Radiative transfer at nanometric scale. Are the usual concepts still valid?

This paper briefly reexamines the basic concepts used to describes radiative properties of opaque surfaces. It first recalls the connection between the specific intensity and the randomly fields produced by a thermal source. Then the paper discusses the concept of reflectivity and shows that there is a fundamental limit related to the uncertainty principle that prohibits defining a local reflectivity in space and in angle as it is usually done. As a consequence, it is shown that it is meaningless to define a reflectivity for an area smaller than the wavelength. On the other hand, the emissivity can be defined for a length scale on the order of the skin depth which can be much smaller than the wavelength