Energy streamlines in near-field radiative heat transfer between hyperbolic metamaterials

Metallodielectric photonic crystals having hyperbolic dispersions are called indefinite materials because of their ability to guide modes with extremely large lateral wavevectors. While this is useful for enhancing near-field radiative heat transfer, it could also give rise to large lateral displacements of the energy pathways. The energy streamlines can be used to depict the flow of electromagnetic energy through a structure when wave propagation does not follow ray optics. We obtain the energy streamlines through two semi-infinite uniaxial anisotropic effective medium structures, separated by a small vacuum gap, using the Green functions and fluctuation-dissipation theorem. The lateral shifts are determined from the streamlines within two penetration depths. For hyperbolic modes, the predicted lateral shift can be several thousand times of the vacuum gap width.