We present an experimental and theoretical study on the gain mechanism in a photonic-crystal-cavity nanolaser with embedded quantum dots. From time-resolved measurements at low excitation power we find that four excitons are coupled to the cavity. At
high excitation power we observe a smooth low-threshold transition from spontaneous emission to lasing. Before lasing emission sets in, however, the excitons are observed to saturate, and the gain required for lasing originates rather from multi-electronic transitions, which give rise to a broad emission background. We compare the experiment to a model of quantum-dot microcavity lasers and find that the number of emitters feeding the cavity must greatly exceed four, which confirms that the gain is provided by multi-electronic states. Our results are consistent with theoretical predictions.
We derive a rigorous theory of the interaction between photons and spatially extended excitons confined in quantum dots in inhomogeneous photonic materials. We show that, beyond the dipole approximation, the radiative decay rate is proportional to a
non-local interaction function, which describes the interaction between light and spatially extended excitons. In this regime, light and matter degrees of freedom cannot be separated and a complex interplay between the nanostructured optical environment and the exciton envelope function emerges. We illustrate this by specific examples and derive a series of important analytical relations, which are useful for applying the formalism to practical problems. In the dipole limit, the decay rate is proportional to the projected local density of optical states and we obtain the strong and weak confinement regimes as special cases.
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.
