Plane-wave Expansion based Modelling of Linear and Non-Linear Response of Resonant Metasurfaces under Realistic Excitation Conditions

It is generally easy to model resonance characteristics of infinitely periodic resonant metasurfaces under plane-wave excitation. However, extending this to finite size arrays and more realistic Gaussian-like excitation beams becomes complex and time-consuming. Extending the linear optical resonances to model the nonlinear optical performance also becomes cumbersome. The use of non-standard, off-axis excitation, for example using reflective objective with central obscuration are also difficult to model with existing simulation tools. Here, we report a unified approach to modelling linear and nonlinear optical characteristics of resonant metasurfaces using a plane wave expansion (PWE) method to realize gaussian excitation with any arbitrary excitation angular profile. As an example, we compare the PWE model with experimental results of linear and third-order sum-frequency generation (TSFG) from 1D gratings with double step profile supporting q-BIC resonances, which we have previously reported experimentally [1].