Discontinuous spirals of stability in an optically injected semiconductor laser

We report a new kind of discontinuous spiral with stable periodic orbits in the parameter space of an optically injected semiconductor laser model, which is a combination of the intercalation of fish-like and cuspidal-like structures (the two normal forms of complex cubic dynamics). The spiral has a tridimensional structure that rolls up in at least three directions. A turn of approximately 2 pi radians along the spiral and toward the center increases the number of peaks in the laser intensity by one, which does not occur when traversing the discontinuities. We show that as we vary the linewidth enhancement factor ( alpha), discontinuities are created (destroyed) through disaggregation (collapses) from (into) the so-called shrimp-like structures. Future experimental verification and applications, as well as theoretical studies to explain its origin and relation with homoclinic spirals that exist in its neighborhood, are needed.