Parametric localized patterns and breathers in dispersive quadratic cavities

Parra‐Rivas, Pedro; Mas-Arabi, C.; Léo, François

doi:10.1103/physreva.101.063817

Cited by 22 publications

(8 citation statements)

References 56 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The bifurcation diagrams found there are much more reminiscent of those for the Lugiato Lefever equation, see e.g. [18–20]. In particular, there is a bistability region between homogeneous steady states, and both peak-like and hole-like localized patterns.…”

Section: Introductionmentioning

confidence: 58%

Unified framework for localized patterns in reaction–diffusion systems; the Gray–Scott and Gierer–Meinhardt cases

Saadi

Champneys

2021

Phil. Trans. R. Soc. A.

View full text Add to dashboard Cite

A recent study of canonical activator-inhibitor Schnakenberg-like models posed on an infinite line is extended to include models, such as Gray–Scott, with bistability of homogeneous equilibria. A homotopy is studied that takes a Schnakenberg-like glycolysis model to the Gray–Scott model. Numerical continuation is used to understand the complete sequence of transitions to two-parameter bifurcation diagrams within the localized pattern parameter regime as the homotopy parameter varies. Several distinct codimension-two bifurcations are discovered including cusp and quadruple zero points for homogeneous steady states, a degenerate heteroclinic connection and a change in connectedness of the homoclinic snaking structure. The analysis is repeated for the Gierer–Meinhardt system, which lies outside the canonical framework. Similar transitions are found under homotopy between bifurcation diagrams for the case where there is a constant feed in the active field, to it being in the inactive field. Wider implications of the results are discussed for other pattern-formation systems arising as models of natural phenomena. This article is part of the theme issue ‘Recent progress and open frontiers in Turing’s theory of morphogenesis’.

show abstract

Section: Introductionmentioning

confidence: 58%

Unified framework for localized patterns in reaction–diffusion systems; the Gray–Scott and Gierer–Meinhardt cases

Saadi

Champneys

2021

Phil. Trans. R. Soc. A.

View full text Add to dashboard Cite

show abstract

“…On top of the dynamics just described, focusing on the single spike LS, one may wonder if LPs coexisting with the previous states below the BD line exhibit a similar dynamical scenario. Indeed, the dynamics of LP-breathers have recently been studied in the context of dispersive optical parametric oscillators, and show very rich and unprecedented behavior (Parra-Rivas et al, 2020b). In our current context, however, this question has not been investigated systematically and remains an open problem.…”

Section: Breathers In the Anomalous Regimementioning

confidence: 95%

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

Parra-Rivas¹,

Knobloch²,

Gelens³

et al. 2020

Preprint

Self Cite

View full text Add to dashboard Cite

Localized coherent structures can form in externally-driven dispersive optical cavities with a Kerr-type nonlinearity. Such systems are described by the Lugiato-Lefever equation, which supports a large variety of dynamical solutions. Here, we review our current knowledge on the formation, stability and bifurcation structure of localized structures in the one-dimensional Lugiato-Lefever equation. We do so by focusing on two main regimes of operation: anomalous and normal second-order dispersion. In the anomalous regime, localized patterns are organized in a homoclinic snaking scenario, which is eventually destroyed, leading to a foliated snaking bifurcation structure. In the normal regime, however, localized structures undergo a different type of bifurcation structure, known as collapsed snaking.

show abstract

“…[ 187,188 ] Theoretical modeling of quadratic combs in singly and doubly resonant SHG systems reveals rich nonlinear behaviors in such quadratic resonator platforms. [ 154,155,189–193 ] Experimental investigation on microcavity quadratic combs have also been carried out using mechanically polished WGMRs made from MgO doped LiNbO 3 . [ 194,195 ] Turning pattern like quadratic combs has been observed.…”

Section: Other Emerging Microcombsmentioning

confidence: 99%

Kerr Frequency Comb Interaction with Raman, Brillouin, and Second Order Nonlinear Effects

Lin

Song

2021

Laser & Photonics Reviews

View full text Add to dashboard Cite

Kerr optical frequency comb as a novel microcomb source has found a variety of key applications from fundamental research to engineering applications. Generation of such microcombs require resonator platforms with small mode volumes and high quality factors, where the interaction of light and matter is resonantly enhanced. In these platforms, other nonlinear photonic effects can be simultaneously excited and interact with Kerr frequency combs. In this review, the focus is on recent progresses on the microcomb development involving its interaction with Raman, Brillouin scattering, and second‐order nonlinear processes such as second harmonic generation (SHG). The resulting transfer of Kerr frequency combs into other spectral windows as referred to Kerr–Raman, Kerr–Brillouin, Kerr–SHG combs is introduced. Additionally, other emerging novel microcombs in microresonators with second‐order nonlinearity including electro‐optical modulation microcombs and quadratic microcombs are reviewed. Challenges and opportunities brought along are also discussed.

show abstract

Parametric localized patterns and breathers in dispersive quadratic cavities

Cited by 22 publications

References 56 publications

Unified framework for localized patterns in reaction–diffusion systems; the Gray–Scott and Gierer–Meinhardt cases

Unified framework for localized patterns in reaction–diffusion systems; the Gray–Scott and Gierer–Meinhardt cases

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

Kerr Frequency Comb Interaction with Raman, Brillouin, and Second Order Nonlinear Effects

Contact Info

Product

Resources

About