  We study nonlinear response of a dimer composed of two identical Mie-resonant
dielectric nanoparticles illuminated normally by a circularly polarized light.
We develop a general theory describing hybridization of multipolar modes of the
coupled nanoparticles, and reveal nonvanishing nonlinear circular dichroism
(CD) in the second-harmonic generation (SHG) signal enhanced by the multipolar
resonances in the dimer provided its axis is oriented under an angle to the
crystalline lattice of the dielectric material. We present experimental results
for this SHG-CD effect obtained for the AlGaAs dimers placed on an engineered
substrate which confirm the basic prediction of our general multipolar
hybridization theory.
