Few-cycle microscopy diagnostic  combining femtosecond time resolution and micrometer spatial resolution allows for direct observation of laser-driven plasma waves. By comparing the period of the wave train and the independently measured in-situ plasma density, we find that existing 1D models [2, 3] tend to overestimate the contribution of laser intensity to the non-linear plasma wave lengthening. Quasi-3D particle-in-cell simulations reproducing our observations suggest that transverse intensity gradient plays an important role in the wave train formation. Furthermore, we show experimental evidence on plasma waves driven by electron bunches generated from a laser wakefield accelerator, paving the way towards research of plasma wakefield acceleration at laser facilities .
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