4.7 Article

Nonlinear dynamics and Kerr frequency comb formation in lattices of coupled microresonators

Journal

COMMUNICATIONS PHYSICS
Volume 6, Issue 1, Pages -

Publisher

NATURE PORTFOLIO
DOI: 10.1038/s42005-023-01438-z

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This paper investigates the application of dissipative Kerr solitons (DKS) based microresonator frequency combs in coupled resonator systems. A model for a one-dimensional lattice of microresonators is derived, and two different dynamical regimes, elliptic and hyperbolic, are identified. Turing patterns, regularized wave collapse, and 2D DKS are studied in these regimes. The study also extends the system to the Su-Schrieffer-Heeger model, showing the dynamics of edge states and edge-bulk interactions initiated by edge-state DKS.
Recently, 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. Recently, the study of optical frequency combs and nonlinear dynamics in optical microresonators demonstrated a vast variety of dissipative structures with a wide range of nonlinear phenomena. In this paper, the authors extend the conventional systems to the chains of resonators, demonstrating rich two-dimensional dynamics in different dynamical regimes.

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