  In this internship report, I have considered the topological laser built by
amplifying the edge of a 2D Harper-Hofstadter photonic lattice, with the
reservoir of carriers being treated explicitly. The dynamical stability of the
resulting chiral laser operation is investigated by means of the Bogoliubov
approach on top of the lasing state. In particular, I propose a mapping to the
1D model of a standard laser which captures the main features of the slow
decaying Goldstone mode. Also, instabilities arising from the interplay of
chiral propagation with refractive index nonlinearities and the non-adiabatic
reservoir of carriers are highlighted.
