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arXiv:physics/0410056 · Physical Review A

Quantitative analysis of directional spontaneous emission spectra from light sources in photonic crystals

Ivan S. Nikolaev, Peter Lodahl, Willem L. Vos

Published May 25, 2005• 54 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.71.053813

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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 have observed strongly modified spontaneous-emission spectra from laser dye in photonic crystals made of inverse opals in titania (TiO2).({\mathrm{TiO}}_{2}).(TiO2​). We identify stop bands with large relative widths of 1515%,15 comparable to the dyes' emission spectrum, and 7575%75 attenuation of the emission strength. For a wide range of angles, two stop bands are simultaneously manifested; their angle-dependent frequencies display an avoided crossing that is corroborated by reflectivity experiments. The edges of the stop bands agree well with band-structure calculations, but differ from simple Bragg diffraction as a result of multiple wave coupling. The strongly reduced dispersion of the Bloch modes likely causes a significant change in the density of states.
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.
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.
Angular distribution of photoluminescence of trivalent rare earth ions embedded inside three-dimensional opal and inverse opal photonic crystals is experimentally shown to be strongly modulated for the emission frequencies near the first and higher photonic stop-bands. Numerical simulations of fractional density of optical states also predict highly directional emission from photonic crystals with an ideal structure. Experimental results are shown to be in a good agreement with calculated angular dependencies of luminescence. However, better agreement between experimental and theoretical data requires smoothing of calculated dependencies, which can be attributed to the presence of structural imperfections in real photonic crystal samples.
Photonic crystals based on silica colloidal crystals (artificial opals) exhibit pronounced stopbands for electromagnetic wave propagation and the corresponding modification of the photon density of states in the visible range. These spectrally selective features can be enhanced by impregnating opals with higher refractive materials like, e.g., polymers. Doping of these structures with dye molecules, semiconductor nanoparticles (quantum dots), and rare-earth ions provides a possibility to examine the challenging theoretical predictions of the inhibited spontaneous emission in photonic bandgap (PBG) materials. First experiments are discussed in which pronounced modification of spontaneous emission spectra and noticeable changes in decay kinetics were observed.