We measure localized and extended mode profiles at the band edge of slow-light photonic-crystal waveguides using phase-sensitive near-field microscopy. High-resolution band structures are obtained and interpreted, allowing the retrieval of the optica
l density of states (DOS). This constitutes a first observation of the DOS of a periodic system with weak disorder. The Van Hove singularity in the DOS expected at the band edge of an ideal 1D periodic structure is removed by the disorder. The Anderson-localized states form a tail in the density of states, as predicted by Lifshitz for solid-state systems.
We perform phase-sensitive near-field scanning optical microscopy on photonic-crystal waveguides. The observed intricate field patterns are analyzed by spatial Fourier transformations, revealing several guided TE- and TM-like modes. Using the reconst
ruction algorithm proposed by Ha, et al. (Opt. Lett. 34 (2009)), we decompose the measured two-dimensional field pattern in a superposition of propagating Bloch modes. This opens new possibilities to study specific modes in near-field measurements. We apply the method to study the transverse behavior of a guided TE-like mode, where the mode extends deeper in the surrounding photonic crystal when the band edge is approached.
The spontaneous emission rate of excitons strongly confined in quantum dots is proportional to the overlap integral of electron and hole envelope wave functions. A common and intuitive interpretation of this result is that the spontaneous emission ra
te is proportional to the probability that the electron and the hole are located at the same point or region in space, i.e. they must coincide spatially to recombine. Here we show that this interpretation is not correct even loosely speaking. By general mathematical considerations we compare the envelope wave function overlap, the exchange overlap integral, and the probability of electrons and holes coinciding and find that the frequency dependence of the envelope wave function overlap integral is very different from that expected from the common interpretation. We show that these theoretical considerations lead to predictions for measurements. We compare our qualitative predictions with recent measurements of the wave function overlap and find good agreement.
We have measured the oscillator strength and quantum efficiency of excitons confined in large InGaAs quantum dots by recording the spontaneous emission decay rate while systematically varying the distance between the quantum dots and a semiconductor-
air interface. The size of the quantum dots is measured by in-plane transmission electron microscopy and we find average in-plane diameters of 40 nm. We have calculated the oscillator strength of excitons of that size and predict a very large oscillator strength due to Coulomb effects. This is in stark contrast to the measured oscillator strength, which turns out to be much below the upper limit imposed by the strong confinement model. We attribute these findings to exciton localization in local potential minima arising from alloy intermixing inside the quantum dots.
We prove Anderson localization in a disordered photonic crystal waveguide by measuring the ensemble-averaged localization length which is controlled by the dispersion of the photonic crystal waveguide. In such structures, the localization length show
s a 10-fold variation between the fast- and the slow-light regime and, in the latter case, it becomes shorter than the sample length thus giving rise to strongly confined modes. The dispersive behavior of the localization length demonstrates the close relation between Anderson localization and the photon density of states in disordered photonic crystals, which opens a promising route to controlling and exploiting Anderson localization for efficient light confinement.
We have performed time-resolved spectroscopy on InAs quantum dot ensembles in photonic crystal membranes. The influence of the photonic crystal is investigated by varying the lattice constant systematically. We observe a strong slow down of the quant
um dots spontaneous emission rates as the two-dimensional bandgap is tuned through their emission frequencies. The measured band edges are in full agreement with theoretical predictions. We characterize the multi-exponential decay curves by their mean decay time and find enhancement of the spontaneous emission at the bandgap edges and strong inhibition inside the bandgap in good agreement with local density of states calculations.
We present time-resolved spontaneous emission measurements of single quantum dots embedded in photonic crystal waveguides. Quantum dots that couple to the photonic crystal waveguide are found to decay up to 27 times faster than uncoupled quantum dots
. From these measurements $beta$-factors of up to 0.89 are derived, and an unprecedented large bandwidth of 20 nm is demonstrated. This shows the promising potential of photonic crystal waveguides for efficient single-photon sources. The scaled frequency where the enhancement is observed is in excellent agreement with theory taking into account that the light-matter coupling is strongly enhanced due to the significant slow-down of light in the photonic crystal waveguide.
The radiative and non-radiative decay rates of InAs quantum dots are measured by controlling the local density of optical states near an interface. From time-resolved measurements we extract the oscillator strength and the quantum efficiency and thei
r dependence on emission energy. From our results and a theoretical model we determine the striking dependence of the overlap of the electron and hole wavefunctions on the quantum dot size. We conclude that the optical quality is best for large quantum dots, which is important in order to optimally tailor quantum dot emitters for, e.g., quantum electrodynamics experiments.
