Nonlinear Waves and Turbulence in Photonics 2022 - Abstract
We will review our recent theoretical results regarding the emergence of dispersive temporal localized structures in optical microcavities. Our work is set within the framework of time delayed dynamical systems. While time delayed systems are usually considered devoid of the essential dispersive effects for pattern formation, we will show how dispersion may appear naturally in singular delayed equations, and make the link with the physical properties of Gires-Tournois interferometers. Furthermore, we demonstrate the existence of reversible conservative time delayed systems considering a dispersive microcavity containing a Kerr medium coupled to a distant external mirror. In the long delay limit, the normal form identifies with the nonlinear Schrödinger equation, thereby allowing for bright and dark solitons although the lack of integrability can be observed at high energies. We unveil some of the symmetries and conserved quantities and recover the Lugiato-Lefever equation in the weakly dissipative regime.