Self-referencing spectral interferometric probing of the onset time of relativistic transparency in intense laser-foil interactions

Irradiation of an ultrathin foil target by a high intensity laser pulse drives collective electron motion and the generation of strong electrostatic fields, resulting in ultrabright sources of high-order harmonics and energetic ions. The ion energies can be significantly enhanced if the foil undergoes relativistic self-induced transparency during the interaction, with the degree of enhancement depending in part on the onset time of transparency. We report on a simple and effective approach to diagnose the time during the interaction at which the foil becomes transparent to the laser light, providing a route to optically controlling and optimizing ion acceleration and radiation generation. The scheme involves a self-referencing approach to spectral interferometry, in which coherent transition radiation produced at the foil rear interferes with laser light transmitted through the foil. The relative timing of the onset of transmission with respect to the transition radiation generation is determined from spectral fringe spacing and compared to simultaneous frequency-resolved optical gating measurements. The results are in excellent agreement, and are discussed with reference to particle-in-cell simulations of the interaction physics and an analytical model for the onset time of transparency in ultrathin foils.