$f(t)$ is the pulse envelop. The peak laser intensity is $I_0 = c \, \varepsilon_0\, E_0^2/2$ ($c$ being velocity of light in vacuum) usually expressed in W/cm$^2$. The net yield in a laser pulse is often characterized by the fluence $\mathcal{F}=\int \textrm dt I(t)\approx I_0T_\mathrm{FWHM}$, [where the latter time $T_{\rm FWHM}$ stands for the Full Width at Half Maximum of the pulse]{}. This allows one to compare the energy impact of laser pulses with different durations.

For the sake of simplicity, we keep in the present discussion a fixed value of $\omega_\mathrm{las}$ but the latter quantity can also be made time-dependent (“chirped”) which can induce interesting effects [@Pas08]. One may also render the phase $\varphi$ time-dependent, which could produce interesting phenomena. We shall not discuss these aspects here. The laser polarization is usually taken linear but there also exists experiments/calculations using circularly polarized light [@Pas08]. Again, we shall not discuss much such cases in the following and thus recur to a linear polarization for the present discussion.

The laser pulse envelop can be varied in a large range. Most flexible, and most widely used, are optical lasers with pulse lengths from nano-seconds down to atto-seconds [@Bra00aR; @Kra09]. Free Electron Lasers 