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At present, optical anapole resonances in nanostructures have attractedincreasing attention due to the strong field confinement and substantiallysuppressed scattering. This study provides the results of three-dimensionalfinite-difference time-domain simulations exhibiting the possibility of theanapole state in high refractive index dielectric nanohole array metasurfaceshaving different profiles of the holes (square, hexagon, and octagon). Behaviorof the effective optical Kerr nonlinearity of the metasurfaces in the vicinityof the anapole state is investigated. Depending on the geometry, the absolutevalue of the effective nonlinear Kerr coefficient of the metasurface may be upto three orders of magnitude greater than that of the unstructured film. Asquare transverse section of the nanohole is preferable for the optical Kerreffect in the holey metasurfaces. The effect of the random rotation of thesquare holes representing the metasurface irregularity on the opticalnonlinearity is examined. As a result, the dielectric nanohole arraymetasurfaces display a concrete possibility to have the anapole state withlarge enhancement of the optical nonlinearity.

Optical Kerr nonlinearity of dielectric nanohole array metasurfaces with different hole shapes near the anapole state