(FEL) [@Fel05; @Pas08] are yet on their way to comparable flexibility, with present pulse lengths down to 20 fs. It should also be noted that the actual shape of $f(t)$ is not exactly known experimentally. In many situations, the actual pulse of interest is built upon a (hopefully harmless) background of a long, low intensity, pulse. Moreover, the peak intensity has a spatial variation decreasing towards the edges of the pulse. This has to be kept in mind when assigning the observed signal to the laser pulse characteristics. Ignoring background, experimental short laser pulses have a pulse profile of Gaussian type. The theoretical situation is simpler as the pulse profile can be exactly specified. The Gaussian profile is theoretically not welcome since it never fully vanishes and requires unnecessarily long computation times to cover the pulse sufficiently well. Therefore, we mostly use for computations a $\sin^2$ pulse : $$f(t) 
  = 
  \sin^2 \left(\frac{t\pi}{T_\mathrm{pulse}} \right) 
  \, \theta(t) \, \theta(T_\mathrm{pulse}-t) 
  \quad. 
\label{eq:cos2}$$ where $\theta$ stands here for the Heaviside function. This pulse is limited to a finite time interval $t\in[0,T_\mathrm{pulse}]$, but soft enough to deliver a clean frequency spectrum. It can be simply characterized by its FWHM which is in this case $T_\mathrm{FWHM}=T_\mathrm{pulse}/2$. 