Isolas of localized structures and Raman-Kerr frequency combs in micro-structured resonators

We theoretically investigate the combined impact of the Kerr and stimulated Raman scattering effect on the formation of localized structures and frequency comb generation. We focus on the regime of traveling wave instability. We first perform a real-order parameter description by deriving a Swift-Hohenberg equation with nonlocal delayed feedback. Second, we characterize the motion of traveling wave periodic solutions by estimating their thresholds as well their speed. By using a numerical continuation method, we construct a bifurcation diagram showing the emergence of traveling wave periodic solutions, as well as bright and dark moving localized structures. Numerical simulations of the generalized Lugiato-Lefever equation confirm evidence of isolas of localized structures. More importantly, we show that the stimulated Raman scattering strongly impacts the dynamics of localized structures by creating isolas consisting of bright and dark localized structures, and by inducing a motion of these structures. Finally, we provide a geometrical interpretation of the formation of isola stacks based on dynamical systems theory.

Automated summary

In this paper, we theoretically investigate the combined impact of the Kerr and stimulated Raman scattering effect on localized structures and frequency comb generation. We focus on the traveling wave instability regime and derive a Swift-Hohenberg equation with nonlocal delayed feedback to describe the system. By estimating thresholds and speeds, we characterize the motion of traveling wave periodic solutions. Numerical simulations confirm the existence of isolas of localized structures, and we demonstrate that stimulated Raman scattering strongly affects the dynamics of these structures and induces their motion. We also provide a geometric interpretation of the formation of isola stacks based on dynamical systems theory.