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 …
1987 with the aim of providing a paradigm for dissipative structure and pattern formation in …
Dynamics of one-dimensional Kerr cavity solitons
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 …
periodic oscillating one-dimensional temporally localized structure excited in a driven …
Dark solitons in the Lugiato-Lefever equation with normal dispersion
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 …
normal chromatic dispersion are described. These localized states are shown to be …
Dynamics of solitons in Lugiato–Lefever cavities with fractional diffraction
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 …
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
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 …
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 …
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
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 …
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
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 …
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 …
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
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 …
explore the impact of linear nonlocality on their domains of existence and stability. Our …