  Phase-locked ultrashort pulses in the rich terahertz (THz) spectral range
have provided key insights into phenomena as diverse as quantum confinement,
first-order phase transitions, high-temperature superconductivity, and carrier
transport in nanomaterials. Ultrabroadband electro-optic sampling of few-cycle
field transients can even reveal novel dynamics that occur faster than a single
oscillation cycle of light. However, conventional THz spectroscopy is
intrinsically restricted to ensemble measurements by the diffraction limit. As
a result, it measures dielectric functions averaged over the size, structure,
orientation and density of nanoparticles, nanocrystals or nanodomains. Here, we
extend ultrabroadband time-resolved THz spectroscopy (20 - 50 THz) to the
sub-nanoparticle scale (10 nm) by combining sub-cycle, field-resolved detection
(10 fs) with scattering-type near-field scanning optical microscopy (s-NSOM).
We trace the time-dependent dielectric function at the surface of a single
photoexcited InAs nanowire in all three spatial dimensions and reveal the
ultrafast ($<$50 fs) formation of a local carrier depletion layer.
