  Confined spin-wave modes are a promising object for studying nonlinear
effects and future quantum technologies. Here, using micromagnetic simulations,
we use a microwave magnetic field from a coplanar waveguide (CPW) to pump a
standing spin-wave confined in the cavity of magnonic crystal. We find that the
frequency of the fundamental cavity mode is equal to the ferromagnetic
resonance frequency of the plane film and overlaps with the magnonic bandgap,
allowing high magnetic field tunability. Multi-frequency harmonics of the
cavity mode are generated once the microwave amplitude surpasses a certain
threshold. Specifically, the second and third harmonics at 0.5 T equate to 48.6
and 72.9 GHz with wavelengths of 44 and 22 nm respectively, which propagate
into the crystal. This effect reaches saturation when the CPW covers the entire
cavity, making the system feasible for realization. These processes show
potential for the advancement of magnonics at high-frequencies and very
short-wavelengths.
