Observation of laser power amplification in a self-injecting laser wakefield accelerator

We report on the depletion and power amplification of the driving laser pulse in a strongly-driven laser wakefield accelerator. Simultaneous measurement of the transmitted pulse energy and temporal shape indicate an increase in peak power from $187 \pm 11$TW to a maximum of $318 \pm 12$ TW after 13 mm of propagation in plasma density of $0.9 \times 10^{18}$ cm$^{-3}$. The power amplification is correlated with the injection and acceleration of electrons in the non-linear wakefield. This process is modeled by including localized redshifting and subsequent group delay dispersion at the laser pulse front.