Global and localised temporal structures in driven ring quantum cascade lasers

• Published in: Chaos, solitons and fractals solitons and fractals, 2021-12, Vol.153, p.111537, Article 111537
• Main Authors: Prati, F., Lugiato, L.A., Gatti, A., Columbo, L., Silvestri, C., Gioannini, M., Brambilla, M., Piccardo, M., Capasso, F.
• Format: Article
• Language: English
• Subjects: Cavity solitons; Pattern formation; Quantum cascade lasers; Snaking
• ISSN: 0960-0779; 1873-2887
• DOI: 10.1016/j.chaos.2021.111537

•Driven ring quantum cascade lasers support different kinds of global and localized temporal structures: roll patterns, temporal solitons, localized multi-peaked structures.•The formation of temporal structures can be described at different levels of complexity.•A model for ring QCL, intermediate between the full set of generalized semiconductor Maxwell-Bloch equation and the generalized Lugiato.Lefever equation (which is a type of forced complex Ginzburg Landau equation) can be derived thanks to fast material variables. 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.