Related papers: Extended temporal Lugiato-Lefever equation and the…
We introduce the generalized Lugiato-Lefever equation describing nonlinear effects in the bottle microresonators. We demonstrate that the nonlinear modes of these resonators can form multiple coexisting and overlapping nonlinear resonances…
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 a general analysis of the regions of existence and…
We investigate frequency comb generation in the presence of polarization effects induced by nonlinear mode coupling in microresonator devices. A set of coupled temporal Lugiato-Lefever equations are derived to model the propagation…
The generation of optical frequency combs in microresonators is considered without resorting to the mean-field approximation. New dynamical regimes are found to appear for high intracavity power that cannot be modeled using the…
A generalized Lugiato-Lefever equation is numerically solved with a Newton-Raphson method to model Kerr frequency combs. We obtain excellent agreement with past experiments, even for an octave-spanning comb. Simulations are much faster than…
We derive a spatiotemporal equation describing nonlinear optical dynamics in Fabry-Perot (FP) cavities containing a Kerr medium. This equation is an extension of the equation that describes dynamics in Kerr-nonlinear ring resonators,…
We are reporting that the Lugiato-Lefever equation describing the frequency comb generation in ring resonators with the localized pump and loss terms also describes the simultaneous nonlinear resonances leading to the multistability of…
Taking advantage of an extended Lugiato--Lefever equation with third-order dispersion, we numerically show that dark cavity solitons formed in normal dispersion of microresonators are capable of emitting dispersive waves in both normal and…
Kerr frequency combs are optical signals consisting of a multitude of equally spaced excited modes in frequency space. They are generated by converting a continuous-wave pump laser within an optical microresonator. It has been observed that…
We present the theory of modulation instability induced by spectrally dependent losses (optical filters) in passive driven nonlinear fiber ring resonators. Starting from an Ikeda map description of the propagation equation and boundary…
We introduce a new model describing multiple resonances in Kerr optical cavities. It perfectly agrees quantitatively with the Ikeda map and predicts complex phenomena such as super cavity solitons and coexistence of multiple nonlinear…
In Ref. [Parra-Rivas at al., 2013], using the Swift-Hohenberg equation, we introduced a mechanism that allows to generate oscillatory and excitable soliton dynamics. This mechanism was based on a competition between a pinning force at…
Using numerical simulations of an extended Lugiato-Lefever equation, we analyze the stability and nonlinear dynamics of Kerr frequency combs generated in microresonators and fiber resonators taking into account third-order dispersion…
We consider a new class of periodic solutions to the Lugiato-Lefever equations (LLE) that govern the electromagnetic field in a microresonator cavity. Specifically, we rigorously characterize the stability and dynamics of the Jacobi…
We analyze the consequences of dissipative heating in driven Kerr microresonators theoretically and numerically, using a thermal Lugiato-Lefever model. We show that thermal sensitivity modifies the stability range of continuous wave in a…
Using the known solutions of the Lugiato-Lefever equation, we derive universal trends of Kerr frequency combs. In particular, normalized properties of temporal cavity soliton solutions lead us to a simple analytic estimate of the maximum…
Microresonator-based optical frequency combs, or "microcombs", have attracted lots of attention in the last few years thanks to their promising applications in telecommunications, spectroscopy and optical clocks. The process of comb…
The Eckhaus instability is a secondary instability of nonlinear spatiotemporal patterns in which high-wavenumber periodic solutions become unstable against small-wavenumber perturbations. We show in this letter that this instability can…
Guided-mode coupling in a microresonator generally manifests itself through avoided crossings of the corresponding resonances. This coupling can strongly modify the resonator local effective dispersion by creating two branches that have…
We analyze the behavior of electromagnetic fields inside a resonant cavity by solving Einstein--Maxwell field equations. It is shown that the modified geometry of space-time inside the cavity due to a propagating mode can affect the…