Wigner diagnostics for the photon accelerator

The wake driven by a short intense laser pulse propagating in a transparent plasma can be used to up-shift or downshift another ultrashort electromagnetic pulse co-propagating with the wake (the photon accelerator). Photon acceleration/deceleration can be a powerful diagnostic for the structure of the wake, and it provides a mechanism to tune the frequency of short laser pulses. We have performed detailed fully relativistic one-dimensional, two-dimensional, and three- dimensional particle-in-cell simulations with osiris 2.0 of the photon accelerator, over a wide range of realistic laboratory conditions for the neutral gas background, the plasma background, the wake field driver, and the probe. Our study relies on the systematic use of the Wigner transform for the electromagnetic field, thus allowing for a complete diagnostic of the frequency modulations in the probe pulse. We demonstrate controlled tunability of the probe pulse, as well as the detailed control of the laser chirp.