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Metasurfaces have attracted a great deal of attention from researchers due to their prominent optical properties. In particular, metasurfaces may consist of structures possessing optical anapole resonances with strong field confinement and substantially suppressed scattering. As a result, such nanostructures display enhanced nonlinear optical properties. In this paper by means of three-dimensional finite-difference time-domain simulations, the ability of anapole modes in high-index dielectric metasurfaces with circular nanopores is shown. In the vicinity of the anapole state, the effective optical Kerr nonlinearity increases by orders of magnitude. Simultaneously, the optical transmission of the metasurface can reach high values up to unity.

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In this Letter, a method is proposed that utilizes three-dimensional finite-difference time-domain simulations of light propagation for restoring the effective Kerr nonlinearity of nanocomposite media. In this approach, a dependence of the phase shift of the transmitted light on the input irradiance is exploited. The reconstructed values of the real parts of the nonlinear refractive index of a structure of randomly arranged spheres are in good agreement with the predictions of the effective medium approximations.

We consider an ensemble of identical semiconductor nanoparticles randomly embedded into dielectric matrix. The nanoparticles are polarized by the laser irradiation having linear polarization. The contribution of dipole-dipole interactions to third-order dielectric susceptibility is calculated by using mean random field method. It is shown that this contribution always has a negative sign, and it can be comparable with the values of optical nonlinearity observed experimentally.

The optical Kerr effect of nanocomposites consisting of high refractive index (GaP) spheres is studied by means of three-dimensional finite-difference time-domain (FDTD) simulations at the wavelength of 532 nm. The effective nonlinear refractive index of 0.8 µm thick nanocomposites and metasurfaces is evaluated. It is shown that the optical Kerr nonlinearity of the nanocomposites rises by orders in proximity to Mie resonances and may exceed the second-order refractive index of the bulk material. The nonlinearity enhancement is more pronounced for the metasurfaces. Unexpectedly, the sign of the effective optical Kerr coefficient is inverted for some range of the sphere sizes above the Mie resonances.

We theoretically determine the probability distribution function of the net field of the random planar structure of dipoles which represent polarized particles. At small surface concentrations c of the point dipoles this distribution is expressed in terms of special functions. At the surface concentrations of the dipoles as high as 0.6 the dipolar field obey the Gaussian law. To obtain the distribution function within transitional region c < 0.6, we propose the method based on the cumulant expansion. We calculate the parameters of the distributions for some specific configurations of the dipoles. The distribution functions of the ordered ensembles of the dipoles at the low and moderate surface concentrations have asymmetric shape with respect to distribution medians. The distribution functions allow to calculate various physical parameters of two-dimensional interacting nanoparticle ensembles.The final publication is available at www.epj.org,