  We report calculated substantial enhancement of the second harmonic
generation (SHG) in cuprous oxide crystals resonantly hybridized with an
appropriate organic material (DCM2:CA:PS 'solid-state solvent'). The quadrupole
origin of the inorganic part of the quadrupole-dipole hybrid provides inversion
symmetry breaking and the organic part contributes to the oscillator strength
of the hybrid. We show that the enhancement of the SHG, compared to bulk
cuprous oxide crystal, is proportional to the ratio of the DCM2 dipole moment
and the effective dipole moment of the quadrupole transitions in the cuprous
oxide. It is also inversely proportional to the line-width of the hybrid and
bulk excitons. The enhancement may be regulated by adjusting the organic blend
(mutual concentration of the DCM2 and CA part of the solvent) and pumping
conditions(varying the angle of incidence in case of optical pumping or
populating the minimum of the lower branch of the hybrid in case of electrical
pumping).
