Anisotropy and effective medium approach in the optical response of two-dimensional material heterostructures

Two-dimensional (2D) materials offer a large variety of optical properties, from transparency to plasmonic excitation. They can be structured and combined to form heterostructures that expand the realm of possibility to manipulate light interactions at the nanoscale. Appropriate and numerically efficient models accounting for the high intrinsic anisotropy of 2D materials and heterostructures are needed. In this article, we retrieve the relevant intrinsic parameters that describe the optical response of a homogeneous 2D material from a microscopic approach. Well-known effective models for vertical heterostructure (stacking of different layers) are retrieved. We found that the effective optical response model of horizontal heterostructures (alternating nanoribbons) depends on the thickness. In the thin layer model, well adapted for 2D materials, a counterintuitive in-plane isotropic behavior is predicted. We confront the effective model formulation with exact reference calculations such as ab initio calculations for graphene, hexagonal boron nitride (hBN), as well as corrugated graphene with larger thickness but also with classical electrodynamics calculations that exactly account for the lateral structuration.