Modulation instability and frequency-comb generation in hybrid quadratic-cubic resonators with spectral filtering

We present an analytical and numerical investigation into the phenomenon of filter-induced modulation instability in passive hybrid optical resonators exhibiting quadratic and cubic nonlinearity. We show that asymmetric spectral losses, with respect to the continuous-wave solution frequency, can trigger sideband amplification in the normal dispersion regime. We calculate the parametric gain and demonstrate the associated pattern formation process. We furthermore show how this parametric process can be exploited to generate optical frequency combs with a tunable repetition rate.