Photon Statistics of Semiconductor Microcavity Lasers

We present measurements of first- and second-order coherence of quantum-dot micropillar lasers together with a semiconductor laser theory. Our results show a broad threshold region for the observed high-$\beta$ microcavities. The intensity jump is accompanied by both pronounced photon intensity fluctuations and strong coherence length changes. The investigations clearly visualize a smooth transition from spontaneous to predominantly stimulated emission which becomes harder to determine for high $\beta$. In our theory, a microscopic approach is used to incorporate the semiconductor nature of quantum dots. The results are in agreement with the experimental intensity traces and the photon statistics measurements.

Figure 1

(a) SEM image of a $3\mu \mathrm{m}$ micropillar. (b) Experimental (top)/theoretical (bottom) verification of the pillar mode spectra ($1\times$, $2\times$ mode degeneracy) for the $4\mu \mathrm{m}$ structure. Inset: Calculated transverse mode profiles with radial/angular quantum numbers $(m,l)$.

Figure 2

(a) ${\tilde{g}}^{(2)}(\tau )$ correlation series for the $3\mu \mathrm{m}$ fundamental pillar mode under varying cw excitation, clearly revealing photon bunching ${\tilde{g}}^{(2)}(0)>1$. Inset: Coherence time fit to the 5.0 mW trace under convolution with the temporal IRF ($\Delta t_{\mathrm{IRF}}\approx 600\mathrm{ps}$). (b) Power-dependent autocorrelation series of the same micropillar under pulsed excitation, again reflecting a strong bunching effect at $\tau =0$.

Figure 3

(a),(b) Integrated intensities (bottom) for the 3 ($4\mu \mathrm{m}$) pillars under nonresonant pulsed excitation. Strong photon bunching ${\tilde{g}}^{(2)}(0)>1$ is found from corresponding correlation measurements (top) over a broadened regime around the threshold.

Figure 4

(a) ${\tilde{g}}^{(2)}(\tau =0)$ autocorrelation results derived from the $3\mu \mathrm{m}$ pillar fundamental mode under cw excitation [see series in Fig. 2a], together with the corresponding mode emission intensity (b). (c) First-order $g^{(1)}(\tau )$ series, revealing a strong ${\tau }_c$ coherence decrease in the low excitation limit.

Figure 5

(a),(b) Calculated output curves (bottom) and $g^{(2)}(0)$ (top) for various $\beta$. (c),(d) Calculated results vs experimental data (pulsed) from Fig. 3a for the $3\mu \mathrm{m}$ pillar. In (c), a convolution (solid line) with the experimental temporal resolution ${\tau }_c$ is shown. (d) Corresponding $\mathrm{I}/\mathrm{O}$ curves, explicitly indicating the effects of pump saturation.