Berlin 2018 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 33: Delay and Feedback Dynamics

DY 33.6: Talk

Tuesday, March 13, 2018, 15:15–15:30, BH-N 334

Localized Structures in an inhomogeneous Lugiato-Lefever equation with time-delayed feedback — •Felix Tabbert¹, Mustapha Tlidi², Krassimir Panajotov^3,4, and Svetlana Gurevich¹ — ¹Institute for Theoretical Physics, University of Münster, Wilhelm-Klemm-Str. 9, D-48149 Münster — ²Faculté des Sciences, Université Libre de Bruxelles (ULB), Code Postal 231, Campus Plaine, Bruxelles B-1050, Belgium — ³Vrije Universiteit Brussel, Department of Applied Physics & Photonics, Pleinlaan 2, B-1050 Brussels, Belgium. — ⁴Institute of Solid State Physics, 72 Tzarigradsko Chaussee Blvd., 1784 Sofia, Bulgaria

We discuss the destabilization mechanisms of localized structures in an inhomogeneous nonlinear cavity subjected to injection and to time-delayed feedback. This simple setup is described by the delayed Lugiato-Lefever equation. We analyze the pinning behavior of spatial inhomogeneities on localized structures by introducing a potential induced by an inhomogeneous injection beam. Further, we identify conditions under which these structures are destabilized and describe different bifurcation scenarios. We show that in the presence of the inhomogeneity, delayed feedback induces an Andronov-Hopf-bifurcation that leads to oscillations of the localized structure around the inhomogeneity. Finally we show that for large values of the feedback strength, the localized structure escapes from the potential well and starts to drift and discuss different scenarios, where inhomogeneities are introduced, e.g. in the detuning parameter.