Towards terahertz oscilloscopes using phase diversity electro-optic sampling.

Recording electric field evolutions in single-shot with terahertz bandwidth is needed in applications ranging from terahertz spectroscopy of irreversible processes, to free-electron lasers and terahertz telecommunication research. However, achieving sub-picosecond resolution over long time windows is still an open problem for electro-optic sampling -- the standard technique for recording terahertz waveforms. We show that, when using chirped laser probes, the issue comes from a fundamental limit, which we call dispersion penalty, and present a solution leading to a dramatic enhancement of the achievable temporal resolution. We validate this new technology in two applications. We first present single-shot recordings of free-propagating terahertz transients with record time windows. Second, we present recordings of ultra-short relativistic electron bunches at the European X-ray Free-Electron Laser. These results show that terahertz signals may be now recorded with arbitrarily long windows, thus enabling the realization of "terahertz oscilloscopes" and single-shot time-domain spectroscopy systems with arbitrary time-bandwidth product