  Laser wakefield acceleration relies on the excitation of a plasma wave due to
the ponderomotive force of an intense laser pulse. However, plasma wave trains
in the wake of the laser have scarcely been studied directly in experiments.
Here we use few-cycle shadowgraphy in conjunction with interferometry to
quantify plasma waves excited by the laser within the density range of
GeV-scale accelerators, i.e. a few 1e18 cm-3. While analytical models suggest a
clear dependency between the non-linear plasma wavelength and the peak
potential a_0, our study shows that the analytical models are only accurate for
driver strength a_0<=1. Experimental data and systematic particle-in-cell
simulations reveal that nonlinear lengthening of plasma wave train depends not
solely on the laser peak intensity but also on the waist of the focal spot.
