Homogenization and Scattering Analysis of Second-Order Nonlinear Metasurfaces

We present an extensive discussion on the homogenization and scattering analysis of second-order nonlinear metasurfaces. We use the generalized sheet transition conditions (GSTCs) in the frequency-domain to model the electromagnetic responses of nonlinear metasurfaces. We present the general second-harmonic scattering relations, in the undepleted pump regime approximation, and the resulting reflectionless, transmissionless and asymmetric reflection and transmission conditions. Finally, to clarify certain misconceptions, we also discuss the concept of nonreciprocal scattering in nonlinear optics.