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.
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