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Physical Review A

Fluorescence lifetimes and linewidths of dye in photonic crystals

Mischa M. Megens, Judith E. G. J. Wijnhoven, Ad Lagendijk, Willem L. Vos

Published Jun 1, 1999• 172 citations
Publisher

Abstract

We have measured spectrally resolved fluorescence lifetimes of dye incorporated in high-quality photonic crystals, made of colloidal spheres. The emission spectrum shows a pronounced Bragg notch. In contrast, the fluorescence lifetime does not depend on the interaction between light and the photonic crystal. The results are explained with a simple model of an atom in a cavity. The effects of homogeneous and inhomogeneous broadening of the emission spectrum of dye inside photonic crystals are discussed.

DOI
10.1103/physreva.59.4727

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The fluorescence spectra and lasing behavior of dye molecules adsorbed on a droplet levitated in an electrodynamic trap have been studied. A simple classical model describes the dye--cavity-mode interaction quantitatively well when the homogeneous linewidth of the dye is wider than the free spectral range of the cavity. When the free spectral range becomes comparable with the homogeneous linewidth, the prediction of the model systematically deviates, indicating that stochastic fluctuations of the radiating dipoles need to be taken into account.

Physical Review A•Sep 1, 1999•16 citations
We have measured spectrally resolved fluorescence lifetimes of dye incorporated in high-quality photonic crystals, made of colloidal spheres. The emission spectrum shows a pronounced Bragg notch. In contrast, the fluorescence lifetime does not depend on the interaction between light and the photonic crystal. The results are explained with a simple model of an atom in a cavity. The effects of homogeneous and inhomogeneous broadening of the emission spectrum of dye inside photonic crystals are discussed.
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 emission spectrum of a single-emitter laser in a photonic crystal is presented. We consider a coherently pumped two-level emitter strongly coupled to a high-quality microcavity engineered within a photonic crystal. We show that the cavity spectrum consists of both elastic and inelastic components, for which we derive analytical expressions. Our study reveals enhanced, spectrally narrower emission resulting from the radiation reservoir of the photonic crystal. The cavity field spectral characteristics are fundamentally distinct from those of a corresponding microcavity in ordinary vacuum. At high pump intensities and for large discontinuities in the photon density of states between Mollow spectral components of atomic resonance fluorescence, the emitted intensity originating from the elastic spectral component increases with the intensity of the pump and the elastic component dominates the spectrum. In the case of a vanishing photon density of states in the spectral range surrounding the lower Mollow sideband and no dipolar dephasing, the cavity spectrum is elastic.
Chapter 1 IntroductionUltimate inhibition of spontaneous emission can be achieved in artificial periodic structures with tailor-made forbidden frequency bands [5].These periodic structures known as photonic crystals consist of different dielectric materials, where the index of refraction varies on length scales comparable to the wavelength of light.Therefore, the periodicity of photonic crystals is about 1000 times as large as that of atomic crystals.Light with specific frequencies is forbidden to propagate along certain directions by wave interference, similarly to Bragg diffraction of x-rays in atomic crystals.Such forbidden frequency ranges are called stopgaps.The larger the contrast of the refractive index between the two materials of a photonic crystal, the more strongly light is influenced, and the broader the stopgaps become.It was predicted in 1987 that an extreme situation may be feasible when light cannot propagate along any direction [6, 7].This situation is called a photonic bandgap.Spontaneous emission is completely inhibited for frequencies inside such a bandgap and, conversely, strongly enhanced for frequencies outside the bandgap.Photonic crystals, therefore, provide an ultimate tool for manipulating with light, which is of extreme interest for scientists and engineers [8, 9].Recent advances in nanotechnology have resulted in ability to synthesize semiconductor structures with dimensions of a few nanometers.Due to the finite sizes, electron-hole pairs (excitons) can be confined in these nanostructures, which leads to discrete excitonic energy levels.The nanocrystals that confine excitons in spherical or circular spaces are known as quantum dots.The discrete structure of the energy levels results in advantageous optical properties of these nanocrystals: narrow and tunable emission spectra.The emission frequencies can be tuned by varying the nanocrystal size: the smaller the size, the higher the emission frequency.These properties make the nanocrystals very promising elementary emitters for new experiments and devices [10, 11]. Outline of the thesisThis thesis describes time-and angle-resolved experiments, in which effects of threedimensional (3D) photonic crystals on spontaneous emission of embedded light sources (quantum dots and dye molecules) were studied.The thesis is organized as follows:In Chapter 2 we review the theoretical basics of the interaction between light and matter.We discuss the factors triggering the process of spontaneous emission and consider in detail the time evolution of the excited state of the emitter that interacts with the quantized 1.
We have performed angle-resolved measurements of spontaneous-emission spectra from laser dyes and quantum dots in opal and inverse opal photonic crystals. Pronounced directional dependencies of the emission spectra are observed: angular ranges of strongly reduced emission adjoin with angular ranges of enhanced emission. It appears that emission from embedded light sources is affected both by the periodicity and by the structural imperfections of the crystals: the photons are Bragg diffracted by lattice planes and scattered by unavoidable structural disorder. Using a model comprising diffuse light transport and photonic band structure, we quantitatively explain the directional emission spectra. This work provides detailed understanding of the transport of spontaneously emitted light in real photonic crystals, which is essential in the interpretation of quantum optics in photonic-band-gap crystals and for applications wherein directional emission and total emission power are controlled.
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.
The fluorescence spectra and lasing behavior of dye molecules adsorbed on a droplet levitated in an electrodynamic trap have been studied. A simple classical model describes the dye--cavity-mode interaction quantitatively well when the homogeneous linewidth of the dye is wider than the free spectral range of the cavity. When the free spectral range becomes comparable with the homogeneous linewidth, the prediction of the model systematically deviates, indicating that stochastic fluctuations of the radiating dipoles need to be taken into account.