Figure 18: Temperature-dependence of the (a) real and (b) imaginary parts of the conductivity spectra obtained on a 15 nm NbN film on MgO substrate (  K). The solid lines are fits with the Mattis-Bardeen equations [27, 28]. The inset of panel (a) shows the temperature dependence of the energy gap , extracted from fits to (symbols) overlaying the normalized transmissivity ratio, TR. The BCS temperature dependence of is shown by the dashed line. The inset to panel (b) displays the transmitted THz transients through the NbN film below and above ; the arrow denotes the time with maximum change in the transmitted electric field (after [108]). (c) The recovery of the imaginary part of the superconducting conductivity for different intensities can be described by a single exponential dependence with  ps [107]. (d) Time evolution of normalized transmissivity ratio (TR), recorded at  mJ/ , together with extracted from fit with the BCS theory [27, 28] (after [108]).