Efficient modeling of resonant electro-optic phase modulator dynamics through a mean-field equation

ring resonators provide a compact route to high-repetition-rate optical frequency comb generation, but efficient modeling becomes challenging in the presence of dispersion and RF detuning. We derive coupled-mode equations for a dynamically modulated ring cavity and obtain a spatiotemporal mean-field equation that captures arbitrary-order dispersion, optical detuning, and off-resonant RF modulation. The steady-state comb spectrum is computed efficiently by solving a tridiagonal linear system. The method reproduces time-domain ordinary differential equation simulations while providing substantial computational speedup, and yields a closed-form estimate of the dispersion-limited comb bandwidth in terms of modulation index and round-trip time.