Review B

Nonexponential decay of spontaneous emission from an ensemble of molecules in photonic crystals

Renaud A. L. Vallée, Kris Baert, Branko Kolarić, Mark Van der Auweraer, Koen Clays

Published Jul 19, 2007• 43 citations
Publisher

Abstract

Photonic crystals (PCs) with relatively low dielectric contrast (i.e., with pseudogaps) have significant influence on the fluorescence decay of internal emitters. Fluorescence decays of ensembles of dye molecules measured at different positions in the PCs exhibit a nonexponential behavior, which is best fitted by a continuous distribution of decay rates. The most frequent decay rates of these distributions are smaller and their widths are narrower in a PC with a pseudogap acting in the emission range of the emitters than in a PC having the pseudogap out of this range. These experimental results have been well accounted for by calculations of the local density of states and rate constant for spontaneous emission.

DOI
10.1103/physrevb.76.045113

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Photonic crystals (PCs) with relatively low dielectric contrast (i.e., with pseudogaps) have significant influence on the fluorescence decay of internal emitters. Fluorescence decays of ensembles of dye molecules measured at different positions in the PCs exhibit a nonexponential behavior, which is best fitted by a continuous distribution of decay rates. The most frequent decay rates of these distributions are smaller and their widths are narrower in a PC with a pseudogap acting in the emission range of the emitters than in a PC having the pseudogap out of this range. These experimental results have been well accounted for by calculations of the local density of states and rate constant for spontaneous emission.
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We have investigated the analytical forms of the photonic density of states (DOS) in a photonic crystal in the interested frequency regime according to the rule of state conservation in a photonic crystal with pseudogaps, which states that, if a valley of the DOS appears in some range of frequencies, it must be compensated for by increasing over some other ranges. By using a model DOS with a state-conservative photonic pseudogap, we have also investigated the enhancement and suppression of spontaneous emission of two-level atoms with different frequency positions and widths of emission spectra in a state-conservative electromagnetic reservoir; and the DOS-induced suppression, enhancement, narrowing and redshifting or blueshifting of spontaneous emission spectra are naturally obtained.
We report on modification of the spontaneous emission of dye molecules embedded in a three-dimensional solid-state photonic crystal exhibiting a stop band in the visible range. Molecules embedded in artificial opal filled with a polymer show a dip in the fluorescence spectrum and nonexponential spontaneous decay kinetics containing both accelerated and inhibited components compared to the dye fluorescence in a reference polymer matrix. Results are interpreted in terms of redistribution of the photon density of states in the photonic crystal.
Photonic crystals affect the photon emission of embedded emitters due to an altered local density of photon states (LDOS). We review the calculation of the LDOS from eigenmodes in photonic crystals and propose a rate equation model for fluorescent emitters to determine the changes in emission induced by the LDOS. We show how to calculate the modifications of three experimentally accessible characteristics: emission spectrum (spectral redistribution), emitter quantum yield, and fluorescence lifetime. As an example, we present numerical results for the emission of the dye Rhodamine B inside an opal photonic crystal. For such photonic crystals with small permittivity contrast, the LDOS is only weakly modified, resulting in rather small changes. We point out that in experiments, however, usually only part of the emitted light is detected, which can have a very different spectral distribution (e.g., due to a photonic band gap in the direction of detection). We demonstrate the calculation of this detected spectrum for a typical measurement setup. With this reasoning, we explain the previously not fully understood experimental observation that strong spectral modifications occurred, while at the same time only small changes in lifetime were found. With our approach, the mentioned effects can be quantitatively calculated for fluorescent emitters in any photonic crystal.
The fluorescence of emitters embedded in a photonic crystal is known to be inhibited by the presence of a photonic pseudo-gap acting in their emission range. Here we present a comparative study of the influence of the pseudo-gap on the fluorescence emission of either organic dyes or nanocrystals embedded within a photonic crystal. Our results clearly show that the optical properties of the emitters are primarily controlled by the presence of a pseudo-gap which causes inhibition of the emission in both cases, regardless of the differences in chemical composition. These findings are mainly attributed to a decrease of the number of available photonic modes for radiative decay of the emitter in a photonic crystal compared to the effective homogeneous medium. Furthermore, we show that a photonic crystal can be used to control the fluorescence energy transfer (FRET) between donor-acceptor (D-A) pairs of dyes. Finally, we show that the application of an external magnetic field can finely tune the emission characteristics of emitters with a permanent magnetic moment.