Unconventional collective normal-mode coupling in quantum-dot-based bimodal microlasers

We analyze the occurrence of normal-mode coupling (NMC) in bimodal lasers attributed to the collective interaction of the cavity field with a mesoscopic number of quantum dots (QDs). In contrast to the conventional NMC, here we observe locking of the frequencies and splitting of the linewidths of the system's eigenmodes in the coherent coupling regime. The theoretical analysis of the incoherent regime is supported by experimental observations where the emission spectrum of one of the orthogonally polarized modes of a bimodal QD micropillar laser demonstrates a distinct two-peak structure.

Figure 1

Peak positions (a),(c) and peak widths (b),(d) [cf. Eq. (10)] vs ${\Delta }_1$ for fixed pump strength [(a),(b), $I=0.3]$ and vs $NI$ [(c),(d), ${\Delta }_1=115\mu \text{eV}]$, $N=42,{\kappa }_1=44\mu \text{eV},{\kappa }_2=36\mu \text{eV},{\Delta }_2=0,\Gamma =1.38$ meV, $g_1=30.4\mu \text{eV}$, and $g_2=30.3\mu \text{eV}$. The shaded regions indicate incoherent coupling. The hatched area indicates the range of $NI$ that corresponds to our experimental results presented below (see Fig. 3). The values of ${\kappa }_{\xi }$ and ${\Delta }_{\xi }$ are measured in the experiment, and the values of $N,\Gamma$, and $g_{\xi }$ are estimated in correspondence to the experiment.

Figure 2

Absolute values of the autocorrelation functions and the frequency spectra (inset, semilogarithmic scale) for the emission in the basis of the cavity modes for $I=0.65,{\Delta }_1=115\mu \text{eV}$, and an estimated cavity-enhanced QD spontaneous emission rate of $20{\text{ns}}^{-1}$. Other parameter values are from Figs. 1 and 1. The vertical lines mark the passive cavity-mode frequencies.

Figure 3

(a) Injection-current-dependent $\mu \text{EL}$ emission spectra in ${90}^{\circ }$ polarization for $2.1\le I_{\text{inj}}/I_{\text{th}}\le 5.5$, plotted relative to the high-energy peak values to compensate for an injection-current-dependent shift of the emission energy [see (d)]. (b) Calculated frequency spectrum in ${90}^{\circ }$ polarization for inversion values $0.63\le I\le 0.67$. Parameter values are the same as in Fig. 2. (c) Calculated inversion (green, crosses) vs injection current and integrated $\mu \text{EL}$ intensity for $0^{\circ }$ and ${90}^{\circ }$ polarizations. (d) Emission energy (relative to the reference point $1.366\text{eV})$ of the $0^{\circ }$ component and the two-mode features in ${90}^{\circ }$ detection vs injection current.