Abstract
AbstractRecently, substantial progress has been made in the understanding of microresonators frequency combs based on dissipative Kerr solitons (DKSs). However, most of the studies have focused on the single-resonator level. Coupled resonator systems can open new avenues in dispersion engineering and exhibit unconventional four-wave mixing (FWM) pathways. However, these systems still lack theoretical treatment. Here, starting from general considerations for the N-(spatial) dimensional case, we derive a model for a one-dimensional lattice of microresonators having the form of the two-dimensional Lugiato-Lefever equation (LLE) with a complex dispersion surface. Two fundamentally different dynamical regimes can be identified in this system: elliptic and hyperbolic. Considering both regimes, we investigate Turing patterns, regularized wave collapse, and 2D (i.e., spatio-temporal) DKSs. Extending the system to the Su-Schrieffer-Heeger model, we show that the edge-state dynamics can be approximated by the conventional LLE and demonstrate the edge-bulk interactions initiated by the edge-state DKS.
Funder
United States Department of Defense | Defense Advanced Research Projects Agency
United States Department of Defense | United States Air Force | AFMC | Air Force Office of Scientific Research
EC | Horizon 2020 Framework Programme
Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung
Publisher
Springer Science and Business Media LLC
Subject
General Physics and Astronomy
Cited by
1 articles.
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