Global and localised temporal structures in driven ring quantum cascade lasers

Starting from a full set of effective Maxwell-Bloch equations for a ring quantum cascade laser in the limit of fast material dynamics we derive a new set of equations which require a considerably lower numerical load because they evolve on the time scale of the electric field. With the further assumption of laser very close to threshold the equations take the form of the generalised Lugiato-Lefever equation. Using the latter, we study the formation and stability of multi-peaked localised structures which can be regarded as portions of a global pattern and exhibit a snaking structure.