Negative Refraction with Superior Transmission in Graphene-Hexagonal Boron Nitride (hBN) Multilayer Hyper Crystal

In this article, we have theoretically investigated the performance of graphene-hexagonal Boron Nitride (hBN) multilayer structure (hyper crystal) to demonstrate all angle negative refraction along with superior transmission. hBN, one of the latest natural hyperbolic materials, can be a very strong contender to form a hyper crystal with graphene due to its excellence as a graphene-compatible substrate. Although bare hBN can exhibit negative refraction, the transmission is generally low due to its high reflectivity. Whereas due to graphene's 2D nature and metallic characteristics in the frequency range where hBN behaves as a type-I hyperbolic material, we have found graphene-hBN hyper-crystals to exhibit all angle negative refraction with superior transmission. Interestingly, superior transmission from the whole structure can be fully controlled by the tunability of graphene without hampering the negative refraction originated mainly from hBN. We have also presented an effective medium description of the hyper crystal in the low-k limit and validated the proposed theory analytically and with full wave simulations. Along with the current extensive research on hybridization of graphene plasmon polaritons with (hyperbolic) hBN phonon polaritons, this work might have some substantial impact on this field of research and can be very useful in applications such as hyper-lensing.