Emergence of collapsed snaking related dark and bright Kerr dissipative solitons with quartic-quadratic dispersion

Abstract

We theoretically investigate the dynamics, bifurcation structure and stability of dark localized states emerging in Kerr cavities in the presence of second- and fourth-order dispersion. These states form through the locking of uniform wave fronts, or domain walls, connecting two coexisting stable uniform states. They undergo a generic bifurcation structure known as collapsed homoclinic snaking. We characterize the robustness of these states by computing their stability and bifurcation structure as a function of the main control parameter of the system. Furthermore, we show that by increasing the dispersion of fourth order, bright localized states can be also stabilized.

References in corpus (8)

• Third-order chromatic dispersion stabilizes Kerr frequency combs
• Effect of Cherenkov radiation on localized states interaction
• Quartic Kerr cavity combs: Bright and dark solitons
• Localized structures in dispersive and doubly resonant optical parametric oscillators
• Dark quadratic localized states and collapsed snaking in doubly resonant dispersive cavity enhanced second harmonic generation
• A normal form for frequency combs and localized states in Kerr-Gires-Tournois interferometers
• Transitions between dissipative localized structures in the simplified Gilad-Meron model for dryland plant ecology
• Temporal localized states and square-waves in semiconductor micro-resonators with strong time-delayed feedback