Temporal solitons in a delayed model of a semiconductor laser

Alexander Pimenov
Weierstrass Institute, Mohrenstr. 39, 10117 Berlin
In the last few years temporal localised structures such as dissipative solitons observed in optical ring cavities received significant experimental and theoretical attention. Under some simplifying assumptions these solitons can be studied phenomenologically in the standard PDE frameworks of Lugiato-Lefever equation (LLE) and Haus master equation. On the other hand, delayed differential equation (DDE) models of semiconductor lasers proved to be very useful in qualitative analysis of various dynamical regimes for very wide realistic parameter ranges, and they can adequately represent different experimental set-ups. Recently, we demonstrated how the effect of chromatic dispersion arising due to dispersive element in the cavity such as a fiber loop can be modelled using a time-delay system, and derived a condition for modulational instability in the anomalous dispersion regime. This result allows us to make a theoretical connection between DDE models and LLE, and discuss the conditions under which solitons can be observed in semiconductor lasers.