Stability Analysis of Localized States and Deterministic Single Soliton Generation in a Kerr Microresonator Under Thermo-Optic Nonlinear Effects

Thermal effects are ubiquitous in high-quality resonators and microcomb-based high precision measurements. We present a stability analysis of the thermodynamics in a driven Kerr microresonator theoretically and numerically, using the thermal Lugiato-Lefever model. We analyze the spatial bifurcation structure and existence range of stationary states depending on the thermal parameters. Our study shows that, the thermal effect causes the original bifurcation structure to change from Hamiltonian-Hopf bifurcation to Belyakov-Devaney bifurcation. In addition, a stability map of various stationary regions in the parameter space of cavity detuning and the pump power is achieved through numerical simulations of thermal Lugiato-Lefever equation, and we propose a deterministic route to obtain the stable cavity soliton state avoiding the chaotic and unstable regions under the influence of thermal effects. Our approach has potential value for obtaining stable solitary Kerr comb sources under practical conditions.