Single envelope equation modeling of multi-octave comb arrays in microresonators with quadratic and cubic nonlinearities

We numerically study, by means of the single envelope equation, the generation of optical frequency combs ranging from the visible to the mid-infrared spectral regions in resonators with quadratic and cubic nonlinearities. Phase-matched quadratic wave-mixing processes among the comb lines can be activated by low-power continuous wave pumping in the near infrared of a radially poled lithium niobate whispering gallery resonator. We examine both separate and coexisting intracavity doubly resonant second-harmonic generation and parametric oscillation processes and find that modulation instabilities may lead to the formation of coupled comb arrays extending over multiple octaves. In the temporal domain, the frequency combs may correspond to pulse trains or even to a single pulse circulating in the cavity.