  There is an active demand to develop efficient nanoscale nonlinear sources
for applications in photonic circuitry, quantum optics and biosensing. To this
end, plasmonic systems have been utilized to boost the nonlinear signal
generation, however high efficiencies of frequency conversion for realistic
applications remain a challenge. Metal-insulator-metal (MIM) nanocavities are
good candidates for strongly concentrating the fields at the nanoscale to
enhance the optical nonlinearities, however they typically suffer from the
requirement to have a quadrupolar resonance at the emission wavelength. Here,
we introduce nonplanar MIM nanocavities with a nonlinear spacer that can
strongly enhance the second harmonic generation (SHG) despite of having
fundamental and emission modes of the same parity. Our experimental and
numerical results indicate that the enhancement is due to the non-planar design
of the cavities and the bulk nonlinearity of the spacer layer.
