Fast and accurate modelling of Kerr-Brillouin combs in Fabry-Perot resonators

We introduce a new mean-field equation for modeling Fabry-Perot resonators filled with a dispersive medium exhibiting both Brillouin and Kerr nonlinearities, e.g. an optical fiber. This model is derived from a unified framework that accounts for Brillouin scattering and four-wave mixing. It involves two coupled nonlinear Schrodinger equations for the forward and backward propagating fields, alongside a single equation governing the acoustic oscillation. Under standard assumptions for mean-field models -such as high finesse, weak nonlinearity, and weak dispersion- we demonstrate that our equation closely matches the original system. The simplified and elegant mathematical structure of our model provides valuable physical insights. As a key example, we derive an expression for the growth rate of harmonic perturbations of steady states. Additionally, our model facilitates fast and accurate numerical simulations using standard Fourier split-step methods. We highlight the effectiveness of this approach by simulating frequency comb generation in state-of-the-art high-Q fiber Fabry-Perot resonators.