“…Recent studies on surface SHG in semiconductors considered regions on the order of a few nanometers at the material/air interface and demonstrated that this effective volume is a good representation of surface SHG. 28,29,34 Therefore, in our modeling, we consider two regions at the air/GaAs and GaAs/AlGaO interfaces with a thickness of 10 nm each and with a symmetry tensor of pointgroup symmetry mm2. When we include both surface and bulk nonlinearities, with the following surface-induced nonlinear coefficients: χ zxx (2,s) = χ zyy (2,s) = 6χ xzy (2) , χ zzz (2,s) = 6χ xzy (2) , χ yxz (2,s) = χ xzy (2,s) = 1.8χ xzy (2) , while maintaining the surface-induced nonlinear tensor symmetry (see Note S1), we successfully retrieve the twofold symmetry in the total SHG intensity (Figure 3a,c, bottom panels).…”