## 2 Laser Fabrication and Experimental Setup  
All DFB diode lasers studied in this letter stem from the same wafer grown in two steps by the low pressure metal organic vapor phase epitaxy (MOVPE) [16]. In the first step the \(n\)-Al\({}_{0.53}\)Ga\({}_{0.47}\)As cladding, 250 nm thick \(n\)-Al\({}_{0.50}\)Ga\({}_{0.50}\)As waveguide, tensile-strained 14 nm GaAs\({}_{0.785}\)P\({}_{0.115}\) active quantum well (QW), 250 nm \(p\)-Al\({}_{0.50}\)Ga\({}_{0.50}\)As waveguide, and the first part (550 nm) of the \(p\)-Al\({}_{0.53}\)Ga\({}_{0.47}\)As cladding were grown on the \(n\)-GaAs substrate. An InGaP/GaAsP/InGaP (90 nm/20 nm/20 nm) layer sequence completed the first growth. A second order grating was formed in this layer sequence by holographic photolithography and wet-chemical etching of the upper GaAsP and InGaP layers (duty cycle of the 2n order grating equals 0.25). After surface cleaning, in the second step the remainder of the \(p\)-Al\({}_{0.53}\)Ga\({}_{0.47}\)As cladding and a \(p\)-GaAs contact layer were grown. A ridge waveguide (RW) with a 2.2 \(\upmu\)m wide ridge was implemented to provide lateral optical confinement.  
The cavity lengths of the DFB diode lasers were 3 mm. In order to quantitatively investigate the effect of the front facet reflectivity of 780 nm DFB diode lasers, in the high output power regime, the DFB diode lasers were prepared with front facet reflections of R < 0.01%, R = 5%, R = 10%, and R = 30%, respectively. First, the facets of the lasers have been made unreactive using ZnSe layers, which was described in [17]. Afterward, thin films of Al\({}_{2}\)O\({}_{3}\) with appropriate thicknesses were used to coat the laser facets for reflections of less than 30%. An additional TiO\({}_{2}\) layer has been employed to obtain a reflectivity of 30%. Commercially available software [18] has been used to calculate the various layer thicknesses. White-light reflectometry has been employed to determine the layer thicknesses actually achieved. The rear facets of the lasers were coated to obtain a reflection of approximately 95% using SiO\({}_{2}\)/Ta\({}_{2}\)O\({}_{5}\) quarter-wave stacks. All lasers were soldered with AuSn on 250 \(\upmu\)m thick CuW submounts, which were then soldered on so-called C-mounts with PbSn.  
In order to determine the laser linewidth, we carried out a self-delayed heterodyne measurement with each laser. The output beam of the DFB diode laser was collimated and guided through a Faraday isolator (Qioptiq DLI, Feldkirchen, Germany, 60 dB) to suppress parasitic optical feedback. Subsequently, the laser beam was injected into an interferometer n which, one arm carried a 2 km (physical length) fiber delay and an acousto-optic modulator (Intra-Action ATM-804 DA2B) to frequency-shift the radiation by 78 MHz. The beat note signal was detected with a fast photodetector (New Focus 1554-B) with a 3-dB bandwidth of 12 GHz and was recorded with an RF-spectrum analyzer (FSW 26 by Rohde & Schwarz GmbH & Co. KG, Munich, Germany). For each of the measurements presented here, a data set of 100 ms was recorded with an IQ bandwidth of 150 MHz. A detailed description of the subsequent determination of the frequency noise PSD can be found in References [19]. Lastly, the laser's intrinsic linewidth was derived from the level of the white noise of the frequency noise PSD by multiplication with \(\pi\)/2.