Responsivity and stability of nonlinear exceptional point lasers with saturable gain and loss

The responsivity of perturbation sensing can be effectively enhanced by using higher-order exceptional points (EPs) due to their nonlinear response to frequency perturbations. However, experimental realization can be difficult due to the stringent parameter conditions associated with these points. In this work we study an EP laser composed of two coupled nonlinear resonators that uses nonlinearity to simplify these tuning requirements. This system demonstrates a distinct cube-root response in the steady-state lasing frequency, with a constant of proportionality that depends on the distribution of linear and saturable gain and loss. This design freedom enables several orders of magnitude higher responsivity than systems with a single nonlinear resonator, which have been previously explored. Maximizing responsivity also improves the robustness of sensing performance against parametric errors. These features are derived from coupled-mode theory and further supported by steady-state ab initio laser theory results at several nonlinear EPs. Through linear stability analysis, we also identify regions of instability within the class-A regime that arise due to mode competition, which can be induced by asymmetric passive losses. In the class-B regime, we show that the interplay between gain dynamics and detuning can lead to restabilization at slow relaxation rates or higher interresonator coupling rates. This regime could be used to increase the maximum achievable responsivity of the system.