The spectrum of a semiconductor laser with incoherent feedback from a distant mirror (i.e. the external round-trip time exceeds the coherence time of the laser) is investigated. As the amount of feedback increases the optical spectrum evolves from a central line with enhanced isolated satellite peaks caused by the relaxation oscillation to a very broad ( approximately 20 GHz) line, where the relaxation oscillation gives rise to shoulders. Moreover, there is an asymmetry for frequencies above or below the central frequency. This drastic change of the spectrum is also found from a recent theoretical description of a semiconductor laser in the coherence collapsed state. The amount of feedback and the damping rate of the relaxation oscillation are obtained from a fit of the theory to the observed time-autocorrelation function. This analysis reveals, that, owing to incoherent feedback, the damping rate of the relaxation oscillation behaves as an effective damping rate that depends almost linearly on the feedback rate.
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