Influence of the spontaneous optical emission factor $\beta$ on the first-order coherence of a semiconductor microcavity laser

A systematic experimental and theoretical study of first-order coherence properties of high-$\beta$ quantum-dot micropillar lasers is presented. A nonlinear increase in the coherence length is found in the transition regime from spontaneous to dominantly stimulated emission. This increase is accompanied by a qualitative change in the first-order field-correlation function $g^{\left(1\right)}\left(\tau \right)$ from a Gaussian-type profile to an exponential behavior, which is in excellent agreement with a microscopic semiconductor laser theory. Our results also demonstrate a decreasing coherence length with increasing spontaneous emission coupling $\beta$, thus raising questions about the practicability of high-$\beta$ lasers for device applications.

Figure 1

(Color online) (a) A typical high-resolution linearly polarized $\mu \text{-PL}$ spectrum taken at $P=0.5\text{mW}$ from a $6\mu \text{m}$ elliptical micropillar showing the fundamental and higher excited modes. (b) Excitation power–dependent output intensity of the fundamental-mode emission from 1.8, 2.6, and $6\mu \text{m}$ pillars in a log-log plot under nonresonant cw-excitation conditions. The curves are shifted for clarity. Due to heating effects at high excitation conditions, the upper branch of the $1.8\mu \text{m}$ pillar is not fully covered. Solid lines represent the calculated curves from which $\beta$ is determined. Theoretical results are shifted to match the milliwatt scale of the experiment.

Figure 2

(Color online) Visibility curves of the fundamental-mode emission from the $2.6\mu \text{m}$ pillar at different excitation powers. A gradual change in the visibility profile from Gaussian-type behavior to a more exponential behavior is obtained with increasing excitation power. The measured results (dots) are in qualitative agreement with the calculation (solid lines). Inset: A typical high-resolution interference fringe from the fundamental mode at a certain delay time with $V\left(\tau \right)$ over 95%.

Figure 3

(Color online) Pump power dependence of the coherence time ${\tau }_c$ of the fundamental-mode emission for 1.8 (squares), 2.6 (spheres), and $6\mu \text{m}$ (triangles) pillars in a log-log plot. A nonlinear increase in coherence time is observed for all pillars. As depicted in the figure, longer coherence times were observed for low-$\beta$ pillars. Excellent agreement with the calculation (solid lines) is presented. Theoretical results are shifted to match the milliwatt scale of the experiment.

Figure 4

(Color online) Theoretical i/o curves (top) and coherence times (bottom) for various values of the $\beta$ parameter. The curve for $\beta =0.01$ equals that of the $6\mu \text{m}$ pillar. For $\beta =0.1$ and $\beta =1$, 50 and 5 QDs have been used, respectively. All other parameters remain unaltered.