Revisiting super-Planckian thermal emission in the far-field regime

We revisit, in the framework of the Landauer theory, the thermal emission in far-field regime, of arbitrary indefinite planar media and finite size systems. We prove that the flux radiated by the former is bounded by the blackbody emission while, for the second, there is in principle, no upper limit demonstrating such possibility for a super-Planckian thermal emission with finite size systems.