From the Lugiato–Lefever equation to microresonator-based soliton Kerr frequency combs

LA Lugiato, F Prati, ML Gorodetsky… - … Transactions of the …, 2018 - royalsocietypublishing.org
The model, that is usually called the Lugiato–Lefever equation (LLE), was introduced in
1987 with the aim of providing a paradigm for dissipative structure and pattern formation in …

Dynamics of one-dimensional Kerr cavity solitons

F Leo, L Gelens, P Emplit, M Haelterman, S Coen - Optics express, 2013 - opg.optica.org
We present an experimental observation of an oscillating Kerr cavity soliton, ie, a time-
periodic oscillating one-dimensional temporally localized structure excited in a driven …

Dark solitons in the Lugiato-Lefever equation with normal dispersion

P Parra-Rivas, E Knobloch, D Gomila, L Gelens - Physical Review A, 2016 - APS
The regions of existence and stability of dark solitons in the Lugiato-Lefever model with
normal chromatic dispersion are described. These localized states are shown to be …

Dynamics of solitons in Lugiato–Lefever cavities with fractional diffraction

S He, BA Malomed, D Mihalache, X Peng, Y He… - Chaos, Solitons & …, 2023 - Elsevier
We study soliton dynamics in a passive optical system governed by the Lugiato–Lefever
equation with effective diffraction represented by a fractional spatial derivative. Two models …

Dynamics of localized and patterned structures in the Lugiato-Lefever equation determine the stability and shape of optical frequency combs

P Parra-Rivas, D Gomila, MA Matías, S Coen, L Gelens - Physical Review A, 2014 - APS
It has been recently uncovered that coherent structures in microresonators such as cavity
solitons and patterns are intimately related to Kerr frequency combs. In this work, we present …

Localized patterns in reaction-diffusion systems

VK Vanag, IR Epstein - Chaos: An Interdisciplinary Journal of …, 2007 - pubs.aip.org
We discuss a variety of experimental and theoretical studies of localized stationary spots,
oscillons, and localized oscillatory clusters, moving and breathing spots, and localized …

[HTML][HTML] Multidimensional localized states in externally driven Kerr cavities with a parabolic spatiotemporal potential: a dimensional connection

Y Sun, P Parra-Rivas, F Mangini, S Wabnitz - Chaos, Solitons & Fractals, 2024 - Elsevier
In this work, we study the bifurcation structures and the stability of multidimensional localized
states within coherently driven Kerr optical cavities with parabolic potentials in 1D, 2D, and …

Origin, bifurcation structure and stability of localized states in Kerr dispersive optical cavities

P Parra-Rivas, E Knobloch, L Gelens… - IMA Journal of Applied …, 2021 - academic.oup.com
Localized coherent structures can form in externally driven dispersive optical cavities with a
Kerr-type non-linearity. Such systems are described by the Lugiato–Lefever (LL) equation …

Bifurcation analysis to the Lugiato–Lefever equation in one space dimension

T Miyaji, I Ohnishi, Y Tsutsumi - Physica D: Nonlinear Phenomena, 2010 - Elsevier
We study the stability and bifurcation of steady states for a certain kind of damped driven
nonlinear Schrödinger equation with cubic nonlinearity and a detuning term in one space …

Impact of nonlocal interactions in dissipative systems: Towards minimal-sized localized structures

L Gelens, G Van der Sande, P Tassin, M Tlidi… - Physical Review A …, 2007 - APS
In order to investigate the size limit of spatial localized structures in a nonlinear system, we
explore the impact of linear nonlocality on their domains of existence and stability. Our …