Theoretical seminar | 09 June 2021

Discovery of Dissipative Kerr Solitons (DKS) in optical microresonators stimulated active research in both applications and the basics of frequency combs. From the mathematical point of view, the DKS are solutions of the driven-damped Nonlinear Schrodinger equation, known as the Lugiato-Lefever equation (LLE). In our work, we generalize this model in order to investigate the nonlinear dynamics in systems with increased dimensionality. We consider two cases: the creation of a synthetic crystal in the frequency dimension and the coupling of the optical resonators in the spatial. In the former, we show how the synthetic Bloch waves affect the DKS dynamics and lead to the formation of Band solitons and chimera-like states. In the latter case, we explore the two-dimensional nature of the system, revealing two fundamentally different dynamical regimes: elliptic and hyperbolic. In these regimes, we explore stable and chaotic states. Further, we generalize our findings to the simplest topological model: the Su-Schrieffer–Heeger (SSH) model.

Main paper/arXiv, related to the seminar, and other references
https://journals.aps.org/pra/abstract/10.1103/PhysRevA.102.023518
https://www.nature.com/articles/s41567-020-01159-y
https://arxiv.org/abs/2104.11731

Short bio
Aleksandr Tusnin is a PhD student at the Swiss Federal Institute of Technology Lausanne (EPFL) in the laboratory of Prof. Kippenberg. He obtained his BSc and MSc in Physics at the Novosibirsk State University and MSc in Applied Mathematics at the ENSTA Paris and at the University of Versailles Saint-Quentin-en-Yvelines.
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