Optical self-energy of superconducting Pb in the THz region

New THz data on the optical conductivity of Pb are presented as well as a detailed Eliashberg analysis with particular emphasis on phonon-assisted processes not included in a BCS approach. Consideration of the optical self-energy instead of the conductivity itself helps highlight the differences with BCS predictions. Predicted coherence peaks are observed in the optical scattering rates. Impurities enhance the optical effective mass at zero frequency by an order of magnitude and induce a large peak at twice the gap in agreement with theory. This work illustrates the usefulness of the optical self-energy for the analysis of data.