Tailoring nonlinear circular dichroism in nanostructures and metasurfaces [Invited]

Nonlinear circular dichroism can emerge in achiral nanostructures made of non-centrosymmetric materials due to the symmetry interplay between the particle and the nonlinear susceptibility tensor $X$$^{(2)}$. In this work, we numerically demonstrate controlled tuning of second-harmonic circular dichroism (SH-CD) in nanostructures and metasurfaces by engineered symmetry breaking. Two mechanisms are considered: uniaxial stretching of a cluster of nanoresonators and local refractive-index modification within a high-symmetry structure. In both cases, symmetry reduction from $C$$_{nv}$ or $D$$_{nh}$ to lower-symmetry configurations enables nonzero SH-CD and allows switching its sign. Contrary to naive intuition, the absence or presence of global structural chirality does not guarantee the absence or presence of nonlinear circular dichroism. We further discuss subtle aspects of these symmetry conditions, their range of applicability, and their relation to geometric-phase concepts and lattice-induced chirality.