Demonstration of sub-luminal propagation of single-cycle terahertz pulses for particle acceleration.

The sub-luminal phase velocity of electromagnetic waves in free space is generally unobtainable, being closely linked to forbidden faster than light group velocities. The requirement of sub-luminal phase-velocity in laser-driven particle acceleration schemes imposes a limit on the total acceleration achievable in free space, and necessitates the use of dispersive structures or waveguides for extending the field-particle interaction. We demonstrate a travelling source approach that overcomes the sub-luminal propagation limits. The approach exploits ultrafast optical sources with slow group velocity propagation, and a group-to-phase front conversion through nonlinear optical interaction. The concept is demonstrated with two terahertz generation processes, nonlinear optical rectification and current-surge rectification. We report measurements of longitudinally polarised single-cycle electric fields with phase and group velocity between 0.77c and 1.75c. The ability to scale to multi-megavolt-per-metre field strengths is demonstrated. Our approach paves the way towards the realisation of cheap and compact particle accelerators with femtosecond scale control of particles.Controlled generation of terahertz radiation with subluminal phase velocities is a key issue in laser-driven particle acceleration. Here, the authors demonstrate a travelling-source approach utilizing the group-to-phase front conversion to overcome the sub-luminal propagation limit.