## 3 Results and Discussion  
Figure 1 shows the effect of front facet coating on the power-current (PI) characteristics at a mount temperature of 25 \({}^{\circ}\)C. Lasers with front facet coatings of R < 0.01% and R = 5% show linearly increasing output power from threshold current up to 500 mA. The higher reflectivity lasers, R = 10% and 30%, have nonlinear PI characteristics. Furthermore, the linear slope efficiency of the lasers decreases from 0.66 W/A (R < 0.01%) to 0.63 W/A (R = 5%), 0.58 W/A (R = 10%) and 0.37 W/A (R = 30%) because of the reduced transmission at the front facets. The output power at 500 mA ranges from 138 mW (R = 30%) to 290 mW (R < 0.01%). At high power operation, DFB diode lasers with front facet reflectivity above 5% show significant instabilities in the PI characteristics, which are most prominently emphasized by several kinks. This behavior is most clearly observed for the device with R = 30% above an injection current of 300 mA. As theoretically shown, DFB lasers can exhibit different types of dynamical instabilities like pitchfork bifurcation [20], bistability [20] and self-pulsations [21; 22]. All of these instabilities are triggered by the dependence of the carrier density, the refractive index and the gain on the  
Figure 1: Power-current characteristics of 3 mm long 780 nm DFB (distributed feedback) diode lasers having different front facet reflections between R < 0.01% (black), 5% (green), 10% (red), and 30% (blue). photon density via stimulated recombination, which results in longitudinal spatial hole burning and non-uniform index and gain profiles in order for, another longitudinal mode to reach the threshold. Moreover, the higher the front facet reflectivity, the smaller the difference of the threshold gain of adjacent modes that favors instabilities [23]. This can result in nonlinear power-current characteristics as well as broadened optical spectra, which was observed experimentally. In Figure 2, we present spectral mappings of the DFB diode lasers with various front facet reflections at 25 \({}^{\circ}\)C. The laser with R \(<\) 0.01% shows single-mode operation from 40 mA to 420 mA injection current. Except for one mode hop, the laser with 5% front facet reflectivity operates in a single-mode in the range from 40 mA to 500 mA. The kinks in the power-current characteristics that can be observed for lasers with higher front facet reflections are related to regions of broad optical spectra visible in Figure 2c,d, which indicates a dynamically unstable behavior. The wavelength shift vs. the injection current is very similar for all devices with values of \(\Delta\lambda/\Delta\mathrm{I}\) in the range between 1.1 pm/mA and 1.6 pm/mA. From the optical spectra we identified the regions of single-mode operation for the investigation of the linewidth. Figure 3 shows the frequency noise PSD of the self-delayed heterodyne beat note signal for each of the lasers when operated at an output power of 85 mW. At this output power, the intrinsic linewidth decreases from 28 kHz to 20 kHz, 14 kHz, and 8 kHz when the front facet reflection increases. Figure 2: Spectral mappings of 780 nm DFB diode lasers with different front facet reflections: R \(<\) 0.01% (a), R \(=\) 5% (b), R \(=\) 10% (c), and R \(=\) 30% (d). The intrinsic linewidths of all lasers were investigated along with the injection current within their single-mode operation ranges. Figure 4 shows the linewidths of the DFB diode lasers vs. output power, which was calculated from the P-I characteristics (Figure 1). The device with R \(<\) 0.01% shows a linewidth reduction from 128 kHz at 20 mW to a value of 25 kHz at 98 mW (factor of 5.1 for a power ratio of 4.9). In the same power region, the device with R = 5% has a linewidth of 63 kHz at 24 mW and 19 kHz at 97 mW (linewidth reduction by a factor of 3.3 for a power ratio of 4.0). The linewidth of the laser with 10% front facet reflectivity reduces from 49 kHz at 22 mW to 14 kHz at 83 mW. This corresponds to a linewidth reduction ratio of 3.4 for a power ratio of 3.7.