Determining second-harmonic generation of nonlinear sandwich metasurface by nonlinear polarizability tensor method

We present an analytical method involving the nonlinear polarizability tensor for calculating the second harmonic generation (SHG) intensity for a nonlinear sandwich metasurface. The theoretical model is that a nonlinear meta-atom can be considered as a nonlinear electric- and magnetic-dipole, which allows the nonlinear polarizability tensors to be calculated from the far-field of the scattered SHG. The results suggest that the simultaneous excitation of electric and magnetic plasmonic resonances improves the SHG intensity, which is quantitatively consistent with the ones by the finite-difference time-domain method. Therefore, various nonlinear metasurfaces can be designed for applications in nonlinear micro-nano photonic devices.