Comparison between the linear and nonlinear homogenization of graphene and silicon

TL;DR

This paper compares linear and nonlinear homogenization methods applied to graphene and silicon metasurfaces, revealing that homogenization accurately models graphene's optical properties but is less precise for silicon near resonances.

Contribution

It provides a comparative analysis of homogenization validity for metallic and dielectric metasurfaces, highlighting conditions for accurate modeling of their optical responses.

Findings

Homogenization effectively models graphene metasurface's optical properties.

Homogenization is less accurate for silicon metasurface near resonances.

Resonance wavelength differences influence homogenization validity.

Abstract

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