Modeling of second-order nonlinear metasurfaces

We present a frequency-domain modeling technique for second-order nonlinear metasurfaces. The technique is derived from the generalized sheet transition conditions (GSTCs), which have been so far mostly used for modeling linear metasurfaces. In this work, we extend the GSTCs to include effective nonlinear polarizations. This allows retrieving the effective nonlinear susceptibilities of a given metasurface and predict its nonlinear scattering responses under arbitrary illumination conditions. We apply this modeling technique to the case of metasurfaces made of a periodic arrangement of T-shaped gold nanoparticles. For verification, several metasurfaces are fabricated and a fair agreement is found when comparing simulated data and experimental results. The proposed model may thus serve as a design platform to implement complex nonlinear metasurface based applications.