Nonlinear dynamics and chaotic routes in lithium niobate microring resonators with double optical feedbacks

The nonlinear dynamics of a lithium-niobate-on-insulator (LNOI) add-drop microring resonator with double optical feedback are investigated using a coupled-mode model. The model couples the intracavity field to photorefractive space-charge and thermo-optic temperature dynamics and represents the two feedback paths by effective power-feedback coefficients, delays, and external phase shifts. Numerical simulations based on time series, power spectra, phase portraits, and bifurcation diagrams identify steady, period-one, period-two, period-four, period-eight, and chaotic responses within the parameter ranges examined. At representative parameter settings, increasing the feedback strength leads to a period-doubling cascade from period-one to period-eight responses, followed by chaotic behavior, whereas other parameter cuts produce reverse transitions toward lower-order responses. Two-dimensional scans show that independently varying the feedback strengths redistributes the dynamical states across the feedback-parameter plane. Corresponding scans of the feedback delays, external phases, pump power, and wavelength detuning, including a phase-domain scan in which one feedback phase is varied under fixed delay conditions, reveal changes in the locations and extents of the assigned state regions. These results clarify how double optical feedback reshapes nonlinear-state transitions in LNOI microring resonators and provide a basis for selecting operating conditions that access or avoid different dynamical regimes.