Homogenization and Scattering Analysis of Second-Harmonic Generation in Nonlinear Metasurfaces

We propose an extensive discussion on the homogenization and scattering analysis of second-order nonlinear metasurfaces. Our developments are based on the generalized sheet transition conditions (GSTCs) which are used to model the electromagnetic responses of nonlinear metasurfaces. The GSTCs are solved both in the frequency domain, assuming an undepleted pump regime, and in the time-domain, assuming dispersionless material properties but a possible depleted pump regime. Based on these two modeling approaches, we derive the general second-harmonic reflectionless and transmissionless conditions as well as the conditions of asymmetric reflection and transmission. We also discuss and clarify the concept of nonreciprocal scattering pertaining to nonlinear metasurfaces.