We present detailed experimental studies of the physical properties of the stable high-gain modes of semiconductor lasers subject to delayed optical feedback. We demonstrate that a sufficient reduction of the linewidth enhancement factor (alpha) is an efficient concept to achieve permanent stable emission on one of these modes. In addition, we confirm major predictions of the Lang-Kobayashi rate equation model concerning the parameter dependence of this stable emission state. Furthermore, we investigate the stability of the stable modes against external perturbations. In particular, we demonstrate that the noise induced escape from the basin of attraction of the stable mode can be well understood if a potential is assumed. Finally, by applying both, external noise, and small signal modulation, we study the interplay of noise, periodic modulation, and determinism in the vicinity of the stable mode. Thereby, we obtain further information about the phase space structure around the stable mode.