Self-compression of few-millijoule laser pulses in non-linear plasma waves

Study of relativistic short laser pulse propagation in underdense plasma is of great interest in high field science, attosecond physics and applications such as plasma based accelerators. Temporal shortening of a laser pulse that drives nonlinear plasma wakefield has been observed using 100TW-class lasers interacting with millimeter scale plasma [1,2]. Here we report on experiments performed using the high repetition rate Lambda-cubed laser at the University of Michigan - a table-top sub-TW power laser systems operating at 500 Hz. The laser (pulse energy up to 8 mJ) was tightly focused (peak intensity $\sim $3$\times $10$^{18 }$W/cm$^{2})$ into a 100 $\mu $m scale length gas jet to generate a plasma with electron density $\sim $10$^{19 }$cm$^{-3}$. The temporal and spectral intensity and phase of the transmitted pulse was measured using second-harmonic-generation (SHG) frequency-resolved optical gating (FROG). The laser pulse was shortened from 37 fs to 16 fs with $>$90{\%} energy transmittance. The dependence on focusing condition, laser intensity and plasma density will be discussed.\\[4pt] [1] J. Faure, \textit{et al.}, Phys. Rev. Lett, \textbf{95}, 205003 (2005).\\[0pt] [2] J. Schreiber, \textit{et al.}, Phys. Rev. Lett. \textbf{105}, 235003 (2010).