  Optical microcavities are often used to realize enhanced nonlinear optical
interactions for highly efficient second-harmonic generation. With increased
pump power, the efficiency of nonlinear frequency conversion can be increased
further, while some other unwanted nonlinear effects will also emerge, leading
to complicated dynamics or instability. Here, we study the interplay between
cascaded second- and third-order nonlinear processes and investigate their
impact on the second-harmonic generation in microcavities. It is found that the
non-degenerate optical parametric oscillation (OPO) appears and the presence of
$\chi^{(3)}$ process can modify the OPO threshold significantly when the
multimode cavity is strongly pumped at the fundamental optical mode. One can
even break the efficiency limitation of the second-harmonic mode restricted by
the OPO by utilizing the interference between the OPO and the four-wave mixing.
The present coherent interplay between nonlinear optical processes in
microcavities is conducive to exploring new physics in the cavity nonlinear
photonics.
