  We developed a frequency-domain model describing optical frequency-comb
generation in optical resonators with second- and third-order nonlinearities.
Compared with time-domain models, our model in principle allows one to express
the cavity dispersion accurately, avoiding the dispersion being truncated
beyond a certain order. Moreover, the frequency-domain model can readily
include frequency dependence of system parameters, such as the linear
absorption and the cavity coupling ratio. To demonstrate the validity of our
model, we numerically simulated quadratic combs in a singly resonant
second-harmonic generation cavity and Kerr combs in a micro-resonator as two
examples. The simulated results obtained from the frequency-domain model agree
well with those given by previous time-domain models. A system containing both
second- and third-order nonlinearities can give rise to many novel physical
dynamics. The developed frequency-domain model will contribute to understanding
optical frequency-comb generation assisted by multi-order nonlinear processes
in various optical resonators.
