Free-electron tomography of few-cycle optical waveforms

Ultrashort light pulses are ubiquitous in modern research, but the electromagnetic field of the optical cycles is usually not easy to obtain as a function of time. Field-resolved pulse characterization requires either a nonlinear-optical process or auxiliary sampling pulses that are shorter than the waveform under investigation, and pulse metrology without at least one of these two prerequisites is often thought to be impossible. Here we report how the optical field cycles of laser pulses can be characterized with a field-linear sensitivity and no short probe events. We let a free-space electron beam cross with the waveform of interest. The randomly arriving electrons interact by means of their elementary charge with the optical waveform in a linear-optical way and reveal the optical cycles as the turning points in a time-integrated deflection histogram on a screen. The sensitivity of the method is only limited by the emittance of the electron beam and can reach the level of thermal radiation and vacuum fluctuations. Besides overturning a common belief in optical pulse metrology, the idea also provides practical perspectives for in-situ characterization and optimization of optical waveforms in higher-harmonics experiments, ultrafast transmission electron microscopes, laser-driven particle accelerators, free-electron lasers or generally any experiments with waveform-controlled pulses in a vacuum environment.