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Physical Review Letters

Broadband Fivefold Reduction of Vacuum Fluctuations Probed by Dyes in Photonic Crystals

A. Femius Koenderink, Lydia Bechger, Henry P. Schriemer, Ad Lagendijk, Willem L. Vos

Published Mar 20, 2002• 132 citations
Publisher

Abstract

We observed for the first time a strong angle-independent modification of spontaneous emission spectra from laser dyes in photonic crystals, made of inverse opals in titania. Comparison with spectra from such crystals with much smaller lattice spacing, for which emission is in the long wavelength limit, reveals inhibition of emission up to a factor approximately 5 over a large bandwidth of 13% of the first order Bragg resonance frequency. The center frequency and bandwidth of the inhibition agree with calculated total density of states, while the measured inhibition of vacuum fluctuations is much larger. Because of the specific location of the dye molecules, we likely probe the strongly modulated local photonic density of states.

DOI
10.1103/physrevlett.88.143903

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•Oct 1, 2014•0 citations
We observed for the first time a strong angle-independent modification of spontaneous emission spectra from laser dyes in photonic crystals, made of inverse opals in titania. Comparison with spectra from such crystals with much smaller lattice spacing, for which emission is in the long wavelength limit, reveals inhibition of emission up to a factor approximately 5 over a large bandwidth of 13% of the first order Bragg resonance frequency. The center frequency and bandwidth of the inhibition agree with calculated total density of states, while the measured inhibition of vacuum fluctuations is much larger. Because of the specific location of the dye molecules, we likely probe the strongly modulated local photonic 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.
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.
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.
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.
In certain three-dimensional crystals, a frequency range exist for all polarizations for which light is not allowed to propagate in any direction, called the 3D photonic band gap: a frequency range where the density of vacuum fluctuations vanishes in an ideal infinitely large and perfect system. The complete absence of vacuum fluctuations can be interpreted as zero density of states and vice versa. It is well known that the characteristics of spontaneous emission of light depend strongly on the environment of the light source. According to quantum electrodynamics, the emission rate of a two-level quantum emitter as described by Fermi’s “golden rule”, is factorized into one part describing the emitter’s properties and a second part describing the effect of the environment on the light field via the local density of optical state (LDOS). The radiative decay rate of the emitters is proportional to the LDOS. The absence of vacuum fluctuations or the zero LDOS leads to complete inhibition of the spontaneous emission. While many great advances towards a band gap have been made, no complete inhibition has ever been observed to date. In this thesis, for the first time, we have studied the spontaneous emission of PbS quantum dots inside real 3D photonic band gap crystal as a function of frequency throughout the band gap. In our experiments we have observed an inhibited emission of 18x in the band gap. The time-resolved decay curves show evidence for intriguing finite-size effects whereby vacuum fluctuations tunnel into the band gap. Unfortunately, most theories assume crystals of infinite extent, where the inhibition in the band gap is also infinite, as vacuum fluctuations don’t exist inside the crystal. Here we propose an original model to calculate the LDOS in the band gap of a finite photonic crystal based on tunneling of the vacuum fluctuations into the crystal. We validate our model for the one-dimensional situation with a direct comparison to the analytic calculations which exist for one-dimensional photonic crystals. For three dimensional crystals, the theory shows an excellent match to the experiment.