  The two-dimensional ferroelectrics GeS, GeSe, SnS and SnSe are expected to
have large spontaneous in-plane electric polarization and enhanced
shift-current response. Using density functional methods, we show that these
materials also exhibit the largest effective second harmonic generation
reported so far. It can reach magnitudes up to $10$ nm/V which is about an
order of magnitude larger than that of prototypical GaAs. To rationalize this
result we model the optical response with a simple one-dimensional two-band
model along the spontaneous polarization direction. Within this model the
second-harmonic generation tensor is proportional to the shift-current response
tensor. The large shift current and second harmonic responses of GeS, GeSe, SnS
and SnSe make them promising non-linear materials for optoelectronic
applications.
