Abstract: Most of the current graphene plasmonic researches are based on the substrates with isotropic dielectric constant such as silicon. In this work, we investigate optical properties of graphene nanoribbon arrays placed on a uniaxially anisotropic substrate, where the anisotropy provides an additional freedom to tune the behaviors of graphene plasmons, and its effect can be described by a simple effective formula. In practice, the substrates of semi-infinite and finite thickness are discussed by using both the formula and full wave simulations. Particularly, the dielectric constants $\varepsilon_ \parallel $ and $\varepsilon_ \bot $ approaching zero are intensively studied, which show different impacts on the transverse magnetic (TM) surface modes. In reality, the hexagonal boron nitride (hBN) can be chosen as the anisotropic substrate, which is also a hyperbolic material in nature.

Key words: graphene, plasmonics, anisotropy, hexagonal boron nitride