  In this paper we demonstrate that asymmetric hyperbolic metamaterials (AHM) can produce strongly directive thermal emission in far-field zone, which exceeds Planck's limit. Asymmetry is inherent in an uniaxial medium, whose optical axes are tilted with respect to medium interfaces and appears as a difference in properties of waves, propagating upward and downward with respect to the interface. It's known that a high density of states (DOS) for certain photons takes place in usual hyperbolic metamaterials, but emission of them into a smaller number in vacuum is preserved by the total internal reflection. However, the use of AHM enhance the efficiency of coupling of the waves in AHM with the waves in free space that results in Super-Planckian far-field thermal emission in certain directions. Different plasmonic metamaterials can be used for realization of AHM. As example, thermal emission from AHM, based on graphene multilayer, is discussed. 
Super-Planckian far-zone thermal emission from asymmetric hyperbolic   metamaterials