Topological cascade lasers for frequency comb generation.*

Recent progress of topological photonics is enabling their applications in integrated devices. Among these novel light sources, topological lasers, relaying on the special edge states of topological insulators, protected against imperfections and disorder, have been recently proposed.
We study theoretically and numerically the laser emission in the one-dimensional Aubry-Andre-Harper model. We show that an engineered cascade of resonant topological chains with varying features realizes frequency comb emitters with tunable spectral features, opening the road to applications as in metrology, sensing and quantum technologies.
With a shaped gain and loss distribution we achieve a PT-symmetric structure and obtain regularly spaced frequencies of the lasing modes.
The modal properties are analysed with the transfer-matrix method allowing to analytically investigate about existence and dispersion of edge states, calculate topological invariants as well as to study the influence of disorder.
We then describe the dynamics of light propagation through finite-difference time-domain Maxwell-Bloch simulations and, by resorting to the nonlinear dissipative Schroedinger equation study the emission on the edge states of the cascaded structure.