# Multimode Physics in the Mode Locking of Semiconductor Quantum Dot Lasers
## 2 Multimode Mode-Locking Approach
### Enhanced Frequency Conversion Efficiency  
In this paragraph, FWM experiments are performed on both QD and QW lasers. The QD Fabry-Perot (FP) laser is directly grown on silicon. Further details about the structure have already been published elsewhere [12]. The QW laser is a commercial FP laser provided by Almae Technologies. Figure 4 depicts the experimental setup for the nondegenerate pump-probe FWM operation. To maximize the FWM efficiency, two single-frequency tunable sources with narrow linewidths serve as the drive and the probe photons. The outputs of those two pump photons are firstly incorporated by a 90/10 fiber-based optical coupler, and then they are sent into the QD or QW laser from port 1 to port 2 of an optical circulator and a lens-end fiber. To further maximize the frequency conversion efficiency, the polarization controllers are added into the paths of the drive and the probe sources to align the polarization of these two pump photons with that of the QD/QW laser. To eliminate the back reflections from the setup, the isolation between port 2 and port 1 of the optical circulator must be higher than 30 dB. The output of the FWM light is finally coupled out from port 2 and it is sent to a high-resolution optical spectrum analyzer (OSA) through port 3. The measurements are performed at 25 \({}^{\circ}\)C, which is controlled by a thermoelectric cooler. Depending on the frequency of the drive and the probe photons, \(v_{d}\) and \(v_{p}\), respectively, the FWM operation includes two processes. The Stokes case takes place when the frequency detuning \(\Delta v=v_{p}-v_{d}\) is negative, whereas the case for anti-Stokes occurs at the positive frequency detuning condition. Benefiting from the three-dimensional charge carrier confinement in QDs, the enhanced third-order nonlinear susceptibility gives rise to the improvement of FWM efficiency. In this study, the FWM efficiency is determined by the relationship between the ratio of the signal power to the drive power \(r_{sd}\) and the ratio of the probe power to the drive power \(r_{pd}\). Figure 5 displays the calculated \(r_{sd}\) as a function of the \(r_{pd}\) for an epitaxial QD laser on Si with p-modulation doping in the active region (solid burgundy line) and for a commercial QW laser (solid jade line), with the frequency detuning \(\Delta v\approx-300\) GHz in the Stokes condition and the bias current fixed to twice the threshold. The calculated dependencies are performed with multimode semiclassical laser theory. The optical nonlinearities are analyzed based on a microscopic level model containing quantum mechanical electron-hole polarization. The theory gives access to the active medium nonlinearities, contributing to gain saturation, mode competition and multi-wave mixing [17]. In particular, it provides the FWM efficiency, which is plotted in Figure 5. The corresponding experimental results are performed by the different markers in the same colors. Despite the fact that the FWM efficiency of the QD laser has not attained its theoretical limit yet, it is still more than 10 times higher than that of the QW device. This remarkable improvement results from both the enhanced third-order optical nonlinearity and the p-type doping, whose presences contribute to the increase in the intensity of the signal photon in the QD laser [17]. Central to single-section ML lasers is the self-mode-locking mechanism allowed by four-wave mixing in the gain medium itself. The improved susceptibility in the QD laser is sufficient to produce stable, sub-picosecond mode-locked pulse trains in InAs QDs grown on Si. However, one clearly sees that both the susceptibility of four-wave mixing and the signal gain are noticeably lower than those of QDs. Figure 4: Experimental setup for nondegenerate four-wave mixing experiments. PC, polarization controller. Figure 5: Four-wave mixing efficiency with the frequency detuning in the Stokes condition \(\Delta v\approx-300\) GHz for the QD (burgundy) and for the QW (jade) laser.