Theory of “Hot” Photoluminescence from Drude Metals

We provide a complete quantitative theory for light emission from Drude metals under continuous wave illumination, based on our recently derived steady-state nonequilibrium electron distribution. We show that the electronic contribution to the emission exhibits a dependence on the emission frequency which is very similar to the energy dependence of the nonequilibrium distribution, and characterize different scenarios determining the measurable emission line shape. This enables the identification of experimentally relevant situations, where the emission lineshapes deviate significantly from predictions based on the standard theory (namely, on the photonic density of states), and enables the differentiation between cases where the emission scales with the metal object surface or with its volume. We also provide an analytic description (which is absent from the literature) of the (polynomial) dependence of the metal emission on the electric field, its dependence on the pump laser frequency, and its nontrivial exponential dependence on the electron temperature, both for the Stokes and anti-Stokes regimes. Our results imply that the emission does not originate from either Fermion statistics (due to e-e interactions), and even though one could have expected the emission to follow boson statistics due to involvement of photons (as in Planck's Black Body emission), it turns out that it deviates from that form as well. Finally, we resolve the arguments associated with the effects of electron and lattice temperatures on the emission, and which of them can be extracted from the anti-Stokes emission.