  In this paper, we use a versatile homogenization approach to model the linear
and nonlinear optical response of two metasurfaces: a plasmonic metasurface
consisting of a square array of graphene cruciform patches and a dielectric
metasurface consisting of a rectangular array of photonic crystal (PhC)
cavities in a silicon PhC slab waveguide. The former metasurface is resonant at
wavelengths that are much larger than the graphene elements of the metasurface,
whereas the resonance wavelengths of the latter one are comparable to the size
of its resonant components. By computing and comparing the effective
permittivities and nonlinear susceptibilities of the two metasurfaces, we infer
some general principles regarding the conditions under which homogenization
methods of metallic and dielectric metasurfaces are valid. In particular, we
show that in the case of the graphene metasurface the homogenization method
describes very well both its linear and nonlinear optical properties, whereas
in the case of the silicon PhC metasurface the homogenization method is less
accurate, especially near the optical resonances

Optics