Correlations between axial and lateral emission of coupled quantum dot–micropillar cavities

We report on optical studies of coupled quantum dot–micropillar cavities using a ${90}^{\circ }$ excitation-and-detection scheme. This specific configuration allows us to excite the micropillar structures either in the axial direction or in the lateral direction and to simultaneously detect emission from both directions. That enables us to reveal correlations between emission into the cavity mode and the leaky modes in the regime of cavity quantum electrodynamics. In particular, we can access and distinguish between axial cavity emission and lateral emission consisting of emission of quantum dots into the leaky modes and losses due to sidewall scattering, respectively. In the multiemitter regime, this technique provides direct access to the respective loss channels and reveals a strong increase of sidewall losses in the low-diameter regime below about 3.0 $\mu \mathrm{m}$. Beyond that, in the single-emitter regime, we observe an anticorrelation between quantum dot emission coupled into the cavity mode and into the leaky modes which is controlled by light-matter interaction in the weak coupling regime. This anticorrelation is absent in the strong coupling regime due to the presence of entangled light-matter states. Moreover, excitation-power-dependent studies demonstrate that the intensity ratio between axial and lateral emission increases strongly above the lasing threshold due to enhanced directionality of emission into the lasing mode. In fact, theoretical studies confirm that this intensity ratio is an additional indicator of laser action in high-$\beta$ microlasers for which the onset of lasing is difficult to identify by the input-output characteristics.

Figure 1

Schematic view of the experimental configuration. The sample is mounted onto the cold finger of a He-flow cryostat and can be accessed in the lateral and axial directions by two independent microscope objectives. Single micropillars under study can be excited optically in either the axial or lateral direction (blue dotted beam path) and the photoluminescence signal can be simultaneously detected in both directions (red solid beam path) via spectrometers 1 and 2.

Figure 2

Comparison of $\mu \mathrm{PL}$ spectra for axial [(a) and (b)] and lateral [(c) and (d)] detection for two pillar diameters $d_c=2.0\mu \mathrm{m}$ [(a) and (c)] and 4.0 $\mu \mathrm{m}$ [(b) and (d)]. The spectra were recorded under lateral excitation at two different excitation conditions: excitation power equal to half of the saturation power (“low excitation,” thin red traces) and at saturation power (“high excitation,” thick black traces) of the QDs emission, respectively. Using axial detection [(a) and (b)], the fundamental cavity mode (C) clearly dominates the spectra, while pronounced QD-related emission lines are visible in the emission detected in the lateral direction [(c) and (d)]. Emission of the cavity mode can hardly be observed under lateral detection in the case of the 4.0-$\mu \mathrm{m}$ micropillar (d). It is much stronger (in comparison to the QD signal) for the smaller micropillar with $d_c=2.0\mu \mathrm{m}$ (c) and clearly dominates the spectrum at high excitation, which is not the case for larger micropillars. This nicely reflects the presence of enhanced lateral losses in the small-diameter regime.

Figure 3

Diameter dependence of the lateral losses. The experimental data (black dots) presents the lateral intensity of the cavity mode signal normalized to the lateral emission of the QDs at saturation. The increase of this intensity in the small-diameter range is a clear signature of enhanced overall lateral losses (sum of intrinsic and sidewall losses). This experimental observation is in agreement with FEM numerical simulations (red trace) showing enhanced intrinsic lateral losses at small pillar diameters.

Figure 4

Study of a weakly coupled QD-micropillar system using axial (a) and lateral (b) detection. Temperature-dependent spectra show a crossing of the QD exciton emission line (X) and the fundamental cavity mode (C) which is characteristic for the weak coupling regime. The investigated micropillar has a diameter of 2.0 $\mu \mathrm{m}$ and a $Q$ factor of $18000$. Pronounced enhancement of the QD emission on resonance due to the Purcell effect can be seen only in axial emission (a). The normalized integrated intensities of the QD in axial and lateral (corrected for the stray light) emission are plotted in (c) and show a pronounced anticorrelation as expected from Eqs. (1) and (2). Respective fits allow us to extract Purcell factors of $F_{P,C}=8.1\pm 2.1$ (black upper trace) and $F_{P,L}=6.7\pm 0.7$ (red lower trace), respectively.

Figure 5

Study of a strongly coupled QD-micropillar system using axial (a) and lateral (b) detection. The micropillar has a diameter of 2.0 $\mu \mathrm{m}$ and a $Q$ factor of $16000$. [(a) and (b)] Temperature-dependent emission spectra detected in the axial (a) and in lateral directions (b). In both cases an anticrossing of the QD exciton (X) and the cavity mode (C) can be observed in the respective energy dispersions (c) from which a vacuum Rabi splitting of 72 $\mu \mathrm{eV}$ was determined. (d) Normalized sum of emission intensities of C and X detected in the axial (black squares) and lateral (red dots) directions. In contrast to Fig. 4, no anticorrelation between emission in the axial and lateral directions as a function of detuning $(\mathrm{\Delta })$ can be observed.

Figure 6

(a) Excitation-power dependence of the intensity of emission detected in the axial (open squares) and lateral (open circles) directions from a QD-micropillar with $d_c=2.0\mu \mathrm{m}$ and $Q=15200$ at $T=10$ K. (b) Ratio $r$ of emission intensity detected in the axial and lateral directions as a function of excitation power. This ratio increases at threshold due to the onset of stimulated emission at about $100\mu \mathrm{W}$, in agreement with the nonlinear increase of the intensity in panel (a) at the same excitation power. In both panels the experimental data (symbols) are well described by the theory (black solid lines/dashes) based on a cluster expansion method with $\beta$ = 0.33, $g=\kappa =0.15/\mathrm{ps},{\mathrm{\Gamma }}_{r,0}=1/\mathrm{ps},{\mathrm{\Gamma }}_r^{\prime }=18/\mathrm{ps},\tilde{\mathrm{\Gamma }}=19\%$, and ${\mathrm{\Gamma }}_{\mathrm{sp}}={\mathrm{\Gamma }}_{\mathrm{nl}}^s={\mathrm{\Gamma }}_{\mathrm{nl}}^p=0.150/\mathrm{ps}$. Moreover, in additional theoretical traces colors and thicknesses of the solid (axial emission) and dashed lines (lateral emission) indicate the influence of the $\beta$ factor on the presented dependencies. The different $\beta$ values, 0.10, 0.43, 0.57, and 0.76, are associated with ${\mathrm{\Gamma }}_{\mathrm{sp}}=0.375/\mathrm{ps},0.112/\mathrm{ps},0.075/\mathrm{ps}$, and $0.0375/\mathrm{ps}$, respectively.