On the nature of Acket's characteristic parameter C in semiconductor lasers

Quasi-static interferometric signals in lasers under feedback arise from slowly varying perturbations of the intracavity electric field resulting from the reinjection of a portion of the emitted field into the cavity. Such interferometric signals are well described by the steady-state solution to the Lang-Kobayashi rate equation model. We give an exact series expansion for this steady-state solution that shows precisely how Acket's characteristic parameter C and Henry's linewidth enhancement factor α influence such signals. We show how the series coefficients can be extracted easily and explain how to determine C and α directly from them. Moreover, we draw a precise analogy between self-mixing and FM signals, showing that C plays exactly the same role in self-mixing as the modulation index does in FM.