Stability of a semiconductor laser with a dispersive extended cavity

We present a theoretical investigation of the stability properties of semiconductor lasers with strong feedback from dispersive extended cavities. Surprisingly, unstable behavior had been observed experimentally for chirped fiber grating lasers, where the stability of the laser was found to depend upon the orientation of the fiber grating. We reproduce this finding through a linear stability analysis, demonstrating that the presence of both the linewidth enhancement of the semiconductor diode, and a negative curvature of the phase of the external cavity reflection coefficient are necessary for instability to occur. In order to explain the role of the linewidth enhancement and phase curvature, we present a second approach based on more approximate model wherein the field evolution is found to be described by an equation that resembles the nonlinear Schrödinger equation ~NLSE!; the curvature of the phase then corresponds to the dispersion coefficient of a usual NLSE, and the linewidth enhancement factor corresponds to the nonlinear coefficient. We find an unstable regime analogous to the anomalous dispersion regime of the usual NLSE, where the boundary between normal and anomalous dispersion depends upon the width of the reflectivity spectrum. We also find that there is an additional unstable region that arises due to the carrier dynamics, and has no analogy in systems with an instantaneous nonlinearity. Further, for lasers with a negatively chirped grating, we find that oscillation tends to occur on the red side of the reflection spectrum peak.