We present a theoretical study of circular dichroism in the second-harmonic signal of single dielectric nanostructures with different symmetries and noncentrosymmetric materials. We show that this effect is defined not only by macroscopic (particle) and lattice symmetries but also by their relative orientation. Using symmetry and modal analysis, we provide a general and very simple formula to determine whether the dichroism exists and a chart with the most significant cases.

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• Crystal symmetry
• Mie scattering
• Nonlinear optics
• Optical activity
• Nanostructures
• Optical microcavities
• Chiral symmetry
• Optical second-harmonic generation