Impact of time-delayed feedback on spatiotemporal dynamics in the Lugiato-Lefever model

We analyze the impact of delayed optical feedback (OF) on the spatiotemporal dynamics of the Lugiato-Lefever model. First, we carry out linear stability analysis and reveal the role of the OF strength and phase on the shape of the bistable curve as well as on Turing, Andronov-Hopf, and traveling-wave instability regions. Further, we demonstrate how the OF impacts the spatial dynamics by shifting the regions with different spatial eigenvalue spectra. In addition, we reveal a clustering behavior of cavity solitons as a function of the OF strength at fixed OF phase. Depending on the feedback parameters, OF can also induce a drift bifurcation of a stationary cavity soliton, as well as an Andronov-Hopf bifurcation of a drifting soliton. We present an analytical expression for the threshold of the drift bifurcation and show that above a certain value of the OF strength the system enters a region of spatiotemporal chaos.