Wakefield generation as the mechanism behind spectral shift of a short laser pulse

An equation describing the dynamics of plasma wave generation by a short intense laser pulse is analyzed to find a relation between the difference in mean-square pulse frequency before and after laser-matter interaction and the electric field amplitude in the wakefield plasma wave generated by the laser pulse. This relation can be effectively used in systems for wakefield diagnostics. The relation is applied to several geometries of interaction between a pulse and an ionizing gas or preformed plasma.