## 1 Introduction  
Narrow-linewidth lasers emitting in the range of 780 nm are suitable sources for atomic spectroscopy, atomic clocks, and Doppler laser cooling, particularly in space missions [1; 2; 3; 4]. There are several approaches to generate narrow-linewidth laser emission in this wavelength region. In Reference [5], a laser output power of 11 W with sub 10 kHz linewidth at 780 nm had been achieved by using a second harmonic generation setup consisting of a fiber laser and a periodically-poled lithium niobate (PPLN) crystal. A Ti:Sapphire tunable laser is able to generate 8 W in the 750-810 nm region with a kHz linewidth [6]. An external wavelength stabilized ridge waveguide diode laser utilizing a volume holographic Bragg grating produced a maximum output power of 380 mW with 18 kHz linewidth (FWHM) [7]. However, there is a demand for miniaturized 780 nm laser systems at high output power with narrow spectral linewidth, which cannot be fulfilled by the previously mentioned systems in terms of compactness and power consumption. Semiconductor-based distributed feedback (DFB) lasers with excellent spectral purity, high energy-conversion efficiency, high reliability, and large frequency modulation bandwidth are attractive candidates for this demand. Some previous studies on the performance of the lasers [8; 9; 10] had shown very promising results for application in quantum optics. Therefore, further development of this diode laser type needs to be done. The aim of this work was to look for the ultimate limits (regarding high optical output power and narrow spectral linewidth) that can be reached with a single-section DFB laser without external stabilization. The influences of laser cavity and the coupling coefficient on the DFB diode laser linewidth have been carefully analyzed in previous studies [8]. A high power DFB diode laser with a linewidth of 11 kHz was reported in Reference [9]. However, in this paper only the aspect of internal laser structure optimization was discussed. The behavior of the spectral linewidth under a variation of the facet reflectivity has not been extensively investigated so far. An increased facet reflectivity impacts the linewidth of a DFB laser in several ways (compare Equation (1) in Reference [8]). First, it leads to a decrease of the threshold gain, the rate of spontaneous emission, and Petermann's K factor which results in a decreased linewidth. Additionally, the effective \(\alpha\)-factor changes but not in a definite manner. Second, compared to a vanishing facet reflectivity, the impact of the phase of the grating at the facet has to be considered, which results in varying linewidths for otherwise identical devices. Third, the difference of the threshold gains of the longitudinal modes decreases which results in a decreased side-mode suppression ratio and, therefore an increased linewidth or in dynamically unstable behavior. Therefore, it is worthwhile to study how the spectral linewidth of DFB diode lasers varies with the facet reflectivity, especially in the high power operation regime. Theoretical analyses of the relation between the spectral linewidth of DFB diode lasers and facet reflectivity have been presented in References [11; 12; 13]. However, these reports do not address a stable single-longitudinal-mode operation of DFB diode lasers. More detailed results were published in References [14]. This work analyzes DFB diode lasers operating at 1300 nm with an output power of a few mW. Theoretically, the results show that higher facet reflectivity leads to narrower spectral linewidth, but at the same time provides a smaller yield of the single-longitudinal-mode operation. The experimental characterization of DFB diode lasers showed that the spectral linewidth takes on its minimum value at a front facet reflectivity of about 5% (with the rear facet as cleaved). An investigation of DFB diode lasers operating at 1500 nm is presented in References [15].