## 3 Results and Discussion
\begin{table}
\begin{tabular}{c c c} \hline
**Parameter** & **Unit** & **Value** \\ \hline thickness QW & nm & 14 \\ confinement factor QW & & 0.018 \\ hole mobility QW & cm\({}^{2}\)/Vs & 170 \\ effective phase index & & 3.3 \\ effective group index & & 3.9 \\ ridge width & \(\mu\)m & 2.2 \\ effective index step & & \(5\times 10^{-3}\) \\ total series resistance of \(p\)-doped layers and \(p\)-contact & \(\Omega\) cm\({}^{2}\) & \(7\times 10^{-5}\) \\ spreading resistance of \(p\)-doped layers & \(\Omega\) & \(1.6\times 10^{4}\) \\ coupling coefficient & cm\({}^{-1}\) & 2 \\ internal optical losses & cm\({}^{-1}\) & 5 \\ \hline \end{tabular}
\end{table} 
Table 1: Summary of important parameters used in the simulation. QW: quantum well. Figure 4: Dependence of the intrinsic linewidth on the output power for the DFB diode lasers with various front facet reflections: R < 0.01% (black solid circle), R = 5% (blue solid square), R = 10% (red solid triangle), and R = 30% (orange open circle). The solid lines show the result of fitting a 1/P dependence to the data. Inset: Linewidth vs. output power in the high power regime. Figure 5 presents the minimum and maximum simulation values of the external differential efficiency \(\eta_{\rm diff}\) of the 780 nm DFB diode lasers. The experimental results of \(\eta_{\rm diff}\) calculated from the power-current characteristics in Figure 1 (0.41, 0.40, 0.36, and 0.23) lie almost within the area of the simulation results, which shows that the coupling coefficient and the internal losses have been properly chosen. The external differential efficiency determined experimentally at the lowest facet reflectivity (corresponding to the highest out coupling losses) is smaller than predicted by the theory. A possible reason is the accumulation of carriers outside the active region not contributing to stimulated emission. This effect not taken into account in the simulation reduces the external differential efficiency. The experimental and the calculated minimum and maximum linewidth power products of the 780 nm DFB diode lasers are shown in Figure 6. The tendency of the experimental linewidth power products agrees with the theoretical prediction. The measured linewidth power product for the lowest front facet coating laser lies between the minimum and maximum simulated values. However, the theory predicts a much steeper drop of the linewidth with an increasing front facet reflection than experimentally observed. We should mention that in the theory we neglected other contributions to the intrinsic linewidth such as those due to fluctuations of the carrier density and of the profile shape of the photon density which should not strongly depend on the feedback strength. However, there is one contribution that rises with a decreasing side-mode suppression ratio due to an increased facet reflectivity, which is the impact of non-vanishing side modes on the linewidth of the main mode that could result in linewidth rebroadening [29]. We assume that this effect could be the cause of the increased deviation between simulated and measured linewidth. As the simulations reveal, the decrease of the intrinsic spectral linewidth by the increase of the front facet reflection is caused by a reduction of the spontaneous emission rate due to the reduction of the threshold gain (partially compensated by an increase of the population inversion factor), a decrease of the Petermann \(K\) factor due to the increase of the resonator quality [11; 12], an increase of the number of photons in the cavity, and a slight decrease of the effective linewidth enhancement factor [25]. The influence of an increasing front facet reflectivity on the linewidth is quite similar to an increasing coupling strength (\(KL\)) which was studied experimentally in Reference [8; 30]. Figure 5: External differential efficiency of 780 nm DFB diode laser at 50 mW output power vs. front facet reflectivity: Minimum simulation values (pink solid triangle), maximum simulation values (blue solid circle), and experimental values (red solid square).