  While two-dimensional (2D) materials have intriguing second-order
nonlinearities with ultrahigh coefficient and electrical tunability, their
atomic layer thicknesses hinder explorations of other optical
frequency-conversions (OFCs) than second harmonic generation (SHG) due to
inefficient light-coupling and unachievable phase-matching. We report, by
resonantly pumping a photonic crystal cavity integrated with a few-layer GaSe,
it is possible to realize multiple second-order nonlinear processes in GaSe
even with microwatts continuous wave pumps, including SHGs, sum-frequency
generations (SFGs), cascaded SFGs and their induced third harmonic generations.
These OFCs arise from the significant cavity-enhancements. The enhancement
factor of a SHG process is estimated exceeding 1,300. The cascaded SFGs have
comparably strong intensities with those of SHGs. To the best of our knowledge,
this is the first observation of cascaded second-order nonlinear processes in
2D materials. The cavity-assisted OFCs could provide a view to study
deterministic OFCs in 2D materials with low pump power and expand their
optoelectronic applications to nonlinear regime.
