  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 effective sub-luminal phase-velocity in
laser-driven particle acceleration schemes imposes a fundamental limit on the
total acceleration achievable in free-space, and necessitates the use of
dielectric structures and waveguides for extending the field-particle
interaction. Here we demonstrate a new travelling-source and free space
propagation approach to overcoming the sub-luminal propagation limits. The
approach exploits the relative ease of generating ultrafast optical sources
with slow group velocity propagation, and a group-to-phase front conversion
through non-linear optical interaction near a material-vacuum boundary. The
concept is demonstrated with two terahertz generation processes, non-linear
optical rectification and current-surge rectification. The phase velocity is
tunable, both above and below vacuum speed of light $c$, and we report
measurements of longitudinally polarized electric fields propagating between
$0.77c$ and $1.75c$. The ability to scale to multi-MV/m field strengths is
demonstrated. Our approach paves the way towards the realization of cheap and
compact particle accelerators with unprecedented femtosecond scale control of
particles.
