Optical Kerr nonlinearity of arrays of all-dielectric high-index nanodisks in the vicinity of the anapole state.

The nonlinear optical properties of the high-index nanoparticles are boosted at the anapole state. Researchers intensively study this phenomenon as being promising for various applications. In this Letter, the nonlinear optical Kerr effect of disordered and square lattice metasurfaces of GaP nanodisks is investigated as a function of the disk size in the vicinity of the anapole state at the wavelength of 532 nm. When the sizes of the nanodisks are close to the anapole state, the effective second-order refractive index of the metasurface increases exponentially. On approaching the anapole state, the sign of the effective second-order refractive index is inverted. The absolute value of the effective nonlinear Kerr coefficient of the square lattice metasurface is higher than that of the disordered array of nanodisks. The absolute value of the effective second-order refractive index in proximity to the anapole state is an order of magnitude higher than that at non-anapole resonances of the disordered metasurfaces consisting of the nanodisks or spheres.